Supplements to some chapters of *Experiencing Geometry*

Chapter 0 *Historical Strands of Geometry*

Experiencing Meaning in Geometry - by David W. Henderson & Daina Taimina

How to Use History to Clarify Common Confusions in Geometry by David W. Henderson & Daina Taimina

Helpful websites:

- History of Mathematics
- Geometry of Ancient Sites
- Symmetry and Pattern the Art of Oriental rugs
- Geometry in Hawaiian History and Culture

Chapter 1 *What is Straight?*

Helpful websites:

- JAVA-based microscope utility for zooming in on vector fields.

Chapter 2 *Straightness on Spheres*

Helpful websites:

**Chapter 3 What is an Angle**

Chapter 4 *Straightness on Cylinders and Cones*

Helpful websites:

**Chapter 5 Straightness on Hyperbolic Planes**

Crocheted Hyperbolic Plane by David W. Henderson & Daina Taimina

Annuli for hyperbolic paper model this is a template to print out for making hyperbolic paper model from anulli

Template for hyperbolic soccer ball this is a template by Keith Henderson to print out for making paper hyperbolic soccer ball. Use three sheets and overlap the hexagons that have the three dots. Also, don't cut the dotted segments, to save time, but cut only solid lines.

Helpful websites:

- Software for hyperbolic geometry
**-**NonEuclid offers straightedge and compass constructions in hyperbolic geometry.

Chapter 6 *Triangles and Congruencies*

Chapter 7 *Area and Holonomy*

Chapter 8 *Parallel Transport*

Chapter 9 *SSS, ASS, SAA, and AAA*

Chapter 10 *Parallel Postulates*

Helpful websites:

Chapter 11 *Isometries and Patterns*

Helpful websites:

Chapter 12 *Dissection Theory*

Helpful websites:

Chapter 13 *Square Roots, Pythagoras, and Similar Triangles*

Square Roots in the Sulbasutra by David W. Henderson

Helpful websites:

Chapter 14 *Projections of a Sphere onto a Plane*

Helpful websites:

- Modeling the Brain - Projecting the surface of the human brain onto a sphere and/or hyperbolic plane with discussions of preserving angles, versus preserving distances, and/or versus preserving areas.
- Geometry of the Earth and Universe
- The Use of Anglyph Glasses in Viewing 3-D Models
- The Visualization of Mathematics

Chapter 15 *Circles*

Helpful websites:

Chapter 16 *Inversions in Circles*

Interactive examples by David W. Henderson (requires a Java 1.1 compatible browser, please be patient first download is slow):

Helpful websites:

Chapter 17 *Projections (Models) of Hyperbolic Planes*

Crocheted Hyperbolic Plane by David W. Henderson & Daina Taimina

Annuli for hyperbolic paper model this is a template to print out for making hyperbolic paper model from anulli

Template for hyperbolic soccer ball this is a template by Keith Henderson to print out for making paper hyperbolic soccer ball. Use three sheets and overlap the hexagons that have the three dots. Also, don't cut the dotted segments, to save time, but cut only solid lines.

Reflection of triangle in upper half plane model interactive example by David W. Henderson (requires a Java 1.1 compatible browser, please be patient first download is slow)

Helpful websites:

- Modeling the Brain - Projecting the surface of the human brain onto a sphere and/or hyperbolic plane with discussions of preserving angles, versus preserving distances, and/or versus preserving areas.

Chapter 18 *Geometric 2-Manifolds*

Helpful websites:

- Klein Bottle
- The Klein Bottle in 4-space
- Fly and Spider
- Distances across the surface of rectangular box

Chapter 19 *Geometric Solutions of Quadratic and Cubic Equations*

Geometric solutions of Quadratic and Cubic Equations by David W. Henderson

Chapter 20 *Trigonometry and Duality*

Chapter 21 *Mechanisms*

Kinematic models for Design Digital Library

Four Bar Linkages

Universal Joint

Reuleaux Triangle

Helpful websites:

- Involutes
- Mechanical linkages using Sketchpad
- Geometrical models of machines in connection with bibliography from Modena
- Every polygon can be untangled paper by R. Connely, E. Demaine, G. Rote
- Kinematic synthesis of robots
- Research on spacial linkages
- Geometry in Motion

**Peaucellier-Lipkin linkage** links:

- http://www.geom.umn.edu/education/math5337/linkage/
- http://www.ams.org/new-in-math/cover/linkages4.html
- http://www.cwi.nl/~zsofi/machines/machines.html

Chapter 22 *3-Spheres and Hyperbolic 3-Spaces*

Chapter 23 *Polyhedra*

Helpful websites:

- Polyhedra, tilings and dissection
- Stereo polyhedras - wonderful examples of analyphic (and other stereo
- imaging) polyhedras
- Regular Polyhedra

Chapter 24 *3-Manifolds the Shape of Space*

Helpful websites:

- Cosmic Microwave Background Research
- WMAP Mission
- Global Topology of Space paper by J. Weeks
- Measuring the Shape of the Universe paper by Cornish and Weeks
- Fourth dimension
- Secret Worlds Universe within
- Geometry of the Earth and Universe