Related to Geometry

Sections:

DC. Dissections and Constructions

GC. Geometry in Different Cultures

HM. History of a Mathematician

LA. Linear Algebra and Geometry

MS. Mathematics and Social Issues

PA. Projective and Affine Mathematics

University of Michigan historic books collection

** **

**AD.
Art and Design**

Albarn,
Keith, Smith, Jenn Mial, Steele, Stanford, and Walker, Dinah. *The Language
of Pattern*. New York: Harper & Row, 1974.

Inspired by Islamic
decorative pattern, the authors of this book, who are all designers, explore
pattern step by step, beginning with simple numerical and geometrical
relationships and progressing through the dimensions

Alexander,
Christopher, Ishikawa, Sara, and Silverstein, Murray. *A Pattern Language:
Towns, Bulidings, Construction*. New York: Oxford University Press,
1977.

A pattern language for
building

Auvil,
Kenneth W. *Perspective Drawing*. Mountain View, CA: Mayfield Publishing,
1997.

Baglivo,
Jenny A. and Graver, ack E. *Incidence and Symmetry in Design and
Architecture*. New York: Cambridge University Press, 1983.

"The purpose of this
text is to develop mathematical topics relevant to the study of the incidence
and symmetry structures of geometrical objects. A secondary purpose is to
expand the reader's geometric intuition. The two fundamental mathematical
topics employed in this endeavor are graph theory and the theory of
transformation groups."

Bain,
George. *Celtic Arts: The Methods of Construction*. London: Constable,
1977.

A description of the
construction of Celtic patterns and designs.

Blackwell,
William. *Geometry in Architecture*. New York: John Wiley & Sons,
1984.

William Blackwell offers a
basic review of the fascinating relationships that exist in linear design. At
the same time, he uncovers new geometric principles and new applications of
geometry that may have a major influence on the state of architecture today.

Coxeter,
H.S.M., Emmer, M., Penrose, R., and Teuber, M.L:.*M.C. Escher: Art and Science*, New York: Elseview Science Publishing Co., Inc., 1986.

Doczi,
György. *The Power of Limits*. Boulder, CO: Shambhala, 1981.

Edgerton,
Samuel Y., Jr. *The Heritage of Giotto's Geometry Art and Science on the eve
of the Scientific Revolution*. Ithaca: Cornell University Press, 1993.

A historical account of the
development of perspective in the art of the Italian Renaisance.

Edmondson,
Amy C. *A Fuller Explanation:The Synergetic Geometry of R. Buckminster Fuller*.
Boston: Birkhauser, 1987.

An account of the geometry
and design ideas of Fuller.

Elam,
Kimberly. *Geometry of Design: Studies in Proposition and Composition*.
New York: Princeton Architectural Press, 2001.

"This book seeks to
explain visually the principles of geometric composition and offers a wide
selection of professional posters, products, and buildings that are visually
analyzed by these principles."

Emmer,
Michele:.*The Visual Mind: Art and Mathematics*, Cambridge: MIT Press, 1993.

Ernst,
Bruno. *The Magic Mirror of M.C. Escher*. New York: Random House,
1976.

Throughout the book Bruno
Ernst describes in detail the conception and execution of Escher's popular
prints, showing with the aid of sketches and diagrams how the artist arrived at
such astonishing creations as "The Balcony" and "Print
Gallery." Careful attention is also paid to the graphic techniques Escher
employed so successfully."

Escher,
M.C. *The Graphic Work of M.C*. New York: Hawthorn Books,Inc.,Publishers,
1960.

It is a fact, however, that
most people find it easier to arrive at an understanding of an image by the
round-about method of letter symbols than by the direct route. So it is with a
view to meeting this need that I myself have written the text.

Field,
Judith Veronica. *The Invention of Infinity: Mathematics and Art in
Renaissance*. Oxford: Oxford University Press, 1997.

Book will look at the
relations between of Renaissance art and mathematics in the period from about
1300 to about 1650.

Fomenko,
Anatolii. *Mathematical Impressions*. Providence,Rhode Island: American
Mathematical Society, 1991.

This book contains more than
80 reproductions of works by Fomenko. In the accompanying captions, Fomenko
explains the mathematical motivation behind the illustrations as well as the
emotional, historical, or mythical subtexts they evoke.

Ghyka,
Matila. *The Geometry of Art and Life*. New York: Dover Publications,
1977.

Gombrich,
Ernst. *The Sense of Order: A Study in the Psychology of Decorative Art*.
Ithaca, NY: Cornell University Press, 1978.

Henderson,
Linda. *The Fourth Dimention and Non-Euclidean Geometry in Modern Art*.
Princeton,NJ: Princeton University Press, 1983.

Hersey,
George L. *Architectgure and Geometry in the Age of the Baroque*. Chicago:
The University of Chicago Press, 2000.

Holt,
Michael. *Mathematics in Art*. London: Studio Vista, 1971.

This book is not an account
of either specialism of the title; that I leave to the acknowledged experts.
Rather it is an attempt to focus on aspects common, it seems to me, to both
mathematics and the visual arts. These aspects form then an anthology of
creative highlights that have caught my eye.

Ivins,
William M., Jr. *Art & Geometry: A Study In Space Intuitions*. New
York: Dover Publications, 1946.

Jacobs,
Michael and Fernández, Francisco. *Alhambra*. New York: Rizzoli,
2000.

Kappraf,
Jay. *Connections: The Geometric Bridge between Art and Science*. New York:
McGraw-Hill, 1991.

There is a hidden harmony in
the works of man and nature. From the great pyramid of Cheops to patterns of
plant growth, natural and artificial designs are all governed by precise
geometric laws. Design Science is the study of these hidden laws; it is the
search for the connections underlying all that is beautiful and functional.

King,
Ross. *Bruelleschi's Dome: How a Renaissance Genius Reinvented Architecture*.
New York: Penquin Books, 2000.

Linn,
Charles. *The Golden Mean: Mathematics and the Fine Arts*. Garden City,
NY: Doubleday, 1974.

Lord,
E.A. and Wilson, C.B. *The Mathematical Description of Shape and Form*.
New york: Halsted Press, 1986.

"Thus, in this survey,
we are not presenting a compendium of unrelated mathematical techniques.
Instead, we have attempted to present a unified view of the mathematics of form
description, emphasising underlying mathematical principles."

Miyazaki,
Kojiv. *An Adventure in Multidimensional Space*. New York: John Wiley and
Sons, Inc., 1983.

The art and geometry of
polygons, polyhedra, and polytopes.

Schattschneider,
Doris. *Visions of Symmetry : Notebooks, Periodic Drawings, and Related Work
of M.C. Escher*. WH Freeman & Co, 1992.

Schattschneider,
Doris, and Emmer, Michele:.*M. C. Escher's Legacy: A Centennial Celebration*,
New York: Springer-Verlag, 2003.

The book features 40
articles, most by presenters at the Escher Centennial Congress in Rome and
Ravello in 1998 and others. There is a rich array of illustrations, both of
Escher's work and of original work by the authors. The CD Rom supplements the book with presentations of art (in
color), as well as some videos, animations, and demo software.

Schneider,
Michael S. *A Beginner's Guide to Constructing the Universe: The Mathematical
Archetypes of Nature, Art, and Science*. New York: HarperPerennial,
1994.

Strosberg,
Eliane. *Art and Science*. New York: Abbeville Press, 2001.

Taylor,
Anne. *Math in Art*. Hayword, CA: Activity Resources Co., Inc., 1974.

This book has been developed
to show children the unique relationship between art and math and to help them
discover concepts in each areas, as they relate to each other.

Watson,
Ernest W. *Creative Perspective for Artists and Illustrators*. Mineola,
NY: Dover Publications, 1992.

Williams,
Robert. *The Geometrical Foundation of Natural Structure: A Source Book of
Design*. 1979: Dover, 1979.

de
Vries, Jan Vredeman. *Perspective*. New York: Dover, 1968.

Reproductions of engravings
from the 1604/1605 edition. Warning: Some of the engravings have geometrically
incorrect perspective.

AG. Analytic Geometry

Hahn,
Liang -shin. *Complex Numbers & Geometry*. Washington DC: Mathematical
Association of America, 1994.

The purpose of the book is
to demonstrate that these two subjects can be blended together beautifully,
resulting in easy proofs and natural generalizations of many theorems in plane
geometry.

Kuipers,
Jack B. *Quaternions and Rotation Sequences: A Primer with Applications to
Orbits, Aerospace, and Virtual Reality*. Princeton: Princeton University
Press, 1999.

"This book is intended
for all those mathematicians, engineers, and physicists who have to know, or
who want to know, more about the modern theory of quaternions. Primarily, as
the title page suggests, it is an exposition of the quaternion and its primary
application as a rotation operator."
Included are applications of spherical geometry.

Postnikov,
M. *Lectures in Geometry Semester I Analytic Geometry*. Moscow: MIR
publishers, 1982.

The subject matter is
presented on the basis of vector axiomatics of geometry with special emphasis
on logical sequence in introduction of the basic geometrical concepts.

Schwerdtfeger,
Hans. *Geometry of Complex Numbers: Circle Geometry, Moebius Transformation,
Non-Euclidean Geometry*. New York: Dover Publications, Inc., 1979.

This book uses complex
numbers to analyze inversions in cricles and then their relationship to
hyperbolic geometry.

Smogorzhevsky,
A.S. *The Method of Coordinates*. Moscow: Mir Publishers, 1984.

From a collection of short
books (phamphlets) for high school students written by Soviet mathematicians
and translated into English.

AN. Analysis

Bishop,
Errett and Douglas,Bridges. *Constructive Analysis*. New York:
Springer-Verlag, 1985.

The main book on
constructive analysis.

Bressoud,
David. *A Radical Approach to Real Analysis*. Washington, DC: Mathematical
Association of America, 1994.

Goldblatt,
Robert. *Lectures on the Hyperreals*. New York: Springer, 1998.

Hairer,
E. and Wanner, G. *Analysis by Its History*. New York: Springer,
1996.

Rudin,Walter.
*Principles of Mathematical Analysis*. New York: McGraw Hill, 1964.

For many years a standard
text in analysis.

Strichartz,
Robert S. *The Way of Analysis*. Boston: Jones and Bartlett Publishers,
1995.

The presentation of the
material in this book is often informal. A lot of space is given to motivation
and a discussion of proof strategies." This is only recent analysis book
that I know of that is direct and honest about Archimedean Axiom.

AT. Ancient Texts

AL-Khawarizmi,
Muhammad Ibn Musa. *Al-Jabr wa-l-Muqabala*. Baghdad: House of Wisdom,
825.

Traslated in English in Karpinski,
L.C., ed., Robert of Chester's Latin Translation of Al'Khowarizmi's Algebra,
New York: Macmillan, 1915.

Perga,
Apollonius of. *On Cutting Off a Ratio*. Fairfield: The Golden Hind Press,
1987.

An Attempt to Recover the
Original Argumentation through a Critical Translation of the Two Extant
Medieval Arabic Manuscript.

Perga,
Apollonius of. *Treatise on Conic Sections*. New York: Dover, 1961.

This is the standard work on
conic sections from the Greek world.

Baudhayana.
*Sulbasutram*. Bombay: Ram Swarup Sharma, 1968.

This is translated from the
Sanskrit manual for the construction of alters. The beginning of the book
contains a discussion the geometry needed for the construction of the altars
this beginning section is apparently the oldest surviving geometry textbook.

Berggren,
J. Lennart and Jones, Alexander. *Ptolemy's /it Geography : an annotated
translation of the theoretical chapters*. Princeton, NJ: Princeton
University Press, 2000.

Berggren,
J.L. and Thomas, R.S.D. *Euclid's Phaenomena: A Translation and Study of a
Hellenistic Treatise in Spherical Astronomy*. New York: Garland Publishing,
1996.

Contains the only accessible
English translation of Euclid's *Phaenomena*. This work is, alas, out of
print, but a brief, and more easily obtained account of its comments can be
found in: Berggren, J.L., and Thomas, R.S.D., "Mathematical
Astronomy in the Fourth Century B.C. as found in Euclid's Phaenomena", *Physis*,
Vol XXIX (1992), 7-33.

Bonasoni,
Paolo. *Algebra Geometrica*. Annapolis: The Golden Hind Press, 1985.

being the only known work of
this nearly forgotten Renaissance mathematician (excepting a still unpublished
treatise on the division of circles).

Cardano,
Girolamo. *The Great Art or the Rules of Algebra*. Cambridge: MIT Press,
1968.

This is the book that first
describes algebraic algorithms for solving most cubic equations.

Coxeter,
H.S.M. and Greitzer, S.L. *Geometry Revisited*. New York: The L.W. Singer
Company, 1967.

"Using whatever means
will best suit our purposes, let us revisit Euclid. Let us discover for
ourselves a few of the newer results. Perhaps we may be able to recapture some
of the wonder and awe that our first contact with geometry aroused."

Descartes,
Rene. *The Geometry of Rene Descartes*. New York: Dover Publications,Inc.,
1954.

This the book in which
Descartes develops the use of what we now call Cartesian coordinates for the
study of curves.

Euclid:
Phaenomena. *Euclidis opera omnia*. Menge H, (eds). anonymous Lipsiae,
B.G. Teubneri, 1883,

Euclid:*Optics*,
. *Journal of the Optical Society of America* 35, no. 5 (1945), 357-372.

This is a translation of
Euclid's work that contains the elements of what we now call perjective
geometry.

Euclid.
*Elements*. New York: Dover, 1956.

This is edition of Eulid's
Elements to which one is usually referred. Heath has added a large collection
of very useful historical and philosophical notes.

Euclid.
*Elements*. London: Dent & Sons, 1933.

Todhunter's translation of
Euclid.

Euclid.
*Elements*. Green Lion Press, 2002.

Thomas L. Heath translation,
edited by Dana Densmore, all in one volume without Heath extensive notes

Galilei,
Galileo: Trattato della Sphaera (1586-87). *Galilei Opere*. Favaro A,
(eds). anonymous Florence, G. Barbera, 1953,

Guthrie,
Kenneth. *The Pythagorean Sourcebook and Library*. Grand Rapids: Phanes
Press, 1987.

An Anthology of Ancient
Writings Which Relate to Pythagoras and Pythagorean Philosophy.

Heath,
T.L. *Euclid: The Thirteen Books of the Elements*. New York: Dover,
1956.

This is edition of Eulid's
Elements to which one is usually referred. Heath has added a large collection
of very useful historical and philosophical notes. His notes are more extensive
than Euclid's text.

Karpinski,
L.C.:.*Robert of Chester's Latin Translation of Al'Khowarizmi's Algebra*, New York: Macmillan, 1915.

Khayyam,
Omar:* a paper (no title)*, . *Scripta
Mathematica* 26 (1963), 323-337.

In this paper Khayyam
discusses algebra in relation to geometry.

In
this paper Khayyam discusses algebra in relation to geometry.

Khayyam,
Omar. *Risâla fî sharh mâ ashkala min musâdarât Kitâb 'Uglîdis*.
Alexandria, Egypt: Al Maaref, 1958.

Khayyam,
Omar. *Algebra*. New York: Columbia Teachers College, 1931.

In this book Khayyam gives
geometric techniques for solving cubic equations.

Plato.
*The Collected Dialogues*. Princeton,NJ: Bollinger, 1961.

Plato discusses mathematical
ideas in many of his dialogues.

Plotinus.
*The Enneads*. Burdette, NY: Larson Publications, 1992.

Proclus.
*Proclus: A Commentary on the First Book of Euclid's Elements*. Princeton:
Princeton University Press, 1970.

These commentaries by
Proclus (Greek, 410-485) are a source of much of our information about the
thinking of mathematicians toward the end of the Greek era.

Saccheri,
Girolamo. *Euclides Vindicatus*. New York: Chelsea pub. Co., 1986.

In this book Girolamo
Sacchri set forth in 1733, for the first time ever, what amounts to the axiom
systems of non-Euclidean geometry." It is not mentioned in this volume
that Saccheri borrowed many ideas from Khayyam's Risâla fî sharh mâ ashkala min
musâdarât Kitâb 'Uglîdis.

Smyrna,
Theon of. *Mathematics Useful for Understanding Plato*. San Diego: Wizards
Bookshelf, 1978.

This work appears to have
been a text book intended for students who were beginning a study of the works
of Plato. In its original form there were five sections: 1) Arithmetic 2) Plane
Geometry 3) Stereometry (solid geometry) 4) Music 5) Astronomy. Sections 2 and
3 on Geometry have been lost while the others remain in their entirety and are
presented here." The section on Astronomy contains discussions of the
shape of space.

Thomas,
Ivor:.*Selections Illustrating the History of Greek Mathematics*, Cambridge, MA: Harvard University Press,
1951.

A collection of primary
sources.

CA. Calculus

Amdahl,
Kenn and Loats, Jim. *Calculus For Cats*. Broomfield, CO: Clearwater
Publishing, 2001.

Berlinski,
David. *a tour of the calculus*. New York: Pantheon Books, 1995.

Cohen,
David W.: Henle, James M. *Conversational Calculus*. Reading, MA:
Addison-Wesley, 1997.

Devlin,
Keith. *An Electronic Companion to Calculus*. Cogito Learning Media, Inc,
1997.

Simmons,
George F. *Calculus Gems*. New York: McGraw-Hill, Inc., 1992.

Grabiner,
Judith V. *The Origins of Cauchy's Rigorous Calculus*. Cambridge: MIT
Press, 1981.

Spivak,
Michael. *The Hitchhiker's Guide to Calculus: A Calculus Course Companion*.
Houston: Polished Pebble Press, 1995.

CE. Cartography, the Earth

Bagrow,
L. *A History of Cartography*. Cabridge, MA: Harvard University Press,
1964.

Monmonier,
Mark. *Drawing the Line: Tales of Mapes and Cartocontroversy*. New York:
Henry Holt and Company, 1995.

Monmonier,
Mark. *How to Lie with Maps*. University of Chicago Press, 1996.

Pottmann,
Helmut: "Rational curves and surfaces with rational offsets", *Computer
Aided Geometric Design*, 12 (1995), 175-192.

Smith,
James R. *Introduction to Geodesy (The History and Concepts of Modern
Geodesy)*. John Wiley Interscience, 1997.

Snyder,
John P. *Flattening the Earth: Two Thousand Years of Map Projections*.
Chicago: University of Chicago Press, 1993.

A history and mathematical
description of numerous map projections of the sphere.

Sobel,
Dava. *Longitude: The True Story of a Lone Genius Who Solved the Greatest
Scientific Problem of His Time*. New York: Penquin Books, 1995.

A account of the struggles
to develop a method for determining the longitude of ships at sea.

Tomilin,
Anatoly. *How People Discovered the Shape of the Earth*. Moscow: Raduga
Publishers, 1984.

A childrens book with nice
colored illustrations.

CG. Computers and Geometry

*Vision
Geometry*, Contemporary
Mathematics.119: Washington DC: American Mmathematical Society, 1989.

"Computer vision is
concerned with obtaining descriptive information about a scene by computer
analysis of images of the scene."

*The
Geometer's Sketchpad: Dynamic Geometry for the 21st Century*, Key Curriculum Press

A program running on Windows
or Mac platforms which allows you to construct geometric drawing with points,
lines, and circles and then to dynamically vary constituent parts.

Angel,
Edward. *Interactive Computer Graphics: A Top-Down Approach with OpenGL*.
Addison-Wesley, 1999.

King,
James. *Geometry Through the Circle with The Geometer's Sketchpad*. Key
Curriculum Press, 1994.

King,
James, and Schattschneider, Doris (editors): *Geometry Turned On: Dynamic
Software in Learning, Teaching and Research*, MAA Notes.41:, 1997.

A book of 26 papers about
aspects of dynamic software for geometry

Kuipers,
Jack B. *Quaternions and Rotation Sequences: A Primer with Applications to
Orbits, Aerospace, and Virtual Reality*. Princeton: Princeton University
Press, 1999.

"This book is intended
for all those mathematicians, engineers, and physicists who have to know, or
who want to know, more about the modern theory of quaternions. Primarily, as
the title page suggests, it is an exposition of the quaternion and its primary
application as a rotation operator."
Included are applications of spherical geometry.

Litchfield,
Dan, Goldenheim, Dave, and Dietrich, Charles H.: "Euclid, Fibonacci, and
Sketchpad", *Math Horizons*, Feb 1997, 9-10.

Lord,
E.A. and Wilson, C.B. *The Mathematical Description of Shape and Form*.
New york: Halsted Press, 1986.

"Thus, in this survey,
we are not presenting a compendium of unrelated mathematical techniques.
Instead, we have attempted to present a unified view of the mathematics of form
description, emphasising underlying mathematical principles."

Mortenson,
Michael E. *Geometric Modeling*. New York: John Wiley and Sons, 1997.

"[This text] offers the
reader a comprehensive look at the indispensable core concepts of geometric
modeling, describing and comparing all the important mathematical structures
for modeling curves, surfaces, and solids, and showing how to shape and
assemble those elements into more complex models."

Pottmann,
Helmut: "Rational curves and surfaces with rational offsets", *Computer
Aided Geometric Design*, 12 (1995), 175-192.

Prenowitz,
Walter and Jordan, Meyer. *Basic Concepts of Geometry*. New York: Ardsley
house Publishers, 1989.

Richter-Gerbert,
Jürgen, and Kortenkamp, Ulrich H.:*Cinderella: The Interactive Geometry
Software*, Heidelberg: Springer-Verlag
(1999)

A Java based dynamic
geometry software.

Rovenski,
V.Y. *Geometry of Curves and Surfaces with MAPLE*. Boston: Birkhäuser,

This concise text on
geometry with computer modeling presents some elementary methods for analytical
modeling and visualization on curves and surfaces.

Taylor,
Jean: *Computing Optimal Geometries*, Providence: American Mathematical
Society (1991)

"This videotape
testifies to the influence of computing and computer graphics in mathematical
research. The material on the videotape was presented in a Special Session on
Computing Optimal Geometries, held at the Joint Mathematics Meetings in San
Francisco in January, 1991."

Taylor,
Walter F. *The Geometry of Computer Graphics*. Grove, CA: Wadsworth &
Brooks/Cole Advanced Books & Software, 1992.

"This book is a direct
presentation of elementary analytic and projective geometry, as modeled by
vectors and matrices and as applied to computer graphics."

CT. College Teaching

Case,
Bette Anne (editors): *You're the Professor, What Next?, Ideas and Resources
For Preparing College Teachers*,
Washington DC.: The Mathematical Association of America, 1994.

Ewing,
John (editors): *Towards Excellence, Leading Dotoral Mathematics Department
In The 21st Century*, Washington
DC.: American Mathematical Society, 1999.

Fisher,
Naomi D., Keynes, Harvey B., and Wagreich, Philip D (editors): *Mathematicians
and Education Reform*, Issues in Mathematics Education.3: Providence, Rhode
Island: American Mathematical Society, 1993.

Sciences,
The ConferenceBoardoftheMathematical. *The Mathematical Education of Teachers*.
Providence, RI: American Mathematical Society, 2001.

DC. Dissections and Constructions

Beskin,
N.M. *Dividing a Segment in a Given Ratio*. Moscow: Mir Publishers,
1975.

From a collection of short
books (phamphlets) for high school students written by Soviet mathematicians
and translated into English.

Boltjansky,
V. and Gohberg, I. *Results and Problems in Combinatorial Geometry*.
Cambridge: Cambridge University Press, 1985.

Boltyanski,
Vladimir G. *Hilbert's Third Problem*. New York: John Wiley & Sons,
1978.

A discussion of dissections
on the plane, sphere, and hyperbolic spaces.

Boltyanski,
Vladimir and Soifer, Alexander. *Geometric Etudes in Combinatorial
Mathematics*. Colorada Springs, CO: Center for Excellence in Mathematical
Education, 1991.

Boltyanskii,
Vladimir G. *The Decomposition of Figures into Smaller Parts*. Chicago:
University of Chicago Press, 1980.

Dudley,
Underwood. *A budget of Trisections*. New York: Springer-Verlag,
1987.

"This book is about
angle trisections and the people who attempt them. Its purposes are to collect
many trisections in one place, inform about trisectors, amuse the reader, and,
perhjaps most importantly, to reduce the number of trisectors."

Eves,
Howard. *A Survey of Geometry*. Boston: Allyn & Bacon, 1963.

A textbook that contains an
extensive coverage of the dissection theory of polygons.

Frederickson,
Greg. *Dissections: Plane and Fancy*. New York: Cambridge University
Press, 1997.

This book is a collection of
interesting dissection puzzles, old and new, and is an instructive manual on
the art and science of geometric dissections.

Frederickson,
Greg. *Hinged Dissections: Swinging & Twisting .* Cambridge, UK:
Cambridge University Press, 2002.

The book explores all manner
of dissections whose pieces are hinged together, along with techniques that
allow you to design them. It is a nice
sequel to it Dissections: Plane & Fancy.

Ho,
Chung -Wu: "Decomposition of a Polygon into Triangles", *Mathematical
Gazette*, 60 (1976), 132-134.

This article contains a
proof that all planar polygons can be dissected into triangles and discusses
the many mistakes made by other (many well-known ones) authors in their
"proofs" of the same result.

Lindgren,
Harry. *Geometric Dissections*. Princeton, NJ: D. Van Nostrand Company,
1964.

Lindgren,
Harry. *Recreational Problems in Geometric Dissection and How to Solve Them*.
New York: Dover, 1972.

Martin,
George E. *Geometric Constructions*. New York: Springer, 1998.

Sah,
C.H. *Hilbert's Third Problem: Scissors Congruence*. London: Pitman,
1979.

A detailed discussion of the
three dimensional dissections.

Soifer,
Alexander. *How Does One Cut a Triangle?* Colorado Springs, CO: Center for
Excellence in Mathematical Education, 1990.

DG. Differential Geometry

Berger,
M. and Gostiaux, B. *Differential Geometry: Manifolds, Curves, and Surfaces*.
New York: Springer-Verlag, 1988.

Bishop,
Richard L. and Goldberg, Samuel I. *Tensor Analysis on Manifolds*. New
York: Dover Publications, 1980.

The subject is treated as a
continuation of advanced calculus. The standards of rigor and logical
completeness are high throughout the text, and many excellent problems are
presented

Bloch,
Ethan D. *A First Course in Geometric Topology and Differential Geometry*.
Boston: Birkhauser, 1997.

Contains the topological
classification and differential geometry of surfaces.

Casey,
James. *Exploring Curvature*. Wiesbaden: Vieweg, 1996.

A truly delightful book full
of "experiments" to physically explore curvature of curves and
surfaces.

Dodson,
C. T. J. and Poston, T. *Tensor Geometry*. London: Pitman, 1979.

A very readable but
technical text using linear (affine) algebra to study the local intrinsic
geometry of spaces leading up to and including the geometry of the theory of
relativity.

Dubrovin,
B.A., Fomenko, A.T., and Novikov, S.P. *Modern Geometry: Methods and
Applications(Part I. The Geometry of Surfaces, Transformation Groups, and
Fields)*. New York: Springer-Verlag, 1984.

A well-written graduate
text.

Gauss,
C.F. *Modern Differential Geometry of Curves and Surfaces*. Hawlett, NY:
Raven Press, 1965.

A translation into English
of Gauss' early papers on surfaces.

Gibson,
C.G. *Elementary Geomery of Differentiable Curves: An Undergraduate
Introduction*. Cambridge, UK: Cambridge University Press, 2001.

Gray,
A. *Modern Differential Geometry of Curves and Surfaces*. CRC, 1993.

This is a very extensive
book based on computations using Mathematica©.

Guggenheimer,
Heinrich. *Differential Geometry*. New York: McGraw Hill, 1963.

Henderson,
David W. *Differential Geometry: A Geometric Introduction*. Upper Saddle
River, NJ: Prentice Hall, 1998.

In this book we will study a
foundation for differential geometry based not on analytic formalisms but
rather on these underlying geometric intuitions.

Hicks,
Noel J. *Notes of Differential Geometry*. New York: Van Nostrand Reinhold
Company, 1971.

The first three chapters of
this book provide a short course on classical differential geometry and could
be used at the junior level with a little outside reading in linear algebra and
advanced calculus.

Koenderink,
Jan J. *Solid Shape*. Cambridge: M.I.T. Press, 1990.

Written for engineers and
applied mathematicians, this is a discussion of the extrinsic properties of
three-dimensional shapes. There are connections with applications and a nice
section "Your way into the literature."

Kreyszig,
Erwin. *Mathematical Expositions No. 11: Differential Geometry*. Toronto:
University of Toronto Press, 1959.

This book provides an
introduction to the differential geometry of curves and surfaces in
three-dimensional Euclidean space... In the theory of surfaces we make full use
of the tensor calculus, which is developed as needed.

Laugwitz,
Detlef. *Differential and Riemannian Geometry*. New York: Academic Press,
1965.

This textbook is intended to
be an introduction to classical differential geometry as well as to the tensor
calculus and to Riemannian geometry.

McCleary,
John. *Geometry from a Differential Viewpoint*. Cambridge, UK: Cambridge
University Press, 1994.

The text serves as both an
introduction to the classical differential geometry of curves and surfaces and
as a history of ... the hyperbolic plane.

Millman,
R.S. and Parker, G.D. *Elements of Differential Geometry*. Englewood
Cliffs, NJ: Prentice-Hall, 1977.

A well-written text, which
uses linear algebra extensively to treat the formalisms of extrinsic
differential geometry.

Morgan,
Frank. *Riemannian Geometry: A Beginner's Guide*. Boston: Jones and
Bartlett, 1993.

An accessible guide to
Riemannian geometry including a chapter on the theory of relativity and the
calculation of the precession in the orbit of Mercury.

Oprea,
John. *Introduction to Differential Geometry and Its Applications*. Upper
Saddle River: Prentice Hall, 1997.

Penrose,
Roger: The Geometry of the Universe. *Mathematics Today*. Steen L, (eds).
New York, Springer-Verlag, 1978,

An expository discussion of
the geometry of the universe.

An
expository discussion of the geometry of the universe.

Prakash.
*Differential Geometry: An Integrated Approach*. New Delhi: Tata
McGraw-Hill Publishing Company Limited, 1981.

Rovenski,
V.Y. *Geometry of Curves and Surfaces with MAPLE*. Boston: Birkhäuser,

This concise text on
geometry with computer modeling presents some elementary methods for analytical
modeling and visualization on curves and surfaces.

Santander,
M.: "The Chinese South-Seeking chariot: A simple mechanical device for
visualizing curvature and parallel transport", *American Journal of
Physics*, 60 (9) (1992), 782-787.

An old mechanical device,
the Chinese South-Seeking chariot, presumably designed to work on a flat plane,
is shown to perform parallel transport on arbitrary surfaces. Its use affords
experimental demonstration and even numerical checking (within a reasonable
accuracy) of all the features of curvature and parallel transport of vectors in
a two-dimensional surface.

Spivak,
Michael. *A Comprehensive Introduction to Differential Geometry*.
Wilmington, DE: Publish or Perish, 1979.

In five(!) volumes Spivak
relates the subject back to the original sources. Volume V contains an
extensive bibliography (up to 1979).

Stahl,
Saul. *The Poincaré Half-Plane*. Boston: Jones and Bartlett Publishers,
1993.

This text is an analytic
introduction to some of the ideas of intrinsic differential geometry starting
from the Calculus.

Thurston,
William. *Three-Dimensional Geometry and Topology, Vol. 1*. Princeton, NJ:
Princeton University Press, 1997.

This is a detailed excursion
through the geometry and topology of two- and three-manifolds. "The style
of exposition in this book is intended to encourage the reader to pause, to
look around and to explore.

Weeks,
Jeffrey. *The Shape of Space*. New York: Marcel Dekker, 1985.

An elementary but deep
discussion of the geometry on different two- and three-dimensional spaces.

Weeks,
Jeffrey. *Shape of Space*. New York: Marcel Dekker, 2002.

do
Carmo, Manfredo Perdigão. *Riemannian Geometry*. Boston: Birkhäuser,
1992.

The object of this book is
to familiarize the reader with the basic language of and some fundamental
theorems in Riemannian Geometry.

DS. Dimensions and Scale

Abbott,
Edwin A. *Flatland*. New York: Dover Publications, Inc., 1952.

A fantasy about
two-dimensional beings in a plane encountering the third dimension.

Banchoff,
Thomas and Wermer, John. *Beyond the Third Dimension: Geometry, Computer
Graphics, and Higher Dimensions*. New York: Springer-Verlag, 1983.

This book treats a number of
themes that center on the notion of dimensions, tracing the different ways in
which mathematicians and others have met them in their work.

Burger,
Dionys. *Sphereland*. New York: Thomas Y. Crowell Co., 1965.

A sequel to Abbott's
Flatland.

Henderson,
Linda. *The Fourth Dimention and Non-Euclidean Geometry in Modern Art*.
Princeton,NJ: Princeton University Press, 1983.

Kohl,
Judith and Kohl, Herbert. *The View from the Oak: The Private Worlds of Other
Creatures*. New York: Sierra Club Books/Charles Scribner's Sons, 1977.

This delightful books
describes the various experiential worlds of different creatures and is a good
illustration of intrinsic ways of thinking. Included are differing dimensions
and scales of these worlds.

Morrison,
Phillip and Morrison, Phylis. *Powers of Ten: About the Relative Size of
Things in the Universe*. New York: Scientific American Books, Inc.,
1982.

A beautiful book (and a
video with the same title) that starts with a square meter on earth and then
zooms out and in by powers of ten describing and illustrating at each power of
ten what can be seen until it reaches (by zooming out) vast stretches of empty
space in the universe or (by zooming in) the empty space within elementary
particles.

Rucker,
Rudy. *Geometry, Relativity and the Fourth Dimension*. New York: Dover,
1977.

[The author's] goal has been
to present an intuitive picture of the curved space-time we call home.

Rucker,
Rudy. *The Fourth Dimension*. Boston: Houghton Mifflin Co., 1984.

A history and description of
various ways that people have considered the fourth dimension.

Sommerville,
D.M.Y. *An Introduction to the Geometry of N Dimensions*. New York: Dover,
1958.

EG. Expositions – Geometry

Artmann,
Benno. *Euclid-The Creation of Mathematics*. New York: Springer,
1999.

Here the present book takes
a clear position: The Elements are read, interpreted, and commented upon from
the point of view of modern mathematics.

Beskin,
N.M. *Dividing a Segment in a Given Ratio*. Moscow: Mir Publishers,
1975.

From a collection of short
books (phamphlets) for high school students written by Soviet mathematicians
and translated into English.

Beskin,
N.M. *Images of Geometric Solids*. Moscow: Mir Publishers, 1985.

Blatner,
David. *The Joy of PI*. New York: Walker Publishing Company, 1997.

Boltjansky,
V. and Gohberg, I. *Results and Problems in Combinatorial Geometry*.
Cambridge: Cambridge University Press, 1985.

Boltyanski,
Vladimir and Soifer, Alexander. *Geometric Etudes in Combinatorial
Mathematics*. Colorada Springs, CO: Center for Excellence in Mathematical
Education, 1991.

Carroll,
Lewis. *Euclid and His Modern Rivals*. New York: Dover Publications, Inc.,
1973.

Yes! Lewis Carroll of Alice
in Wonderland fame was a geometer. This book is written as a drama; Carroll has
Euclid defending himself against modern critics.

Coxeter,
H.S.M. and Greitzer, S.L. *Geometry Revisited*. New York: The L.W. Singer
Company, 1967.

"Using whatever means
will best suit our purposes, let us revisit Euclid. Let us discover for
ourselves a few of the newer results. Perhaps we may be able to recapture some
of the wonder and awe that our first contact with geometry aroused."

Darley,
George. *Geometrical Companion: in which the Elements of Abstract Geometry
are Familiarised, Illustrated, and Rendered Practically Useful to the Various
Purposes of Life*. London: Taylor and Walton, 1841.

Edwards,
A.W.F. *Cogwheels of the Mind: The Story of Venn Diagrams*. Baltimore, MD:
Johns Hopkins University Press, 2004.

geometric and historical
aspects of Venn diagrams, including Venn diagrams on the sphere.

Fetisov,
A.I. *Proof in Geometry*. Moscow: Mir Publishers, 1978.

Gaffney,
Matthew P. and Steen, Lynn Arthur. *Annotated Bibliography of Expository
Writing in the Mathematical Sciences*. Washington, DC: M.A.A., 1976.

Gorini,
Catherine A. (editors): *Geometry at Work: Papers in Applied Geometry*,
MAA Notes.Number 53: Washington, DC: Mathematical Association of America, 2000.

Gorini,
Catherine. *Facts on File Geometry Handbook*. New York: Facts On File,
2003.

Hansen,
Vagn Lundsgaard. *Shadows of the circle: conic sections, optimal figures and
non-Euclidean geometry*. River Edge, NJ: World Scientific, 1998.

Hargittai,
István and Hargittai, Magdolna. *Symmetry: A Unifying Concept*. Bolinas,
CA: Shelter Publications, 1994.

"The single, most
important purpose of this book is to help you notice the world around you, to
train your eye and mind to see new patterns and make new connections."

Hilbert,
David and Cohn-Vossen, S. *Geometry and the Imagination*. New York:
Chelsea Publishing Co., 1983.

They state "it is our
purpose to give a presentation of geometry, as it stands today [1932], in its
visual, intuitive aspects." It includes an introduction to differential
geometry, symmetry, and patterns (they call it "crystallographic
groups"), and the geometry of spheres and other surfaces. Hilbert is the
most famous mathematician of the first part of this century.

Juster,
Norton. *The Dot and the Line: A Romance in Lower Mathematics*. New York:
Random House, 1963.

A mathematical fable.

Kaplan,
Robert and Kaplan, Ellen. *The Art of the Infinite: The Pleasures of
Mathematics*. Oxford: Oxford University Press, 2003.

Kutepov,
A. and Rubanov, A. *Problems in Geometry*. Moscow: MIR publishers,
1978.

"The book contains a
collection of 1351 problems (with answers) in plane and solid geometry for
technical schools and colleges."

Lang,
Serge. *The Beauty of Doing Mathematics: Three Public Dialogues*. New
York: Springer-Verlag, 1985.

Expository work by a famous
mathematician.

Lyubich,
Yu.I. and Shor, L.A. *The Kinematic Method in Geometrical Problems*.
Moscow: Mir Publishers, 1980.

Lyusternik,
L.A. *The Shortest Lines*. Moscow: Mir Publishers, 1983.

Markushevich,
A.I. *Areas and Logarithms*. Moscow: Mir Publishers, 1981.

Markushevich,
A.I. *Complex Numbers and Conformal Mappings*. Moscow: Mir Publishers,
1982.

Markushevich,
A.I. *Remarkable Curves*. Moscow: Mir Publishers,

Mlodinow,
Leonard. *Euclid's Window, The Story of Geometry from Parallel Lines to
Hyperspace*. New York: The Free Press, 2001.

Nelsen,
Roger B. *Proofs Without Words: Exercises in Visual Thinking*. Washington,
D.C.: MAA, 1993.

Nelson,
Roger B. *Proofs Without Words II: More Exercises in Visual Thinking*.
Washington, DC: The Mathematical Association of America, 2000.

Nikulin,
V. V. and Shafarevich, I. R. *Geometries and Groups*. New York:
Springer-Verlag, 1987.

"This book is devoted
to the theory of geometries which are locally Euclidean, in the sense they are
identical to the geometry of the Euclidean plane or Euclidean 3-space... The
basic method of study is the use of groups of motions, both discrete groups and
the groups of motions of geometries."

Polster,
Burkard. *A Geometrical Picture Book*. New York: Springer, 1998.

Pritchard,
Chris. *The Changing Shape of Geometry: Celebrating a Century of Geometry and
Geometry Teaching*. Cambridge University Press and MAA, 2002.

The book is an expanded
collection of 57 articles published in Mathematical Gazette and Mathematics in
School — two journals of The Mathematical Association, a British organization
for teachers of mathematics — over about one hundred years.

Rosenfeld,
B.A. and Sergeeva, N.D. *Stereographic Projection*. Moscow: Mir
Publishers, 1977.

Sharygin,
I. F. *Problems in Solid Geometry*. Moscow: MIR publishers, 1986.

Smogorzhevsky,
A.S. *Lobachevskian Geometry*. Moscow: Mir Publishers, 1982.

Smogorzhevsky,
A.S. *The Method of Coordinates*. Moscow: Mir Publishers, 1984.

Smogorzhevsky,
A.S. *The Ruler in Geometrical Constructions*. New York: Blaisdell
Publishing COmpany, 1961.

Soifer,
Alexander. *How Does One Cut a Triangle?* Colorado Springs, CO: Center for
Excellence in Mathematical Education, 1990.

Sved,
Marta. *Journey into Geometries*. Washinton, DC: Mathematical Association
of America, 1991.

"This book, though not
a text, is first and foremost about geometry. It is neither comprehensive, not
can it claim to go very deep into the chosen topics, yet hopefully, it may
initiate a spark to light the way into further progress. The central topic in
this book is non-Euclidean geometry. The approach to it is made via the
Poincare model, ..."

Tanton,
James. *Solve This, Math Activities For Students And Clubs*. Washington
DC.: The Mathematical Association of America, 2001.

Valens,
Evans G. *The Number of Things: Pythagoras, Geometry and Humming Strings*.
New York: E.P. Dutton and Company, 1964.

This is a book about ideas
and is not a textbook. Valens leads the reader through dissections, golden
mean, relations between geometry and music, conic sections, etc.

Vasilyev,
N. and Gutenmacher, V. *Straight Lines and Curves*. Moscow: Mir Publishers,
1985.

Walser,
Hans. *The Golden Section*. Washington, DC: The Mathematical Association
of America, 2001.

Wells,
David. *The Penguin Dictionary of Curious and Interesting Geometry*.
London: Penguin, 1991.

"Entire books have been written about tessellations alone, or
topological curiosities, or geometric extremal properties, beside the wealth of
classical geometry. This is my selection from that cornucopia."

EM. Expositions – Mathematics

Dewdney,
A.K. *A Mathematical Mystery Tour: Discovering the Truth and Beauty of the
Cosmos*. New York City: John Wiley & Sons, 1999.

"The mathematical
odyssey herein explores two key questions about mathematics and its
relationship to reality: Why is mathematics so amazingly successful in
describing the structure of physical reality? Is mathematics created, or is it
discovered?" Chapter 4 of this book is about mapping the spheres, and
whole book is written in a language accessible to general audience, not only
mathematicians.

Farmer,
David W. and Stanford, Theodore B. *Knots and Surfaces, A Guide to Disovering
Mathematics*. Washington DC: American Mathematical Society, 1996.

GIlbert,
George T. and Hatcher, Rhonda L. *Mathematics Beyond the Numbers*. New
York: John Wiley & Sons, 2000.

Gaffney,
Matthew P. and Steen, Lynn Arthur. *Annotated Bibliography of Expository
Writing in the Mathematical Sciences*. Washington, DC: M.A.A., 1976.

Gamow,
George. *One, Two, Three ... Infinity*. New York: Bantam Books, 1961.

A well-written journey
through mathematical ideas.

Gerdes,
Paulus. *Geometrical Recreations of Africa*. Maputo, Mozambique: African
Mathematical Union and Higher Pedagogical Institute's Faculty of Science,
1991.

Guillen,
Michail. *Bridges to Infinity: The Human Side of Mathematics*. Los
Angeles: Jeremy P. Tarcher, 1983.

Hilton,
Peter, Holton, Derek, and Pedersen, Jean. *Mathematical Vistas, From a room
with many windows*. New York: Springer, 2002.

Honsberger,
Ross. *Mathematical Gems*. Washington, DC: M.A.A., 1973.

Expository stories about
mathematics.

Honsberger,
Ross. *Mathematical Gems II*. Washington, DC: M.A.A., 1976.

Expository stories about
mathematics.

Honsberger,
Ross. *Mathematical Morsels*. Washington, DC: M.A.A., 1978.

Expository stories about
mathematics.

Honsberger,
Ross. *Mathematical Plums*. Washington, DC: M.A.A., 1979.

Expository stories about
mathematics.

Honsberger,
Ross. *Mathematical Chestnuts from Around the World*. Washingon, DC: The
Mathematical Association of America, 2001.

Ifrah,
Georges. *From One to Zero: A Universal History of Numbers*. New York:
Penguin Books, 1987.

Johnson,
Art. *Famous Problems and their Mathematicians*. Englewood, CO: Teacher
Ideas Press, 1999.

Krantz,
Steven G. *Mathematical Apocrypha: Stories and Anecdotes of Mathematicians
and the Mathematical*. Washinton, DC: The Mathematical Association of
America, 2002.

Lacskovich,
Miklós. *Conjecture and Proof*. Washington, DC: The Mathematical
Association of America, 2001.

Lang,
Serge. *The Beauty of Doing Mathematics: Three Public Dialogues*. New
York: Springer-Verlag, 1985.

Expository work by a famous
mathematician.

Lieber,
Lillian R. *The Education of T.C. Mits (The Celebrated Man in the Street)*.
New York: W.W. Norton, 1972.

A mathematical fantasy.

Pappas,
Theoni. *Mathematical Scandals*. San Carlos, CA: Wide World Publishing/Tetra,
1997.

Parks,
Harold, Musser, Gary, Burton, Robert, and Siebler, William. *Mathematics in
Life, Society, and the World*. Upper Saddle River, NJ: Prentice-Hall,
1997.

Peterson,
Ivars. *Mathematical Treks: From Surreal Numbers to Magic Circles*.
Washington, DC: The Mathematical Association of America, 2002.

Pickover,
Clifford A. *The Mathematics of OZ: Mental Gymnastics from Beyond the Edge*.
New York: Cambridge University Press, 2002.

Péter,
Rozsa. *Playing with Infinity*. New York: Dover Publishing, Inc.,
1961.

"Mathematical
explorations and excursions."

Restivo,
Sal, Paul, Jean, Bendegem, Van, and Fischer, Roland (editors): *MathWorlds*, New York: State University of New York
Press, 1993.

Rota,
Gian -Carlo. *Indiscrete Thoughts*. Boston: Birkhäuser, 1997.

Sadovski,
L.E. and Sadovskii, A.L. *Mathematics and Sports*. Washington DC.:
American Mathematical Society, 1993.

Sawyer,
W.W. *Prelude to Mathematics*. New York: Dover, 1982.

"An account of some of
the more stimulating and surprising branches of mathematics, introduced by an
analysis of the mathematical mind, and the aims of the mathematician."

Shenitzer,
Abe, and Stillwell, John (editors): *Mathematical Evolutions*, Spectrum
Series Washington, DC: The Mathematical Association of America, 2002.

Steen,
Lynn Arthur (editors): *Mathematics Today: Twelve Informal Essays*, New York: Springer-Verlag, 1978.

Steen,
Lynn Arthur (editors): *Mathematics Tomorrow*, New York: Springer-Verlag, 1981.

Expository essays

Stein,
Sherman. *Strength in Numbers: Discovering the Joy and Power of Mathematics
in Everyday Life*. New York: John Wiley & Sons, 1996.

Stewart,
Ian. *The Problems of Mathematics*. Oxford: Oxford University Press,
1987.

Stewart,
Ian, and Jaworski, John (editors): *Seven years of manifold: 1968-1980*, Nantwich, Cheshire, UK: Shiva Publishing
Limited, 1987.

A collection of articles
from a mathematics magazine published at Universtiy of Warwick, England

Tanton,
James. *Solve This: Math Activities for Students and Clubs*. Washington,
DC: Mathematical Association of America, 2001.

Uspensky,
V.A. *Gödel's Incompleteness Theorem*. Moscow: Mir Publishers, 1987.

Vaderlind,
Paul, Guy, RIchard, and Larson, Loren. *The Inquisitive Proiblem Solver*.
Washington, DC: The Mathematical Association of America, 2002.

Wells,
D.G. *Recreations in Logic*. New York: Dover Publications, 1979.

Wells,
David. *The Penguin Dictionary of Curious and Interesting Numbers*.
London: Penquin Books, 1986.

Wells,
David. *The Penguin Dictionary of Curious and Interesting Geometry*.
London: Penguin, 1991.

"Entire books have been
written about tessellations alone, or topological curiosities, or geometric
extremal properties, beside the wealth of classical geometry. This is my
selection from that cornucopia."

Wells,
David. *You Are a Mathematician: A Witty and Wise Introduction to the Joy of
Numbers*. New York: John Wiley & Sons, 1995.

Wells,
David. *The Penquin Book of Curious and Interesting Mathematics*. London:
Penquin Books, 1997.

FO. Foundations of Geometry

Forder,
H.G. *The Foundations of Geometry*. Cambridge, UK: Cambridge University
Press, 1927.

Frankland,
William Barrett. *Theories of Parallelism: An Historical Critique*. The
Cornell Library Historical Mathematics Monographs, 1910. **online: http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=00100002&seq=7**

Hilbert,
David. *Foundation of Geometry (Grundlagen der Geometrie)*. LaSalle, IL:
Open Court Press, 1971.

FR. Fractals

Edgar,
Gerald A. *Measure, Topology, and Fractal Geometry*. New York: Springer
Verlag New York Inc., 1990.

This is a mathematics book.
It is not about how fractals come up in nature; that is the topic of
Mandelbrot's book. It is not about how to draw fractals on your computer...
Complete proofs of the main results will be presented, whenever that can
reasonably be done.

Eglash,
Ron. *African Fractals: Modern Computing and Indigenous Design*. New
Brunswick: Rutgers University Press, 1999.

Frame,
M.L., and Mandelbrot, B.B. (editors): *Fractgals, Graphics, and Mathematics
Education*, MAA Notes Series.58: Washington, DC: The Mathematical
Association of America, 2002.

Lauwerier,
Hans. *Fractals: Endlessly Repeated Geometric Figures*. Princeton, NJ:
Princeton University Press, 1991.

Mandelbrot,
Benoit B. *The Fractal Geometry of Nature*. New York: W.H. Freeman and
Company, 1983.

The book that started the
popularity of fractal geometry.

Mumford,
David, Series, Caroline, and Wright, David. *Indra's Pearls: The Vision of
Felix Klein*. Cambridge, UK: Cambridge University Press, 2002.

GC. Geometry in Different Cultures

Albarn,
Keith, Smith, Jenn Mial, Steele, Stanford, and Walker, Dinah. *The Language
of Pattern*. New York: Harper & Row, 1974.

Inspired by Islamic
decorative pattern, the authors of this book, who are all designers, explore
pattern step by step, beginning with simple numerical and geometrical
relationships and progressing through the dimensions

Ascher,
Marcia. *Ethnomathematics: A Multicultural View of Mathematical Ideas*.
Pacific Grove, CA: Brooks/Cole, 1991.

A mostly anthropological
look at the mathematics indigenous to several ancient cultures.

Bain,
George. *Celtic Arts: The Methods of Construction*. London: Constable,
1977.

A description of the
construction of Celtic patterns and designs.

Datta.
*The Science of the Sulba*. Calcutta: University of Calcutta, 1932.

A discussion of the
mathematics in the Sulba Sutra and traditional Hindu society.

Eglash,
Ron. *African Fractals: Modern Computing and Indigenous Design*. New
Brunswick: Rutgers University Press, 1999.

Fukagawa,
Hidetosi and Pedoe, Dan. *Japanese Temple Geometry Problems: San Gaku*.
Winnipeg: The Charles Babbage Research Centre, 1989.

Gerdes,
Paulus. *Geometrical Recreations of Africa*. Maputo, Mozambique: African
Mathematical Union and Higher Pedagogical Institute's Faculty of Science,
1991.

Gerdes describes and
discusses the mathematical aspects of the central African sona sand drawings.

Gerdes,
Paulus. *The African Pythagoras: A Study in Culture and Mathematics Education*.
Maputo, Mozambique: Instituto Superior Pedagógico, 1994.

Gerdes makes the case that
the ideas behind what we call the Pythagorean Theorem could possibly have had
their origins in Sub-Saharan Africa and argues for the africanization of the
teaching on mathematics in Africa.

Gerdes,
Paulus. *Ethnomathematics and Education in Africa*. Stockhoms Universitet,
1995.

Gerdes,
Paulus. *Women, Art and Geometry in Southern Africa*. Trenton: Africa
World Press, Inc., 1998.

The main objective of the
book Women, Art and Geometry in Southern Africa is to call attention to some
mathematical aspects and ideas incorporated in the patterns invented by women
in Southern Africa.

Gerdes,
Paulus. *Geometry From Africa: Mathematical and Educational Explorations*.
Washington: Mathematical Association of America, 1999.

... we learn of the
diversity, richness, and pleasure of mathematical ideas found in Sub-Saharan
Africa. Form a careful reading and working through this delightful book, one
will find a fresh approach to mathematical inquiry as well as encounter a
subtle challenge to Eurocentric discourses concerning the when, where, who, and
why of mathematics.

Holme,
Audun. *Geometry, Our Cultural Heritage*. New York: Springer, 2002.

Høyrup,
Jens. *In Measure, Number, and Weight: Studies in Mathematics and Culture*.
Albany: State University of New York Press, 1994.

Jean,
Geoerges. *Signs, Symbols and ciphers: Decoding the Message*. London:
Thames & Hudson, 1998.

Kline,
Morris. *Mathematics in Western Culture*. New York: Oxford University
Press, 1961.

Yan,
Li and Shiran, Du. *Chinese Mathematics: A Concise History*. Oxford:
Clarendon, 1987.

Mikami,
Yoshio. *The Development of Mathematics in China and Japan*. New York:
Chelsea, 1974.

Mohen,
Jean -Pierre. *Standing Stones: Stonehenge, Carnac and the World of Megaliths*.
London: Thames & Hudson, 1999.

"... this book
considers the special significance -- religious and cultural, architectural and
scientific -- of these enigmatic Neolithic stone structures ..."

Nasr,
Seyyed Hossein. *Islamic Science: An Illustrated Study*. World of Islam
Festival Publishing, 1976.

Neihardt,
John G. *Black Elk Speaks: Being the Life Story of a Holy Man of the Oglala
Sioux*. Lincoln, NE: University of Nebraska Press, 1961.

Contains descriptions of
geometric ideas in Oglala Sioux culture

Pinxten,
R., Dooren, Ingrid van, and Harvey, Frank. *The Anthropology of Space*.
Philadelphia: University of Pennsylvania Press, 1983.

Concepts of geometry and space
in the Navajo culture.

Selin,
Helaine, and D'Ambrosio, Ubiratan (editors): *Mathematics Across Cultures:
The History of Non-Western Mathematics*,
Boston: Kluwer Academic Publishers, 2000.

"Every culture has
mathematics. That is not to say that every culture has forms of [enumeration
and calculation] ... But enumeration and calculation are only parts of
mathematics; a broader definition that includes 'the study of measurements,
forms, patterns, variability and change' encompasses the mathematical systems
of many non-Western cultures."

Zaslavsky,
Claudia. *Africa Counts*. Boston: Prindle, Weber, and Schmidt, Inc.,
1973.

A presentation of the
mathematics in African cultures.

GS. Geometry and Science

Abraham,
Ralph H. and Shaw, Christopher D. *Dynamics: The Geometry of Behaviour (in 4
volumes)*. Santa Cruz, CA: Aerial Press,

Dynamics is emerging as an
important conceptual scheme, unifying the sciences -- physical, biological, and
social -- in a common geometric model... All four [volumes] are written for a
general audience, without the assumption of extensive training in math or the
sciences. Visual presentation, the hallmark of the Visual Mathematics Library,
makes the ideas accessible.

Abraham,
Ralph H. and Shaw, Christopher D. *Dynamics: A Visual Introduction*.
Plenum Publishing Corporation, 1987.

A dynamical system is one
whose state may be represented as a point in a space, where each point is
assigned a vector specifying the evolution. The basic ideas of the mathematical
theory of dynamical systems are presented here visually, with a minimum of
discussion, using examples in low dimensions... While working together on the
illustrations for a book, we discovered that we could explain mathematical
ideas visually, within an easy and pleasant working partnership.

Blay,
Michel. *Reasoning with the Infinite: From the Closed World to the
Mathematical Universe*. Chicago and London: The University of Chicago Press,
1993.

"The present essay has
the object of the explaining in the development of mathematical physics on the
basis of the actual process of geometrization, the difficulties that arose from
trying to take the infinite into account, as well as the techniques developed
to resolve or to avoid them, insofar as the neglect of the question of meaning
grew out of these very difficulties.

Kline,
Morris. *Mathematics and the Physical World*. New York: Thomas Y. Crowell
Company, 1959.

To display the role of
mathematics in the study of nature is the purpose of this book. Subordinate,
but by no means incidental, objectives may also be fulfilled. We may see
mathematics in the process of being born... The precise manner in which
mathematics produces answers to physical problems... how and why mathematics
has become the essence of scientific theories.

Schneider,
Michael S. *A Beginner's Guide to Constructing the Universe: The Mathematical
Archetypes of Nature, Art, and Science*. New York: HarperPerennial,
1994.

Schutz,
Bernard. *Geometrical methods of mathematical physics*. New York:
Cambridge University Press, 1993.

This book aims to introduce
the beginning or working physicist to a wide range of analytic tools which have
their origin in differential geometry and which have recently found increasing
use in theoretical physics.

Shaw,
Robert. *The Dripping Faucet as a Model Chaotic System*. Santa Cruz:
Aerial Press, Inc., 1984.

Water drops falling from an
orifice present a system which is both easily accessible to experiment and
common in everyday life. As the flow rate is varied, many features of the
phenomenology of nonlinear systems can be seen, including chaotic transitions,
familiar and unfamiliar bifurcation sequences, hysteresis, and multiple basins
of attraction.

Sumners,
De Witt L. (editors): *New Scientific Applications of Geometry and Topology*,
Proceedings of Symposia in Applied Mathematics.45: Providence, Rhode Island:
American Mathematical Association, 1992.

"Recently, some of the
methods and results of geometry and topology have found new utility in both
wet-lab and theoretical science. Conversely, science is influencing
mathematics, from posing questions which call for construction of mathematical
models to the importation of theoretical methods of attack on long-standing
problems of mathematical interest."

HI. History of Mathematics

Beckmann,
Peter. *A History of Pi*. Boulder, CO: The Golem Press, 1970.

A well-written enjoyable
book about all aspects of pi.

A
well-written enjoyable book about all aspects of pi.

Berggren,
J.L. *Episodes in the Mathematics of Medieval Islam*. New York:
Springer-Verlag, 1986.

Describes many examples that
are difficult to find elsewhere of the mathematical contributions from Medieval
Islam.

Boi,
Luciano. *Le Probléme Mathématique de l'Espace: Une Quéte de l'Intelligible*.
Berlin: Springer, 1995.

A historical account of
non-Euclidean spaces with many interesting photos (for example, paper models of
hyperbolic space constructed by Beltrami.

Bold,
Benjamin. *Famous Problems of Geometry and How to Solve Them*. New York:
Dover Publications, Inc., 1969.

Bonola,
Roberto. *Non-Euclidean Geomtry: A critical and Historic Study of its
Developments, and "The theory of Parallels" by Nicholas Lobachevski
with a supplement containing "The Science of Absolute Space" by John
Bolyai*. New York: Dover, 1995.

Bonola's Non-Euclidean
Geometry is an elementary historical and ciritcal study of the development of
that subject

Calinger,
Ronald. *Classics of Mathematics*. Englewood Cliffs, NJ: Prentice Hall,
1995.

Mostly a collection of
original sources in Western mathematics.

Calinger,
Ronald. *A Contextual History of Mathematics: to Euler*. Upper Saddle
River, NJ: Prentice Hall, 1999.

Carroll,
Lewis. *Euclid and His Modern Rivals*. New York: Dover Publications, Inc.,
1973.

Yes! Lewis Carroll of Alice
in Wonderland fame was a geometer. This book is written as a drama; Carroll has
Euclid defending himself against modern critics.

Cohen,
Patricia Cline. *A Calculating People: The Spread of Numeracy in Early
America*. Chicago: The University of Chicago Press, 1982.

Cooke,
Roger. *The History of Mathematics: A Brief Course*. New York: John Wiley
& Sons, 1997.

Eves,
Howard. *Great Moments in Mathematics (after 1650), Dolciani Mathematical
Expositions*. Washington, DC: M.A.A. --AB-- This small book contains 20
lectures: 2 on non-Euclid geometry and one on Klien's "Erlanger
Program" which set out to delineate various, 1981.

Fauvel,
John and Gray, Jeremy. *The History of Mathematics: A Reader*. London:
Macmillan Press, 1987.

The selection of readings
has been made for students of the Open University course MA290 Topics in the
History of Mathematics ...

Fauvel,
John, and van Maanen, Jan (editors): *History in Mathematics Education: The
ICMI Study*, Dordrecht: Kluwer
Academic publishers, 2000.

Field,
Judith Veronica. *The Invention of Infinity: Mathematics and Art in
Renaissance*. Oxford: Oxford University Press, 1997.

Book will look at the
relations between of Renaissance art and mathematics in the period from about
1300 to about 1650.

Frankland,
William Barrett. *Theories of Parallelism: An Historical Critique*. The
Cornell Library Historical Mathematics Monographs, 1910. **online: http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=00100002&seq=7**

Goldman,
Jay R. *The Queen of Mathematics: A Historically Motivated Guide to Number
Theory*. Wellesley, MA: AK Peters, 1998.

Gray,
Jeremy. *Ideas of Space: Euclidean, Non-Euclidean and Relativistic*.
Oxford: Oxford University Press, 1989.

A mostly historical account
of Euclidean, non-Euclidean and relativistic geometry. "I shall discuss
Greek and modern geometry, in particular what came to be known as the problem
of parallels, that 'blot on geometry' as Saville called it in 1621."

Guedj,
Denis. *Numbers: The Universal Language*. New York: Harry N. Abrams, Inc.,
1997.

A beautifully illustrated
history of numbers from cave drawing to the present day.

Heath,
T.L. *Euclid: The Thirteen Books of the Elements*. New York: Dover,
1956.

This is edition of Eulid's
Elements to which one is usually referred. Heath has added a large collection
of very useful historical and philosophical notes. His notes are more extensive
than Euclid's text.

Heilbron,
J.L. *Geometry Civilized: History, Culture, and Technique*. Oxford:
Clarendon Press, 2000.

For many centuries, geometry
was part of high culture as well as an instrument of practical utility.

Joseph,
George. *The Crest of the Peacock*. New York: I.B. Tauris, 1991.

A non-Eurocentric view of
the history of mathematics.

Kaplan,
Robert. *The Nothing That Is: A Natural History of Zero*. New York: Oxford
University Press, 2000.

"Look at zero and yoou
see nothing, but look through it and you see the world."

Katz,
Victor (editors): *Using History to Teach Mathematics: An International
Perspective*, MAA Notes.#51: Washington, D.C.: Mathematical Association of
America, 2000.

Katz,
Victor J. *A History of Mathematics: An Introduction*. Reading, MA:
Addison-Wesley Longman, 1998.

"... designed for
junior or senior mathematics majors who intend to teach in college or high
school and thus concentrates on the history of those topics typically covered
in an undergraduate curriculum or in elementary or high school.

Kline,
Morris. *Mathematics in Western Culture*. New York: Oxford University
Press, 1961.

Kline,
Morris. *Mathematical Thought from Ancient to Modern Times*. Oxford:
Oxford University Press, 1972.

A complete Eurocentric
history of mathematical ideas including differential geometry (mostly the
analytic side).

Laubenbacher,
Reinhard and Pengelley, David. *Mathematical Expeditions: Chronicles by the
Explorers*. New York: Springer, 1999.

Contains a 53-page chapter
on "Geometry: The Parallel Postulate".

Laugwitz,
Detlef: ""Infinitely Small Quantities in Cauchy's
Textbooks,"", *Historia Mathematica*, 14 (1987), 258-274.

Lewinter,
Marty and Widulski, William. *The Saga of Mathematics: A Brief History*.
Upper Saddle River, NJ: Prentice-Hall, 2002.

Maor,
Eli. *e: The Story of a Number*. Princeton, NJ: Princeton University
Press, 1994.

Maor,
Eli. *Trigonometric Delights*. Princeton, NJ: Princeton Unversity Press,
1998.

Monastyrsky,
Michael. *Modern Mathematics in the Light of the Fields Medals*.
Wellesley, MA: AK Peters, 1998.

Newell,
Virginia K. (editors): *Black Mathematicians and Their Works*, Ardmore, PA: Dorrance, 1980.

Richards,
Joan. *Mathematical Visions*. Boston: Academic Press, 1988.

The pursuit of geometry in
Victorian England.

Rosenfeld,
B.A. *A History of Non-Euclidean Geometry: Evolution of the Concept of a
Geometric Space*. New York: Springer-Verlag, 1989.

A extensive history of
non-Euclidean geometry based on original sources.

Schmandt-Besserat,
Denise. *Before Writing*. Austin: University of Texas Press, 1992.

This lavishly illustrated
book develops the theory that human writing developed from counting devices.

Seidenberg,
A.: ""The Ritual Origin of Geometry,"", *Archive for the
History of the Exact Sciences*, 1 (1961), 488-527.

In this article Seidenberg
makes the case that much geometry originated from the needs of various
religious rituals.

Selin,
Helaine, and D'Ambrosio, Ubiratan (editors): *Mathematics Across Cultures:
The History of Non-Western Mathematics*,
Boston: Kluwer Academic Publishers, 2000.

"Every culture has
mathematics. That is not to say that every culture has forms of [enumeration
and calculation] ... But enumeration and calculation are only parts of
mathematics; a broader definition that includes 'the study of measurements,
forms, patterns, variability and change' encompasses the mathematical systems of
many non-Western cultures."

Singh,
Simon. *Fermat's Enigma: The Quest to Solve the World's Greatest Mathematical
Problem*. New York: Walker and Company, 1997.

Description of the history
of proving Fermat's Last Theorem and methods used by Andrew Wiles, but also
there is some nice geometry in it.

Smeltzer,
Donald. *Man and Number*. New York: Emerson Books, 1958.

History and cultural aspects
of mathematics

Smith,
David Eugene. *A Source Book in Mathematics*. New York: Dover
Publications, Inc., 1959.

Stillwell,
John. *Mathematics and Its History*. New York: Springer-Verlag, 1989.

"This book aims to give
a unified view of undergraduate mathematics by approaching the subject though
its history."

Struik,
D.J. (editors): *A source Book in Mathematics 1200-1800*, Princeton, NJ: Princeton University Press,
1986.

Suzuki,
Jeff. *A History of Mathematics*. Uppeer Saddle River, NJ: Prentice Hall,
2002.

Swetz,
Frank J. *Capitalism & Arithmetic: The New Math of the 15th Century*.
La Salle, IL: Open Court, 1987.

Swetz,
Frank, Fauvel, John, and Bekken, Otto (editors): *Learn From The Masters*, Washington DC.: The Mathematical Association
of America, 1995.

Thomas,
Ivor (editors): *Selections Illustrating the History of Greek Mathematics*, Cambridge, MA: Harvard University Press,
1951.

A collection of primary
sources.

Toth,
I. *"Non-Euclidean Geometry before Euclid", Scientific American*.
1969.

Discusses the evidence of
non-Euclidean geometry before Euclid.

Valens,
Evans G. *The Number of Things: Pythagoras, Geometry and Humming Strings*.
New York: E.P. Dutton and Company, 1964.

This is a book about ideas
and is not a textbook. Valens leads the reader through dissections, golden
mean, relations between geometry and music, conic sections, etc.

Williams,
Trevor I. *A History of Invention: From Stone Axes to Silicon Chips*. New
York: Checkmark Books, 2000.

van
der Waerden, B.L. *Science Awakening I: Egyptian, Babylonian, and Greek
Mathematics*. Princeton Junction, NJ: The Scholar's Bookshelf, 1975.

"It is the intention to
make this book scientific, but at the same time accessible to any one who has
learned some mathematics in school and in college, and who is interested in the
history of mathematics."

HM. History of a Mathematician

Artmann,
Benno. *Euclid-The Creation of Mathematics*. New York: Springer,
1999.

Here the present book takes
a clear position: The Elements are read, interpreted, and commented upon from
the point of view of modern mathematics.

Batterson,
Steve. *Stephen Smale: The Mathematician Who Broke the Dimension Barrier*.
American Mathematical Society, 2000.

Bühler,
W.K. *Gauss: A Biographical Study*. New York: Springer-Verlag, 1981.

This biography contains many
quotations and lengthy passages from Gauss's writings.

Descartes,
Rene. *The Geometry of Rene Descartes*. New York: Dover Publications,Inc.,
1954.

This the book in which
Descartes develops the use of what we now call Cartesian coordinates for the
study of curves.

Feferman,
Solomon, Dawson, John W., Kleene, Stephen C., Moore, Gregory H., Solovay,
Robert M., and van Heijenoort, Jean (editors): *Kurt Gödel: Collecdted Works,
Volume I, Publications 1929-1936*,
New York: Oxford University Press, 1986.

Field,
Judith Veronica and Gray, Jerome J. *The Geometrical Work of Girard Desargues*.
New York: Springer-Verlag, 1987.

Flannery,
Sarah. *In Code: A Young Woman's Mathmatical Journey*. Chapel Hill, NC:
Algonquin Books of Chapel Hill, 2001.

Halmos,
Paul R. *I Want To Be a Mathematician: An Automathography In Three Parts*.
Washington, D.C.: MAA, Springer-Verlag, 1985.

Hardy,
G.H. *A Mathematician's Apology*. Cambridge, UK: Cambridge University
Press, 1967.

Heath,
T.L. *Mathematics in Aristotle*. Oxford: Clarendon Press, 1949.

Discusses the mathematical
contributions of Aristotle.

Hoffman,
Paul. *The Man Who Loved Only Numbers: The Story of Paul Erdös and the Search
for Mathematical Truth*. London: Fourth Estate, 1998.

Kiss,
Elemér. *Mathematical Gems From the Boylai Chests: János Bolyai's discoveries
in Number Theory and Algebra as recently deciphered from his manuscripts*.
Budapest: Akadémiai Kiadó & TypoTEX, 1999.

Marchisotto,
Elena Anne and Smith, James T. *The Legacy of Mario Pieri in Arithmetic and
Geometry*. Boston: Birkhauser, 2004.

Newell,
Virginia K. (editors): *Black Mathematicians and Their Works*, Ardmore, PA: Dorrance, 1980.

Riemann,
Bernard. *Gesammelte Mathematische Werke*. Leipzig: B.G. Teubner, 1902.

Rosenblatt,
Murray (editors): *ERRETT BISHOP: Reflections on Him and His Research*,
Contermporary Mathematics.39: Providence, RI: American Mathematical Society,
1985.

Shasha,
Dennis and Lazere, Cathy. *Out Of Their Minds: The Lives and Discoveries of
15 Great Computer Scientists*. New York: Copernicus, 1998.

Sobel,
Dava. *Galileo's Daughter: A Historical Memoir of Science, Faith, and Love*.
New York: Penquin Putman, 1999.

A story of Galileo's life
and works as chronicled in his correspondences with his daughter

Yaglom,
I.M. *Felix Klein and Sophus Lie: Evolution of the Idea of Symmetry in the
Nineteenth Century*. Boston: Birkhäuser, 1988.

HY. Hyperbolic Geometry

Batterson,
Steve. *Stephen Smale: The Mathematician Who Broke the Dimension Barrier*.
American Mathematical Society, 2000.

Boi,
Luciano. *Le Probléme Mathématique de l'Espace: Une Quéte de l'Intelligible*.
Berlin: Springer, 1995.

A historical account of
non-Euclidean spaces with many interesting photos (for example, paper models of
hyperbolic space constructed by Beltrami.

Bonola,
Roberto. *Non-Euclidean Geomtry: A critical and Historic Study of its
Developments, and "The theory of Parallels" by Nicholas Lobachevski
with a supplement containing "The Science of Absolute Space" by John
Bolyai*. New York: Dover, 1995.

Bonola's Non-Euclidean
Geometry is an elementary historical and ciritcal study of the development of
that subject

Coxeter,
H.S.M. *Non-Euclidean Geometry*. Toronto: University of Toronto Press,
1965.

Efimov,
N. V.: "Generation of singularities on surfaces of negative curvature
[Russian]", *Mat. Sb. (N.S.)*, 106 (1964), 286-320.

Efimov proves that it is
impossible to have a C2 isometric embedding of the hyperbolic plane onto a
closed subset of Euclidean 3-space.

Fenchel,
Werner. *Elementary Geometry in Hyperbolic Space*. Berlin: Walter de
Gruyter, 1989.

Greenberg,
Marvin J. *Euclidean and Non-Euclidean Geometries: Development and History*.
New York: Freeman, 1980.

This is a very readable
textbook that includes some philosophical discussions.

Hartshorne,
Robin: "Non-Euclidean III.36", *American Mathematical Monthly*,
110 (2003), 495-502.

Power of a point on sphere
and hyperbolic plane

Hilbert,
David: "Über Flächen von konstanter gausscher Krümmung, Transactions of
the A.M.S", (1901), 87-99.

Hilbert proves here that the
hyperbolic plane does not have a real analytic (or C4) isometric embedding onto
a closed subset of Euclidean 3-space.

Kuiper,
Nicolas: "On c1-isometric embeddings ii, Nederl. Akad. Wetensch. Proc.
Ser. A", (1955), 683-689.

Kuiper shows that there is a
C1 isometric embedding of the hyperbolic plane onto a closed subset of
Euclidean 3-space.

Milnor,
Tilla: "Efimov's theorem about complete immersed surfaces of negative
curvature,Advances in Math", 8
(1972), 474-543.

Milnor clarifies for
English-reading audiences Efimov's result in [NE: Efimov].

Moise,
Edwin E. *Elementary Geometry from an Advanced Standpoint*. Reading, MA:
Addison-Wesley Publishing, 1990.

Nikulin,
V. V. and Shafarevich, I. R. *Geometries and Groups*. New York:
Springer-Verlag, 1987.

"This book is devoted
to the theory of geometries which are locally Euclidean, in the sense they are
identical to the geometry of the Euclidean plane or Euclidean 3-space... The
basic method of study is the use of groups of motions, both discrete groups and
the groups of motions of geometries."

Petit,
Jean -Pierre. *Euclid Rules OK? The Adventures of Archibald Higgins*.
London: John Murray, 1982.

A pictorial, visual tour of
non-Euclidean geometries.

Prenowitz,
Walter and Jordan, Meyer. *Basic Concepts of Geometry*. New York:
Blaisdell Publishing, 1965.

Rosenfeld,
B.A. *A History of Non-Euclidean Geometry: Evolution of the Concept of a
Geometric Space*. New York: Springer-Verlag, 1989.

A extensive history of
non-Euclidean geometry based on original sources.

Ryan,
Patrick J. *Euclidean and Non-Euclidean Geometry: An Analytic Approach*.
Cambridge: Cambridge University Press, 1986.

Schwerdtfeger,
Hans. *Geometry of Complex Numbers: Circle Geometry, Moebius Transformation,
Non-Euclidean Geometry*. New York: Dover Publications, Inc., 1979.

This book uses complex
numbers to analyze inversions in cricles and then their relationship to
hyperbolic geometry.

Singer,
David A. *Geometry: Plane and Fancy*. New York: Springer, 1998.

"This book is about ...
the idea of curvature and how it affects the assumptions about and principles
of geometry."

Smogorzhevsky,
A.S. *Lobachevskian Geometry*. Moscow: Mir Publishers, 1982.

Sommerville,
D.M.Y. *Bibliography of Non-Euclidean Geometry*. New York: Chelsea
Publishing Company, 1970.

This book contains 410 pages
of bibliographic references up to 1968.

Stahl,
Saul. *The Poincaré Half-Plane*. Boston: Jones and Bartlett Publishers,
1993.

This text is an analytic
introduction to some of the ideas of intrinsic differential geometry starting
from the Calculus.

Sved,
Marta. *Journey into Geometries*. Washinton, DC: Mathematical Association
of America, 1991.

"This book, though not
a text, is first and foremost about geometry. It is neither comprehensive, not
can it claim to go very deep into the chosen topics, yet hopefully, it may
initiate a spark to light the way into further progress. The central topic in
this book is non-Euclidean geometry. The approach to it is made via the
Poincare model, ..."

Thurston,
William. *Three-Dimensional Geometry and Topology, Vol. 1*. Princeton, NJ:
Princeton University Press, 1997.

This is a detailed excursion
through the geometry and topology of two- and three-manifolds. "The style
of exposition in this book is intended to encourage the reader to pause, to
look around and to explore.

Trudeau,
Richard J. *The Non-Euclidean Revolution*. Boston: Birkhäuser, 1987.

"Trudeau's book
provides the reader with a non-technical description of the progress of thought
from Plato and Euclid to Kant, Lobachevsky, and Hilbert."

Zage,
Wayne: "The Geometry of Binocular Visual Space", *Mathematics
Magazine*, 53 (1980), 289-294.

"... we relate the
results of experiments in binocular vision to geometric models to arrive at the
conclusion that the geometry of binocular visual space is [...]
hyperbolic."

IN. Inversions

Davis,
Chandler, Grunbaum, Branko, and Sherk, F.A. (editors): *The Geometric Vein*, New York: Springer-Verlag, 1981.

Book has many addresses,
essays, lectures on geometry and is dedicated to H. S. M. Coxeter. There is a
chapter on Inversive Geometry written by J. B. Wilker with nice examples of the
use of inversions.

Dupuis,
N.F. *Elementary Synthetic Geometry of the Point, Line and Circle in the
Plane*. London: Macmillan and Co., 1889.

Section IV of this book is
on inversion and inverse figures which gives more examples on use of inversion
in solution geometric problems. Book available in Cornell Library.

Lachlan,
R. *An Elementary Treatise on Modern Pure Geometry*. London: Macmillan and
Co., 1893. **online**: http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=Lach015&seq=7

Chapter XIV is on theory of
inversions giving good examples of use of inversion.

Sommerville,
D.M.Y. *Bibliography of Non-Euclidean Geometry*. New York: Chelsea
Publishing Company, 1970.

This book contains 410 pages
of bibliographic references up to 1968.

Townsend,
Richard. *Chapters on the Modern Geometry of the Point, Line, and Circle;
being the Substance of Lectures Delivered in the University of Dublin to the
Candidates for Honors of the first Year in Arts*. Dublin: Hodges, Smith, and
Co., 1863. **online**: (volume 1) http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=00720002&seq=5
(volume 2) http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=01060002&seq=5

Title
of the book already explains what is in it, but special interest may be found
in Chapter IX "Theory of Inverse Points with Respect to the
Circle".

LA. Linear Algebra and Geometry

Banchoff,
Thomas and Wermer, John. *Linear Algebra Through Geometry*. New York:
Springer-Verlag New York, Inc., 1983.

"In this book we lead
the student to an understanding of elementary linear algebra by emphasizing the
geometric significance of the subject. Our experience in teaching beginning
undergraduates over the years has convinced us that students learn the new
ideas of linear algebra best when these ideas are grounded in the familiar
geometry of two and three dimensions."

Dodson,
C. T. J. and Poston, T. *Tensor Geometry*. London: Pitman, 1979.

A very readable but
technical text using linear (affine) algebra to study the local intrinsic
geometry of spaces leading up to and including the geometry of the theory of
relativity.

Fekete,
Anton E. *Real Linear Algebra*. New York: Marcel Dekker, 1985.

Hannah,
John: ""A Geometric Approach to Determinants,"", *The
American Mathematical Monthly*, 103 (1996), 401-409.

Hay,
G. E. *Vector and Tensor Analysis*. New York: Dover, 1953.

"First published in
1953, this is a simple clear introduction to classical vector and tensor
analysis for students of engineering and mathematical physics."

Hestenes,
David and Sobczyk, Garret. *Clifford Algebra to Geometric Calculus: A Unified
Language for Mathematics and Physics*. Boston: D. Reidel Publishing Company,
1984.

"Matrix algebra has
been called "the arithmetic of higher mathematics" [...]. We think
the basis for a better arithmetic has long been available, but its versatility
has hardly been appreciated, and it has not yet been integrated into the
mainstream of mathematics. We refer to the system commonly called 'Clifford
Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford
himself."

Kuipers,
Jack B. *Quaternions and Rotation Sequences: A Primer with Applications to
Orbits, Aerospace, and Virtual Reality*. Princeton: Princeton University
Press, 1999.

"This book is intended
for all those mathematicians, engineers, and physicists who have to know, or
who want to know, more about the modern theory of quaternions. Primarily, as
the title page suggests, it is an exposition of the quaternion and its primary
application as a rotation operator."
Included are applications of spherical geometry.

Murtha,
James A. and Willard, Earl R. *Linear Algebra and Geometry*. New York:
Holt, Reinhart and Winston, Inc., 1966.

Includes affine and
projective geometry.

Postnikov,
M. *Lectures in Geometry: Semester II - Linear Algebra and Differential
Geometry*. Moscow: Mir, 1982.

Postnikov,
M. *Lectures in Geometry: Semester V - Lie Groups and Lie Algebras*.
Moscow: Mir Publishers, 1986.

"The theory of Lie
groups relies on Cartan's theorem on the equivalence of the category of simply
connected Lie groups to that of Lie algebras. This book presents the proof of
the Cartan theorem and the main results... The theory of Lie algebras has been
developed to an extent necessary for the Cartan theorem to be proved."

Solow,
Daniel. *How to read and do proofs, an introduction to mathematical thought
process*. New York: John wiley and Sons, Inc., 1982.

Taylor,
Walter F. *The Geometry of Computer Graphics*. Grove, CA: Wadsworth &
Brooks/Cole Advanced Books & Software, 1992.

"This book is a direct
presentation of elementary analytic and projective geometry, as modeled by
vectors and matrices and as applied to computer graphics."

Weinreich,
Gabriel. *Geometrical Vectors*. Chicago: The University of Chicago Press,
1998.

"Years of teaching
Mathematical Methods of Physics at the University of Michigan to seniors and
first-year graduate students convinced me that existing textbooks don't do an
adequate job in the area of vector analysis: all too often, their treatment is
a repetition of what students had already seen in earlier courses, with little
or no insight into the essentially geometrical structure of the subject."

LS. Learning/Students

Solow,
Daniel. *How to read and do proofs, an introduction to mathematical thought
process*. New York: John wiley and Sons, Inc., 1982.

Tall,
David (editors): *Advanced Mathematical Thinking*, .11: Boston: Kluwer
Academic Publishers, 1991.

ME. Mechanisms

Agricola, Georg. *De re metallica*. (Basil: E. König, 1657.) Translated from the first Latin ed. of 1556, with biographical introd., annotations, and appendices upon the development of mining methods, metallurgical processes, geology, mineralogy & mining law from the earliest times to the 16th century, by Herbert Clark Hoover and Lou Henry Hoover, New York, Dover Publications, 1950. Some excerpts can be found on various online sites.

I. I. Artobolevskii, I.I.. *Mechanisms for the Generation of Plane Curves*. New York: The Macmillan Company, 1964.

Connelly, R, Demiane, E. D., and Rote, G.. "Straightening Polygonal Arcs and Convexifying Polygonal Cycles." *Discrete & Computational Geometry* 2003; 30:205–239.

DeCamp, L. Sprague. *The Ancient Engineers*. New York: Ballantine Books, 1974.

Dyson, George B. *Darwin among the Machines: The Evolution of Global Intelligence*. Reading, MA: Perseus Books, 1997.

Ferguson,
Eugene S.: "Kinematics of Mechanisms from the Time of Watt", *United
States National Museum Bulletin*, 228Washington, D.C.: Smithsonian
Institute (1962), 185-230.

Ferguson,
Eugene S. *Engineering and the Mind's Eye*. Cambridge, MA: The MIT Press,
2001.

Finch,
James Kip (editors): *The Story of Engineering*, Garden City, NJ: Anchor Books, 1960.

Florman,
Samuel C. *The Existential Pleasures of Engineering*. New York: St,
Martin's Griffin, 1994.

Galle,
A. *Mathematische Instrumente*. Leipzig: B. G. Teubner, 1912.

Gille,
Bertrand. *Engineers of the Renaissance*. Cambridge, MA: The MIT Press,
1966.

Hinkle,
Rolland T. *Kinematics of Machines*. Englewood Cliffs, NJ: Prentice-Hall,
1960.

Hodges,
Henry. *Technology in the Ancient World*. New York: Barnes & Noble
Books, 1992.

Horsburgh,
E. M. (editors): *Modern Instruments and Methods of Calculation: A Handbook
of the Napier Tercentenary Exhibitions*,
London: G. Bell and Sons, 1914.

Huckert,
Jesse. *Analytical Kinematics of Plane Motion Mechanisms*. New York: The
Macmillan Company, 1958.

Hunt,
K.H. *Kinematic Geometry of Mechanisms*. Oxford: Clarendon Press,
1978.

Institution
of Mechanical Engineers. *Engineering Heritage: Highlights from the History
of Mechanical Engineering: Volume I*. London: Heinemann, 1963.

Institution
of Mechanical Engineers. *Engineering Heritage: Highlights from the History
of Mechanical Engineering, Volume Two*. London: Heinemann Educational Books,
1966.

KMODDL.
*Kinematic Models for Design Design Library*. Cornell University
Libraries, 2004. **online: **http://KMODDL.library.cornell.edu

Kempe,
A. B.: "On a General Method of Describing Plane Curves of the n-th Degree
by Linkages", * Proc. Lon. Math.
Soc*, VII (1876), 213-215.

Kempe,
A.B. *How to Draw a Straight Line*. London: Macmillan, 1877.

This small book contains a
discussion and description of numerous curve drawing devices including ones
that will draw straight lines.

Kirby,
R.S., Withington, S., Darling, A.B., and Kilgour, F.G. *Engineering in
History*. New York: McGraw-Hill Book Company, 1956.

McCarthy,
J. Michael. *Geometric Design of Linkages*. New York: Springer, 2000.

Moon,
Francis C.: "Franz Reuleaux: Contributions to 19th Century Kinematics and
the Theory of Machines", *Applied Mechanics Reviews*, 56 (2003),
1-25.

Ramelli,
Agostino. *The Various and Ingenious Machines of Agostino Ramelli: A Classic
Sixteenth-Century Illustrated Treatise on Technology*. New York: Dover
Publications, 1976.

Reuleaux,
Franz. *The Kinematics of Machinery*. London: Macmillan and Co., 1876. **online**:** http://historical.library.cornell.edu/cgi-bin/kmoddl/docviewer?did=029&seq=7**

Reynolds,
Terry S. (editors): *The Engineer in America: A Historical Anthology From
"Technology and Culture"*,
Chicago: The University of Chicago Press, 1991.

Shigley,
Joseph Edward. *Kinematics Analysis of Mechanisms*. New York: McGraw-Hill
Book Company, 1969.

Uicker,
John J., Jr., Pennock, Gordon R., and Shigley, Joseph E. *Theory of Machines
and Mechanisms*. New York: Oxford University Press, 2003.

*A History of Inventions: From Stone Axes to Silicon Chips*. New York: Checkmark Books, 2000.

Yates,
Robert. *Tools: A Mathematical Sketch and Model Book*. Louisiana State
University, 1941.

MI. Minimal Surfaces

Boys,
C. V. *Soap-Bubbles: Their Colours and the Forces Which Mold Them*. New
York: Dover, 1959.

Hoffman,
David: ""The computer aided discovery of new embedded minimal
surfaces,"", *Mathematcal Intelligencer*, (1987), 8-21.

Morgan,
Frank. *Geometric Measure Theory: A Beginner's Guide*. Boston: Academic
Press, 1988.

Morgan,
Frank. *"Compound soap bubbles, shortest networks, and minimal
surfaces,"AMS Video*. Providence, RI: AMS, 1992.

Morgan,
Frank. *The Math Chat Book*. MAA, 2000.

Charming little book
includes short version of Double Bubble Conjecture story. Also see http://www.maa.org/news/mathchat.html

Osserman,
Robert. *A Survey of Minimal Surfaces, 2nd edition*. New York: Dover,
1986.

Osserman,
Robert. *"Minimal Surfaces in R3," Global Differential Geometry*.
Washington,DC: M.A.A., 1989.

MP. Models and Polyhedra

Barnette,
David. *Map Colouring, Polyhedra, and the Four-Colour Problem, Dolciani
Mathematical Expositions*. Washington, DC: M.A.A., 1983.

Barr,
Stephen. *Experiments in Topology*. New York: Crowell, 1964.

Experimental topology that
goes beyond the Möbius Band.

Experimental
topology that goes beyond the Möbius Band.

Cundy,
M.H. and Rollett, A.P. *Mathematical Models*. Oxford: Clarendon,
1961.

Directions on how to make
and understand various geometric models.

Lyusternik,
L.A. *Convex Figures and Polyhedra*. Boston: Heath, 1966.

An detailed but elementary
study of convex figures.

Row,
T. Sundra. *Geometric Exercises in Paper Folding*. New York: Dover,
1966.

How to produce various
geometric constructions merely by folding a sheet of paper.

Senechal,
Marjorie, and Fleck, George (editors): *Shaping Space: A Polyhedral Approach,
Design Science Collection*, Boston:
Birkhauser, 1988.

This book is an accessible
"exploration of the world of polyhedra, beginning with [an introduction]
and concluding with an examination of the significance of polyhedral models in
contemporary science and a survey of some recent advances and unsolved problems
in mathematics."

Weinreich,
Gabriel. *Geometrical Vectors*. Chicago: The University of Chicago Press,
1998.

"Years of teaching
Mathematical Methods of Physics at the University of Michigan to seniors and
first-year graduate students convinced me that existing textbooks don't do an
adequate job in the area of vector analysis: all too often, their treatment is
a repetition of what students had already seen in earlier courses, with little
or no insight into the essentially geometrical structure of the subject."

Zawadowski,
Waclaw. *The Cube Made Interesting*. New York: Pergamon Press, 1964.

"This book arose from
popular scientific talks to teachers and school children." The discussion
is illustrated with 3-d pictures using special glasses.

MS. Mathematics and Social Issues

Cohen,
Patricia Cline. *A Calculating People: The Spread of Numeracy in Early
America*. Chicago: The University of Chicago Press, 1982.

Keitel,
Christine, Damerow, Peter, Bishop, Alan, and Gerdes, Paulus (editors): *Mathematics,
Education, and Society: A Fifth Day Special Programme at the 6th International
Congress on Mathematical Education, Budapest, 27 July - 3 August, 1988*,
Science and Technology Education Document Series.No. 35: Budapest: UNESCO,
1989.

Restivo,
Sal, Paul, Jean, Bendegem, Van, and Fischer, Roland (editors): *MathWorlds*, New York: State University of New York
Press, 1993.

Swetz,
Frank J. *Capitalism & Arithmetic: The New Math of the 15th Century*.
La Salle, IL: Open Court, 1987.

Vatter,
Terry. *Civic Mathematics, Fundamentals in the Context of Social Issues*.
Englewood, Colorado: Teacher Ideas Press, 1996.

NA. Geometry in Nature

Cook,
T.A. *The Curves of Life*. New York: Dover Publications, 1979.

Subtitle: Being an Account
of Spiral Formations and their Applications to Growth in Nature, to Science,
and to Art.

Doczi,
György. *The Power of Limits*. Boulder, CO: Shambhala, 1981.

Ghyka,
Matila. *The Geometry of Art and Life*. New York: Dover Publications,
1977.

Hildebrandt,
Stefan and Tromba, Anthony. *Mathematics and Optimal Form*. New York:
Scientific American Books, Inc., 1985.

"Combining striking
photographs with a compelling text, authors ... give us a thoughtful account of
the symmetry and regularity of nature's forms and patterns."

Kemp,
Martin. *Visualizations: The Nature Book of Art and Science*. Berkeley,
CA: The University of California Press, 2000.

Kohl,
Judith and Kohl, Herbert. *The View from the Oak: The Private Worlds of Other
Creatures*. New York: Sierra Club Books/Charles Scribner's Sons, 1977.

This delightful books
describes the various experiential worlds of different creatures and is a good
illustration of intrinsic ways of thinking. Included are differing dimensions
and scales of these worlds.

Mandelbrot,
Benoit B. *The Fractal Geometry of Nature*. New York: W.H. Freeman and
Company, 1983.

The book that started the
popularity of fractal geometry.

McMahon,
Thomas and Bonner, James. *On Size and Life*. New York: Scientific
American Library, 1983.

A geometric discussion of
the shapes and sizes of living things.

Neihardt,
John G. *Black Elk Speaks: Being the Life Story of a Holy Man of the Oglala
Sioux*. Lincoln, NE: University of Nebraska Press, 1961.

Contains descriptions of
geometric ideas in Oglala Sioux culture

Osserman,
Robert. *A Survey of Minimal Surfaces, 2nd edition*. New York: Dover,
1986.

Ravielli,
Anthony. *Adventure in Geometry*. New York: Viking Press, 1966.

A beautifully illustrated
children's book. "Whether we realize it or not, much of the beauty we
admire in the world around us is a result of nature's geometric skill. Every
living thing -- a tree, a flower, or an insect -- is a lesson in geometry at
its exquisite best."

Row,
T. Sundra. *Geometric Exercises in Paper Folding*. New York: Dover,
1966.

How to produce various
geometric constructions merely by folding a sheet of paper.

Schneider,
Michael S. *A Beginner's Guide to Constructing the Universe: The Mathematical
Archetypes of Nature, Art, and Science*. New York: HarperPerennial,
1994.

Thom,
Rene. *Structural Stabililty and Morphogenesis*. Redwood City, CA:
Addison-Wesley, 1989.

A geometric and analytic
treatment of "Catastrophe Theory."

Thompson,
D'Arcy. *On Growth and Form*. Cambridge: Cambridge University Press, 1961.

A classic on the geometry of
the natural world.

Tomilin,
Anatoly. *How People Discovered the Shape of the Earth*. Moscow: Raduga
Publishers, 1984.

A childrens book with nice
colored illustrations.

Zebrowski,
Ernest, Jr. *A History of the Circle: Mathematical Reasoning and the Physical
Universe*. New Brunswick, NJ: Rutgers University Press, 1999.

PA. Projective and Affine Geometry

Brannan,
David A., Esplen, Matthew F., and Gray, Jeremy J. *Geometry*. Cambridge:
Cambridge University Press, 1999.

Geometry textbook for the
Open University.

Coxeter,
H.S.M. *The Real Projective Plane*. New York: Cambridge University Press,
1955.

"This introduction to
projective geometry can be understood by anyone familiar with high-school
geometry and algebra. The restriction to real geometry of two dimensions makes
it possible for every theorem to be illustrated by a diagram."

Farin,
Gerald E. *NURBS: From Projective Geometry to Practical Use, Second Edition*.
Natick, MA: A. K. Peters, 1999.

NURBS is an industry
standard for curve and surface design based on projective geometry.

Krylov,
N., Lobandiyevsky, P., and Men, S. *Descriptive Geometry*. Moscow: MIR
Publishers, 1974.

"This book is a text
for students of civil engineering colleges and embraces a full course of
descriptive geometry. It gives detailed information on orthogonal projections,
axonometry, linear perspective and projections with elevations."

Prasolov,
V.V. and Tikhomirov, V.M. *Geometry*. Providence, RI: American
Mathematical Society, 2001.

Prenowitrz,
Walter. *A Contemporary Approach to Classical Geometry*. Published as a
supplement to the American Mathematical Monthly, Vol 68, No 1, January 1961,
1961.

Watson,
Ernest W. *Creative Perspective for Artists and Illustrators*. Mineola,
NY: Dover Publications, 1992.

Whicher,
Olive. *Projective Geometry: Creative Polarities in Space and Time*.
London: Rudolf Steiner Press, 1971.

Projective geometry is the
geometry of perception and prospective drawings.

PH. Philosophy of Mathematics

Abraham,
Ralph H. *Chaos. Gaia. Eros: A Chaos Pioneer Uncovers the Three Great Streams
of History*. New York: HarperSanFrancisco, A Division of HarperCollins
Publishers, 1994.

Changeux,
Jean -Pierre and Connes, Alain. *Conversations on Mind, Matter, and
Mathematics*. Princeton: Princeton University Press, 1995.

"Why order should exist
in the world at all--and why it should be comprehensible by human beings--is
the question that lies at the heart of these remarkable dialogues" between
a neurobiologist and a mathematician.

Derrida,
Jacques, and Allison, David B. (editors): *Edmund Husserl's Origin of
Geometry: An Introduction*, USA:
Nicolas Hays,Ltd., 1978.

"In this
commentary-interpretation of the famous appendix to Husserl's Crisis, Derrida
relates writing to such key concepts as differing, consciousness, presence, and
historicity."

Dewdney,
A.K. *A Mathematical Mystery Tour: Discovering the Truth and Beauty of the
Cosmos*. New York City: John Wiley & Sons, 1999.

"The mathematical
odyssey herein explores two key questions about mathematics and its
relationship to reality: Why is mathematics so amazingly successful in
describing the structure of physical reality? Is mathematics created, or is it
discovered?" Chapter 4 of this book is about mapping the spheres, and
whole book is written in a language accessible to general audience, not only
mathematicians.

Fitzgerald,
Janet A. *Alfred North Whitehead's Early Philosophy of Space and Time*.
Washington, D.C.: University Press of America, 1979.

Franz,
Marie-Louise von. *Number and Time: Reflections Leading toward a Unification
of Depth Psychology and Physics*. Evanston, IL: Northwestern University
Press, 1974.

Gray,
Jeremy. *Ideas of Space: Euclidean, Non-Euclidean and Relativistic*.
Oxford: Oxford University Press, 1989.

A mostly historical account
of Euclidean, non-Euclidean and relativistic geometry. "I shall discuss
Greek and modern geometry, in particular what came to be known as the problem
of parallels, that 'blot on geometry' as Saville called it in 1621."

Grunbaum,
Adolf. *Geometry and Chronometry in Philosophical Perspective*.
Minneapolis: University of Minnesota Press, 1968.

This is a philosophical
treatise on the empiracle(physical) status of spatial geometry.

Hofstadter,
Douglas R. *Gödel, Escher, Bach: An Eternal Golden Braid*. New York: Basic
Books, 1979.

A general audience book
which probes the meaning of mind.

Iamblichus.
*The Theology of Arithmetic: On the Mystical, Mathematical and Cosmological
Symbolism of the First Ten Numbers*. Grand Rapids: Phanes Press, 1988.

Kaplan,
Robert. *The Nothing That Is: A Natural History of Zero*. New York: Oxford
University Press, 2000.

"Look at zero and yoou
see nothing, but look through it and you see the world."

Kline,
Morris. *Mathematics: The Loss of Certainty*. New York: Oxford University
Press, 1980.

"This book treats the
fundamental changes that man has been forced to make in his understanding of
the nature and role of mathematics."

Koyré,
Alexandre. *From the Closed World to the Infinite Universe*. Baltimore:
Johns Hopkins University Press, 1976.

"During the sixteenth
and seventeenth centuries a radical change occurred in the patterns and
framework of European thought. The root and fruit of this revolution are modern
science and modern philosophy. Dr. Koyré interprets this revolution in terms of
the change that occurred in man's conception of his universe and of his own
place in it and demonstrates the primacy of this change in the development of
the modern world."

Kyburg,
Jr., Henry E. *Theory and Measurement*. Cambridge, UK: Cambridge
University Press, 1984.

"[The author] proposes
here an original, carefully worked out theory the foundations of measurement,
to show how quantities can be defined, why certain mathematical structures are
appropriate to them and what meaning attaches to the results generated. Crucial
to his approach is the notion of error -- it can not be eliminated entirely and
from its introduction and control, he argues, arises the very possibility of
measurement."

Lachterman,
David Rapport. *The Ethics of Geometry: A Genealogy of Modernity*. New
York: Routledge, 1989.

Lakatos,
I. *Proofs and Refutations*. Cambridge: Cambridge University Press,
1976.

A deep but accessible book
that uses an imaginary classroom dialogue in which the actual historical words
of mathematicians are used to explore the evolving nature of mathematical ideas
and to support the author's quasi empirical view of mathematics.

Lakatos,
Imre. *Mathematics, Science and Epistomology: Philosophical Papers, vol.2*.
Cambridge: Cambridge University Press, 1978.

Lakatos,
Imre. *The Methodology of Scientific Research Programmes: Philosophical
Papers, vol.1*. Cambridge: Cambridge University Press, 1978.

Posy,
Carl J. (editors): *Kant's Philosophy of Mathematics: Modern Essays*, Boston: Kluwer, 1992.

"The present volume
includes the classic papers from the 1960s and 1970s which sparked this
renaissance of interest, together with updated postscripts by their authors. It
includes the most important recent work on Kant's philosophy of
mathematics"

Reichenbach,
Hans. *The Philosophy of Space and Time*. New York: Dover Publications,
Inc., 1958.

Rothstein,
Edward. *Emblems of Mind: The Inner Life of Music and Mathematics*. New
York: Times Books, 1995.

Rucker,
Rudy. *Infinity and the Mind: The Science and Philosophy of the Infinite*.
Boston: Birkhauser, 1982.

"This book discusses
every kind of infinity: potential and actual, mathematical and physical,
theological and mundane. Talking about infinity leads to many fascinating
paradoxes. By closely examining these paradoxes we learn a great deal about the
human mind, its powers, and its limitations."

Russell,
Bertrand. *An Essay on the Foundations of Geometry*. New York: Dover
Publications, Inc., 1956.

"The problem Russell
analyzes and solves, at least to his satisfaction in 1897, is: What geometrical
knowledge must be the logical starting point for a sceince of space and must
also be logically necessary to the experience of any form of externality?"

Sacks,
Oliver. *The Man Who Mistook His Wife for a Hat: and Other Clinical Tales*.
New York: Harper & Row, 1987.

Shapiro,
Stewart. *Thinking About Mathematics: The Philosophy of Mathematics*.
Oxford: Oxford University Press, 2000.

Sklar,
Lawrence. *Space, Time, And Spacetime*. Berkley: University of California
Press, 1977.

"The major aim of this
book is to cast as much doubt as possible on the view that science and
philosophy are independent pursuits that can be carried out in total ignorance
of each other."

Stein,
Charles (editors): *Being = Space X Action*, IO.41: Berkeley, CA: North
Atlantic Books, 1988.

"Searches for Freedom
of Mind through Mathematics, Art, and Mysticism."

Tragesser,
Robert S. *Husserl and Realism In Logic and Mathematics*. Cambridge:
Cambridge University Press, 1984.

Tymoczko,
Thomas. *New Directions in the Philosophy of Mathematics*. Boston:
Birkhauser, 1986.

An updated (to 1986)
collection of readings.

Uspensky,
V.A. *Gödel's Incompleteness Theorem*. Moscow: Mir Publishers, 1987.

Webb,
Judson Chambers. *Mechanism, Mentalism, and Metamathematics: An Essay on
Finitism*. Dordrecht: D. Reidel Publishing Company, 1980.

Wertheim,
Margaret. *The Pearly Gates of Cyberspace: A History of Space from Dante to
the Internet*. New York: W.W. Norton & Company, 1999.

"Can cyberspace be a
new realm for the soul? In this povocative book Margaret Wertheim traces the
evolution of our concept of space from the Middle Ages through the rise of
modern science and on to cyberspace. Linking the science of space to wider
cultrual history, Wertheim challenges the current spiritualizing of cyberspace
and suggests that it cannot sustain religious dreams."

Wittgenstein,
Ludwig. *Remarks on the Foundations of Mathematics*. Cambridge, MA: The
MIT Press, 1983.

Zebrowski,
Ernest, Jr. *A History of the Circle: Mathematical Reasoning and the Physical
Universe*. New Brunswick, NJ: Rutgers University Press, 1999.

RN. Real Numbersal, Ebbinghaus et. *Numbers*. New York:
Springer-Verlag, 1991.

A lively story about the
concept of number.

Goldblatt,
Robert. *Lectures on the Hyperreals*. New York: Springer, 1998.

Laugwitz,
Detlef: ""Infinitely Small Quantities in Cauchy's
Textbooks,"", *Historia Mathematica*, 14 (1987), 258-274.

Moore,
Ramon. *Methods and Applications of Interval Analysis*. Philadelphia: Society
of Industrial and Applied Mathematics, 1979.

Interval analysis "an
approach to computing that treats an interval as a new kind of number."

Russell,
Bertrand. *An Essay on the Foundations of Geometry*. New York: Dover
Publications, Inc., 1956.

"The problem Russell
analyzes and solves, at least to his satisfaction in 1897, is: What geometrical
knowledge must be the logical starting point for a sceince of space and must
also be logically necessary to the experience of any form of externality?"

Simpson:
""The Infidel Is Innocent,"", *The Mathematical
Intelligencer*, 12 (1990), 42-51.

An accessible expositon of
the nonstandard reals.

Turner,
Peter R.: ""Will the 'Real' Real Arithmetic Please Stand
Up?"", *Notices of the A.M.S.*, 38 (1991), 298-304.

An article about various
finite representations of real numbers used in computing.

SA. Sacred and Spiritual Geometry

al,
Ebbinghaus et. *Numbers*. New York: Springer-Verlag, 1991.

A lively story about the
concept of number.

Howell,
Alice O. *The Web in the Sea: Jung, Sophia, and the Geometry of the Soul*.
Wheaton: Quest Books, 1993.

Iamblichus.
*The Theology of Arithmetic: On the Mystical, Mathematical and Cosmological
Symbolism of the First Ten Numbers*. Grand Rapids: Phanes Press, 1988.

Koyré,
Alexandre. *From the Closed World to the Infinite Universe*. Baltimore:
Johns Hopkins University Press, 1976.

"During the sixteenth
and seventeenth centuries a radical change occurred in the patterns and
framework of European thought. The root and fruit of this revolution are modern
science and modern philosophy. Dr. Koyré interprets this revolution in terms of
the change that occurred in man's conception of his universe and of his own
place in it and demonstrates the primacy of this change in the development of
the modern world."

Lachterman,
David Rapport. *The Ethics of Geometry: A Genealogy of Modernity*. New
York: Routledge, 1989.

Lawlor,
Robert. *Sacred Geometry: Philosophy and practice*. New York: Crossroad,
1982.

"This is an introduction
to the geometry which, as the ancients taught and modern science confirms,
underlies the structure of the universe."

Lundy,
Miranda. *Sacred Geometry*. New York: Walker & Company, 1998.

Mann,
A.T. *The Round Art: The Astrology of Time and Space*. New York: Galley
Press, 1979.

Mohen,
Jean -Pierre. *Standing Stones: Stonehenge, Carnac and the World of Megaliths*.
London: Thames & Hudson, 1999.

"... this book
considers the special significance -- religious and cultural, architectural and
scientific -- of these enigmatic Neolithic stone structures ..."

Pennick,
Nigel. *Sacred Geometry: Symbolism and Purpose in Religious Structures*.
San Francisco: Harper & Row, 1982.

Perkins,
James S. *A geometry of Space-Consciousness*. Adyar, Madras 600020, India:
Theosophical Publishing House, 1978.

"There are two
geometries: the geometry of form in physical space, and the geometry of motion
in man's consciousness."

Plummer,
L. Gordon. *The Mathematics of the Cosmic Mind*. Wheaton, IL: The
Theosophical Publishing House, 1970.

"To study the
Pythagorean Solids as embodying mathematically the keys to the mysteries about
Man and the Universe."

Plummer,
L. Gordon. *By The Holy Tetraktys!: Symbol and Reality in Man and Universe*.
Point Loma, CA: Point Loma Publications, 1982.

Vandenbroeck,
André. *Philosophical Geometry*. Rochester, VT: Inner Traditions
International, Ltd., 1987.

"Philosophical Geometry
covers the activity of establishing a necessary conduct for mind through a set
of signs denoting a necessary conduct of facts."

Wertheim,
Margaret. *The Pearly Gates of Cyberspace: A History of Space from Dante to
the Internet*. New York: W.W. Norton & Company, 1999.

"Can cyberspace be a
new realm for the soul? In this povocative book Margaret Wertheim traces the
evolution of our concept of space from the Middle Ages through the rise of
modern science and on to cyberspace. Linking the science of space to wider
cultrual history, Wertheim challenges the current spiritualizing of cyberspace
and suggests that it cannot sustain religious dreams."

SG. Symmetry and Groups

*Vision
Geometry*, Contemporary
Mathematics.119: Washington DC: American Mmathematical Society, 1989.

"Computer vision is
concerned with obtaining descriptive information about a scene by computer
analysis of images of the scene."

Field,
Mike and Golubitsky, Martin. *Symmetry in Chaos: A Search for Pattern in
Mathematics, Art, Aand Nature*. New York: Oxford University Press,
1992.

Gardner,
Martin. *Penrose Tiles to Trapdoor Ciphers*. W.H. Freeman & Co,
1989.

Giacovazzo,
C. (editors): *Fundamentals of Crystallography*, New York: Oxford University Press, 1985.

Grünbaum,
Branko and Shepard, G.C. *Tilings and Patterns*. New York: W.H. Freeman,
1987.

A 700 page book detailing
what is know about plane tilings and patterns.

Hargittai,
István and Hargittai, Magdolna. *Symmetry: A Unifying Concept*. Bolinas,
CA: Shelter Publications, 1994.

"The single, most important
purpose of this book is to help you notice the world around you, to train your
eye and mind to see new patterns and make new connections."

Horne,
Clare E. *Geometric symmetry in patterns and tilings*. Boca Raton, FL: CRC
Press, 2000.

Jones,
Owen. *The Grammar of Ornament*. New York: Dorling Kindersley, 2001.

"A unique collection of
more than 2,350 classic patterns"

Lyndon,
Roger C. *Groups and Geometry*. New York: Cambridge University Press,
1985.

"This book is intended
as an introduction, demanding a minimum of background, to some of the central
ideas in the theory of groups and in geometry. It grew out of a course, for
advanced undergraduates and beginning graduate students"

Macgillavry,
Caorline H. *Symmetry Aspects of M.C. Escher's Periodic Drawings*.
Utrecht: Published for the International Union of Crystallography by A.
Oosthoek's Uitgeversmaatschappij NV, 1965.

Martin,
George E. *Transformation Geometry: An Introduction to Symmetry*. New
York: Springer-Verlag, 1982.

"Our study of the
automorphisms of the plane and of space is based on only the most elementary
high-school geometry. In particular, group theory is not a prerequisite here.
On the contrary, this modern approach to Euclidean geometry gives the concrete
examples that are necessary to appreciate an introduction to group
theory."

Montesinos,
José María. *Classical Tessellations and Three-Manifolds*. New York:
Springer-Verlag, 1985.

"This book explores a
relationship between classical tessellations and three-manifolds."

Radin,
Charles. *Miles of Tiles*. Providence, RI: American Mathematical Society,
1999.

"In this book, we try
to display the value (and joy!) of starting from a mathematically amorphous
problem and combining ideas from diverse sources to produce new and significant
mathematics -- mathematics unforeseen from the motivating problem ..." The
common thread throughout this book is aperiodic tilings.

Robertson,
Stewart A. *Polytopes and Symmetry*. New York: Cambridge University Press,
1985.

"These notes are intended
to give a fairly systematic exposition of an approach to the symmetry
classification of convex polytopes that casts some fresh light on classical
ideas and generates a number of new theorems."

Senechal,
M. *Quasicrystals and Geometry, , 1995*. Cambridge, UK: Cambridge
University Press, 1995.

Weyl,
Hermann. *Symmetry*. Princeton, NJ: Princeton University Press, 1952.

A readable discussion of all
mathematical aspects of symmetry especially its relation to art and nature -
nice pictures. Weyl is a leading mathematician of this century.

Yaglom,
I.M. *Geometric Transformations III*. New York: Random House, Inc.,
1973.

Yale,
Paul B. *Geometry and Symmetry*. New York: Dover, 1988.

"This book is an
introduction to the geometry of Euclidean, affine and projective spaces with
special emphasis on the important groups of symmetries of these spaces."

SP. Spherical Geometry

Bonnet,
Pierre Ossian. *Astronomie sphérique; notes sur le cours professé pendant
l'année 1887*. The Cornell Library Historical Mathematics Monographs,
1887. **online: http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=03500002&seq=9**

Coxeter,
H.S.M. *The Real Projective Plane*. New York: Cambridge University Press,
1955.

"This introduction to
projective geometry can be understood by anyone familiar with high-school
geometry and algebra. The restriction to real geometry of two dimensions makes
it possible for every theorem to be illustrated by a diagram."

Davies,
Charles. *Elements of Descriptive Geometry, with their application to
spherical trigonometry, spherical projections, and warped surfaces*. The
Cornell Library Historical Mathematics Monographs, 1859. **online: http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=03190002&seq=3**

Davies,
Charles. *Elements of Geometry and Trigonometry from the works of A. M.
Legendre: adapted to the course of mathematical instruction in the United
States*. The Cornell Library Historical Mathematics Monographs, 1890. **online: http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=04850002&seq=5&frames=0&view=50**

Farin,
Gerald E. *NURBS: From Projective Geometry to Practical Use, Second Edition*.
Natick, MA: A. K. Peters, 1999.

NURBS is an industry
standard for curve and surface design based on projective geometry.

Hartshorne,
Robin: "Non-Euclidean III.36", *American Mathematical Monthly*,
110 (2003), 495-502.

Power of a point on sphere
and hyperbolic plane

Hearn,
George Whitehead. *Researches on curves of the second order*. London: G.
Bell, 1846.

Subtitle: also on cones and spherical conics treated
analytically, in which the tangencies of Apollonius are investigated, and
general geometrical constructions deduced from analysis; also several of the
geometrical conclusions of M. Chasles are analytically resolved, together with
many properties entirely original.
Electronic Access: http://resolver.library.cornell.edu/math/1849296

Henderson,
David W. *Experiencing Geometry on Plane and Sphere*. Upper Saddle River,
NJ: Prentice Hall, 1996.

"This book will lead
the reader on an exploration of the notion of straightness and the closely
related notion of parallel on the plane and on the sphere."

Lénárt,
István. *Non-Euclidean Adventures on the Lénárt Sphere: Activities comparing
planar and spherical geometry*. Berkley: Key Curriculum Press, 1995.

Singer,
David A. *Geometry: Plane and Fancy*. New York: Springer, 1998.

"This book is about ...
the idea of curvature and how it affects the assumptions about and principles
of geometry."

Tan,
A.: "A Bird's Eye View of Spherical Triangles", *Mathematical
Spectrum*, 32:2 (1999-2000), 25-28.

Taylor,
Charles. *An introduction to the ancient and modern geometry of conics*.
Cambridge [Eng.]: Deighton, Bell and co, 1881.

Subtitle: being a
geometrical treatise on the conic sections with a collection of problems and
historical notes and prolegomena. Electronic Access: http://resolver.library.cornell.edu/math/1849306

Todhunter,
Isaac. *Spherical Trigonometry: For the Use of Colleges and Schools*.
London: Macmillan, 1886. **online: http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=00640001&seq=5**

All you want to know, and more, about trigonometry on the sphere.
Well written with nice discussions of surveying.

Yale,
Paul B. *Geometry and Symmetry*. New York: Dover, 1988.

"This book is an
introduction to the geometry of Euclidean, affine and projective spaces with
special emphasis on the important groups of symmetries of these spaces."

TG. Teaching Geometry

Case,
Bette Anne (editors): *You're the Professor, What Next?, Ideas and Resources
For Preparing College Teachers*,
Washington DC.: The Mathematical Association of America, 1994.

Malkevitch,
Joseph and Proceedings of a COMAP conference "of a small group of
geometers to study what could be done to revitalize geometry in our colleges,
and what effects this might have on the teaching of geometry in general.".
*Geometry's Future, second edition*. USA: COMAP, 1991.

Mammana,
Carmelo, and Villiani, Vinicio (editors): *Perspectives on the Teaching of
Geometry for the 21st Century: An ICMI Study*, New ICMI Study Series
Dordrecht: Kluwer, 1998.

Todhunter,
Isaac. *Spherical Trigonometry: For the Use of Colleges and Schools*.
London: Macmillan, 1886. **online: http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=00640001&seq=5**

All you want to know, and more, about trigonometry on the sphere.
Well written with nice discussions of surveying.

Zimmermann,
Walter and Cunningham, Steve. *Visualization in Teaching and Learning
Mathematics*. Washinton, DC: Mathematical Association of America, 1991.

"A project sponsored by
the Committee on Computers in Mathematics Education of M.A.A."

TM. Teaching MathematicsKrantz, Steven G. *How to Teach Mathematics: A
Personal Perspective*. Providence, RI: American Mathematical Society,
1993.

Smith,
Seaton E., Jr., and Backman, Carl A. (editors): *Games and Puzzles for
Elementary and Middle School Mathematics: Readings from the Arithmetic Teacher*, Reston, VA: National Council of Teachers of
Mathematics, 1975.

Stanley
and Usiskin. *Mathematics for High School Teachers, An Advanced Perspective*.
Pre-Print,

Stueben,
Michael and Sandford, Diane. *Twenty Years Before the Blackboard: The Lessons
and Humor of a Mathematics Teachers*. Washington, DC: The Mathematical
Association of America, 1998.

Sciences,
The ConferenceBoardoftheMathematical. *The Mathematical Education of Teachers*.
Providence, RI: American Mathematical Society, 2001.

Zimmermann,
Walter and Cunningham, Steve. *Visualization in Teaching and Learning
Mathematics*. Washinton, DC: Mathematical Association of America, 1991.

"A project sponsored by
the Committee on Computers in Mathematics Education of M.A.A."

TP. Topology

Barr,
Stephen. *Experiments in Topology*. New York: Crowell, 1964.

Experimental topology that
goes beyond the Möbius Band.

Experimental
topology that goes beyond the Möbius Band.

Farmer,
David W. and Stanford, Theodore B. *Knots and Surfaces, A Guide to Disovering
Mathematics*. Washington DC: American Mathematical Society, 1996.

Francis,
G.K. *A Topological Picturebook*. New York: Springer Verlag, 1987.

Francis presents elaborate
and illustrative drawings of surfaces and provides guidelines for those who
wish to produce such drawings.

Francis,
G.K., and Weeks, Jeffrey R.: "Conway's ZIP Proof", *American
Mathematical Monthly*, 106 (1999), 393-399.

A new proof of the
classification of (triangulated) surfaces (2-manifolds).

Hurewics,
W. and Wallman, H. *Dimension Theory*. Princeton: Princeton University
Press, 1941.

Contains a proof of the
Invariance of Domain in the context of the theory of the dimension of
topological spaces.

Newman,
M.H.A. *Elements of the Topology of Plane Sets of Points*. Cambridge:
Cambridge University Press, 1964.

Contains a proof of the
Invariance of Domain that is the most geometric.

Prasolov,
V.V. *Intuituve Topology*. Washington DC.: American Mathematical Society,
1995.

Singer,
I.M. and Thorpe, John A. *Lecture Notes on Elementary Topology and Geometry*.
Glenview: Scott, Foresman and Company, 1967.

"What the student has
learned in algebra and advanced calculus are used to prove some fairly deep
results relating geometry, topology, and group theory."

Sossinsky,
Alexei. *Knots: Mathematics with a Twist*. Cambridge, MA: Harvard
University Press, 2002.

Spanier.
*Algebraic Topology*. New York: McGraw Hill Book Company, 1966.

Contains a proof of the
Invariance of Domain based on algebraic topology.

TX. Geometry Texts

Brannan,
David A., Esplen, Matthew F., and Gray, Jeremy J. *Geometry*. Cambridge:
Cambridge University Press, 1999.

Geometry textbook for the
Open University.

Coxeter,
H.S.M. *Non-Euclidean Geometry*. Toronto: University of Toronto Press,
1965.

Davies,
Charles. *Elements of Geometry and Trigonometry from the works of A. M.
Legendre: adapted to the course of mathematical instruction in the United
States*. The Cornell Library Historical Mathematics Monographs, 1890. **online: http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=04850002&seq=5&frames=0&view=50**

Eves,
Howard. *A Survey of Geometry*. Boston: Allyn & Bacon, 1963.

A textbook that contains an
extensive coverage of the dissection theory of polygons.

Greenberg,
Marvin J. *Euclidean and Non-Euclidean Geometries: Development and History*.
New York: Freeman, 1980.

This is a very readable
textbook that includes some philosophical discussions.

Hansen,
Vagn Lundsgaard. *Shadows of the circle: Conic Sections, Optimal Figures and
Non-Euclidean Geometry*. Singapore: World Scientific, 1998.

"It is my hope that
these topics will be an inspiration in connection with teaching of geometry at
various levels including upper secondary school and college education."

Hartshorne,
Robin. *Companion to Euclid: A course of geometry, based on Euclid's Elements
and its modern descendants*. Providence, RI: American Mathematical Society,
1997.

"The course begins ...
with a critical of Euclid's Elements... Then ... we study Hilbert's axiom
system to bring the subject up to a modern standard of rigor... Then, depending
on the taste of the instructor, one can follow a more geometric path by going
directly to non-Euclidean [hyperbolic] geometry ..., or a more algebraic one,
exploring the relation between geometric constructions and field extensions
..."

Hartshorne,
Robin. *Geometry: Euclid and Beyond*. New York: Springer, 2000.

Henderson,
David W. *Experiencing Geometry on Plane and Sphere*. Upper Saddle River,
NJ: Prentice Hall, 1996.

"This book will lead
the reader on an exploration of the notion of straightness and the closely
related notion of parallel on the plane and on the sphere."

Henderson,
David W. and Taimina, with Daina. *Experiencing Geometry: in Euclidean,
Spherical, and Hyperbolic Spaces*. Upper Saddle River, NJ: Prentice Hall,
2000.

revised and expanded second
edition of Experiencing Geometry

Henle,
Michael. *Modern Geometries: The Analytic Approach*. Upper Saddle River:
Prentice-Hall, 1997.

Jacobs,
Harold R. *Geometry*. San Fransisco: W.H. Freeman and Co., 1974.

A high-school-level text
based on guided discovery.

Jennings,
George. *Modern Geometry with Applications*. Springer-Verlag, 1994.

Katz,
Victor (editors): *Using History to Teach Mathematics: An International
Perspective*, MAA Notes.#51: Washington, D.C.: Mathematical Association of
America, 2000.

Kay,
David C. *College Geometry*. New York: Holt, Rinehart and Winston,
1969.

A unified treatment of
axiomatic spherical and hyperbolic geometries

Kay,
David C. *College Geometry: A Discovery Approach*. New York: HarperCollins
College Publishers, 1994.

"This book was written
for an introductory, college level course in geometry for mathematics majors or
students in mathematics education seeking teachers certification in secondary
school mathematics. The latter purpose is fully recognized throughout the text,
with the development traditional lines, and numerous problems and examples
coming from current secondary school textbooks."

King,
James. *Geometry Through the Circle with The Geometer's Sketchpad*. Key
Curriculum Press, 1994.

Martin,
George E. *Geometric Constructions*. New York: Springer, 1998.

A geometry textbook based on
ruler and compass constructions.

Meserve,
Bruce E. *Fundamental Concepts of Geometry*. New York: Dover, 1983.

"The primary purpose of
this book is to help the reader (i) to discover how Euclidean plane geometry is
related to, and often a special case of, many other geometries, (ii) to obtain
a practical understanding of "proof," (iii) to obtain the concept of
geometry as a logical system based upon postulates and undefined elements, and
(iv) to appreciate the historical evolution of our geometrical concepts and the
relation of Euclidean geometry to the space in which we live."

Meyer,
Walter. *Geometry and Its Applications*. San Diego: Academic Press,
1999.

"... a solid
introduction to axiomatic Euclidean geometry, some non-Euclidean geometry, and
a substantial amount of transformation geometry. ... We pay significant
attention to applications, we provide optional dynamic geometry courseware for
use with The Geometer's Sketchpad ..."

Millman,
Richard S. and Parker, George D. *Geometry: A Metric Approach with Models*.
New York: Springer-Verlag, 1981.

"This book is intended
as a first rigorous course in geometry. As the title indicates, we have adopted
Birkoff's metric approach (i.e., through use of real numbers) rather than
Hilbert's synthetic approach to the subject."

Moise,
Edwin E. *Elementary Geometry from an Advanced Standpoint*. Reading, MA:
Addison-Wesley Publishing, 1963.

Noronha,
M. Helena. *Euclidean and Non-Euclidean Geometries*. Upper Saddle River,
NJ: Prentice Hall, 2002.

Pedoe,
Dan. *Geometry: A Comprehensive Course*. New York: Dover Publications,
Inc., 1970.

"The main purpose of
the course was to increase geometrical, and therefore mathematical
understanding, and to help students to enjoy geometry. This is also the purpose
of my book."

Pogorelov,
A. *Geometry*. Moscow: MIR publishers, 1987.

"The book is... aimed
at professional training of the school or university teacher-to-be. The first
part, analytic geometry, is easy to assimilate, and actually reduced to
acquiring skills in applying algebraic methods to elementary geometry. The
second part, differential geometry, contains the basics of the theory of curves
and surfaces. The third part, foundations of geometry, is original. The fourth
part is devoted to certain topics of elementary geometry."

Posamentier,
Alfred S. *Advanced Euclidean Geometry: Excursions for Secondary Teachers and
Students*. Emeryville, CA: Key College Publishing, 2002.

Prasolov,
V.V. *Intuituve Topology*. Washington DC.: American Mathematical Society,
1995.

Prasolov,
V.V. and Tikhomirov, V.M. *Geometry*. Providence, RI: American
Mathematical Society, 2001.

Prenowitz,
Walter and Jordan, Meyer. *Basic Concepts of Geometry*. New York:
Blaisdell Publishing, 1965.

Serra,
Michael. *Discovering Geometry: An Inductive Approach*. Berkeley, CA: Key
Curriculum Press, 1989.

Shurman,
Jerry. *Geometry of the Quintic*. New York: John Wiley & Sons, Inc.,
1997.

An advanced undergraduate
text which uses the icosahedron to solve quintic equations. Along the way, he
explores the Riemann sphere, group representations, and invariant functions.

Sibley,
Thomas Q. *The Geometric Viewpoint: A Survey of Geometries*. Reading, MA:
Addison Wesley, 1998.

"Geometry combines
visual delights and powerful abstractions, concrete intuitions and general
theories, historical perspective and contemporary applications, and surprising
insights and satisfying certainty. In this textbook, I try to weave together
these facets of geometry. I also want to convey the multiple connections that
different topics in geometry have with each other and that geometry has with
other areas of mathematics."

Singer,
David A. *Geometry: Plane and Fancy*. New York: Springer, 1998.

"This book is about ...
the idea of curvature and how it affects the assumptions about and principles
of geometry."

Smart,
James R. *Modern Geometries, Fifth Edition*. Pacific Grove: Brooks/Cole
Publishing Company, 1998.

"This fifth edition of
Modern Geometries is designed for one or more courses in modern geometry at the
junior-senior level in universities. The central text of the theme is the
presentation of many different geometries, rather than any single geometry. The
use of both groups of transformations and sets of axioms to classify geometries
continues to be of central importance."

Stahl,
Saul. *Geometry From Euclud to Knots*. Upper Saddle River, New Jersey:
Pearson Education, Inc., 2003.

Stanley
and Usiskin. *Mathematics for High School Teachers, An Advanced Perspective*.
Pre-Print,

Wallace,
Edward C. and West, Stephen F. *Roads to Geometry*. Upper Saddle River,
NJ: Prentice Hall, Inc., 1998.

"The goal of this book
is to provide a geometric experience which clarifies, extends, and unifies
concepts which are generally discussed in traditional high school geometry
courses and to present additional topics which assist in gaining a better
understanding of elementary geometry."

UN. The Physical Universe

Ferguson,
Kitty. *Measuring the Universe*. New York: Walker & Co, 1999.

A history of the attempts to
measure the universe.

Ferris,
Timothy. *The Whole Shebang: A State-of-the-Universe(s) Report*. New York
City: Simon & Schuster, 1997.

"This book aims to
summarize the picture of the universe that science has adduced ..., and to
forecast an exciting if unsettling new picture that may emerge in the near
future."

Guth,
Alan H. *The Inflationary Universe: The Quest for a New Theory of Cosmic
Origins*. Reading, MA: Perseus Books, 1997.

"The inflationary
universe is a theory of the 'bang' of the big bang."

Osserman,
Robert. *Poetry of the Universe: A Mathematical Exploration of the Cosmos*.
New York: Anchor Books, 1995.

"What is the shape of
the universe, and what do we mean by the curvature of space? One aim of this
book is to make absolutely clear and understandable both the meanings of those
questions and the answers to them. Little or no mathematical background is
needed..."

Penrose,
Roger: The Geometry of the Universe. *Mathematics Today*. Steen L, (eds).
New York, Springer-Verlag, 1978,

An expository discussion of
the geometry of the universe.

An
expository discussion of the geometry of the universe.

Penrose,
Roger, Shimony, Abner, Cartwright, Nancy, and Hawking, Stephen. *The Large,
The Small and the Human Mind*. Cambridge, UK: Cambridge University Press,
1997.

"This volume provides
an accessible, illuminating and stimiulating introdution to Roger Penrose's
vision of theoretical physics for the 21st Century."

Proctor,
Richard A. *A Treatise on The Cycloid and all forms of Cycloidal Curves and
on the use of such curves in dealing with the motions of planets, comets,
&c. and of matter projected from the sun*. The Cornell Library
Historical Mathematics Monographs, 1878.
**online: http://historical.library.cornell.edu/cgi-bin/cul.math/docviewer?did=02260001&view=50&frames=0&seq=9**

Rees,
Martin. *Before the Beginning: Our Universe and Others*. Reading, MA:
Perseus Books, 1997.

"This book presents an
individual view on cosmology -- how we perceive our universe, what the current
debates are about, and the scope and limits of our future knowledge."

Stahl,
Saul. *Geometry From Euclud to Knots*. Upper Saddle River, New Jersey:
Pearson Education, Inc., 2003.

Toben,
Bob. *Space-Time and Beyond: Toward an Explanation of the Unexplainable*.
New York: E.P. Dutton, 1975.

Wertheim,
Margaret. *The Pearly Gates of Cyberspace: A History of Space from Dante to
the Internet*. New York: W.W. Norton & Company, 1999.

"Can cyberspace be a
new realm for the soul? In this provocative book Margaret Wertheim traces the
evolution of our concept of space from the Middle Ages through the rise of
modern science and on to cyberspace. Linking the science of space to wider
cultrual history, Wertheim challenges the current spiritualizing of cyberspace
and suggests that it cannot sustain religious dreams."

Zebrowski,
Ernest, Jr. *A History of the Circle: Mathematical Reasoning and the Physical
Universe*. New Brunswick, NJ: Rutgers University Press, 1999.

**The University of Michigan historic books
collection****
has following books on-line, which can be useful in geometry class:**

**Casey, John***A treatise on spherical trigonometry, and its application to geodesy and astronomy, with numerous examples*.**Chauvenet, William***A treatise on plane and spherical geometry*.**Church, Albert E. (Albert Ensign)***Elements of descriptive geometry; with its applications to spherical projections, shades and shadows, perspective and isometric projections*.**Coddington, Emily,***A brief account of the historical development of pseudospherical surfaces from 1827 to 1887*...**Craig, Thomas,***A treatise on projections*.**Field, Peter,***Projective geometry, with applications to engineering*.**Granville, William Anthony***Plane and spherical trigonometry, and Four-place tables of logarithms*.**Hammer, E. (Ernst)***Lehrbuch der ebenen und sphärischen trigonometrie. Zum gebrauch bei selbstunterricht und in schulen, besonders als vorbereitung auf geodäsie und sphärische astronomie, bearb.***Klein, Felix***Famous problems of elementary geometry: the duplication of the cube; the trisection of an angle; the quadrature of the circle*; an authorized translation of F. Klein's Vorträge über ausgewählte fragen der elementargeometrie, ausgearbeitet von F. Tägert, by Wooster Woodruff Beman and David Eugene Smith ...**Lobachevskii, N. I.***Geometrical researches on the theory of parallels*,... tr. from the original by George Bruce Halsted ... .**Lyman, Elmer A.***Plane and spherical trigonometry*,**National Committee of fifteen on geometry syllabus.: Final report of the Naitonal committee of fifteen on geometry syllabus. Authorized jointly by the National education association and the American federation of teachers of the mathematical and natural sciences.****Newman, Francis William***The difficulties of elementary geometry, especially those which concern the straight line, the plane, and the theory of parallels*.**Passano, Leonard M.***Plane and spherical trigonom*etry.**Taylor, T. U.***The elements of plane and spherical trigonometry*.**Wentworth, G. A.***Plane and spherical trigonometry, surveying and tables*.