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.