Experiencing Geometry

in Euclidean, Spherical, and Hyperbolic Spaces

(tentative title)

A preliminary expanded and revised version of Experiencing Geometry on Plane and Sphere

written and used in 1999

David W. Henderson

Cornell University

with writing input from

Daina Taimina

Notice: This material is in draft form and may not be duplicated or quoted without the author's written permission, except for purposes of review or trying out the material with students. As always comments are welcome and will affect the final draft. Send comments to dwh2@cornell.edu.

Added 28 Mar 99: I have just now changed all figures to JPEG format because not all browsers will load PNG. Also, these documents contain many characters from the "SYMBOL" font so be sure that your computer has symbol font loaded (most do). The symbols work fine in Netscape 3 and above, I do not know about other browsers. If you have trouble loading these documents please send me a message and tell me what browser you are using and what is the nature of your problem. Also, remember to use the "Reload" button to make sure that you are not viewing an old version of these chapters that has been stored in your cache. If you want to test your browser, try out this test page.

New Material -- these are tentative and will be updated frequently

• Cinderella Interactive Examples. Updated 24 August 99
• Supplements. Updated 10 July 99
• Title Pages. Updated 27 June 99
• Contents. Updated 27 June 99
• Preface. Updated 27 June 99
• Chapter Dependencies. Updated 27 June 99
• How to Use This Book. Updated 27 June 99
• Message to the Reader. Updated 27 June 99
• Chapter 01: Straightness and Symmetry. Updated 27 June 99
  [From the old Ch 1, and a very little new material.]
• Chapter 02: Straightness on Sphere, Cylinder, and Cone. Updated 27 June 99
  [From the old Ch 2 and part of Ch 4, and a little new material.]
• Chapter 03: Angles, ITT, and Circles. Updated 27 June 99
  [includes old Ch 4, part of Ch 7 and new material]
• Chapter 04: Circles in the Plane. Updated 4 September 99
  [all new material which is a prerequisite to parts of Ch 5.]
• Chapter 05: The Hyperbolic Plane. Updated 4 September 99
  [all new material introducing hyperbolic planes]
• Chapter 06: Transformations and Triangles. Updated 27 June 99
  [This is the old Ch 5 (SAS & ASA) with new hyperbolic material added
  and new material on geodesics and transformations.]
• Chapter 07: Area and Holonomy. Updated 27 June 99
  [This is the old Chapter 6 with considerable new hyperbolic material
  I particularly like the new material on the area of a hyperbolic triangle.
  I have removed the area formulas from the statement of the problems
  I have included a problem on the sum of the angles of a triangle.]
• Chapter 08: Parallel Transport. Updated 27 June 99
  [This is the old Ch 8 with new hyperbolic material added]
• Chapter 09: SSS, ASS, SAA, and AAA. Updated 27 June 99
  [This is part of the old Ch 7 and all of the old Ch 9 with new hyperbolic material]
• Chapter 10: Parallel Postulates. Updated 27 June 99
  [This is the all Ch 10 with new hyperbolic material added]
• Chapter 11: Geometric 2-manifolds and Coverings. Updated 27 June 99
  [This includes some material from the old Problem 5a and much new material.]
• Chapter 12: 3-spheres and Hyperbolic 3-space. Updated 27 June 99
  [This includes a rewriting of most of the old Chapter 11 plus new material on hyperbolic 3-space.]
• Chapter 13: Dissection Theory. Updated 21 Apr 99
  [This includes the old Chapter 12 and new hyperbolic material.]
• Chapter 14: Square Roots, Pythagoras, and Similar Triangles. Updated 21 Apr 99
  [This includes the old Chapter 13, slightly changed.]
• Chapter 15: Geometric Solutions of Quadratc and Cubic Equations. Updated 21 Apr 99
  [This includes the old Chapter 14 and new material on Square Roots in the Sulba Sutra.]
• Chapter 16: Projections of a Sphere and Models of a Hyperbolic Plane. Updated 27 June 99
  [This includes the old Chapter 15 and new hyperbolic material.]
• Chapter 17: Duality and Trigonometry. Updated 27 June 99
  [This includes the old Chapter 16 and new hyperbolic material.]
• Chapter 18: Isometries and Patterns. Updated 27 June 99
  [This includes the old Chapter 17 and new hyperbolic material.]
• Chapter 19: Polyhedra. Updated 27 June 99
  [This includes the old Chapter 18 and new hyperbolic material.]
• Chapter 20: 3-Manifolds & Shape of Space. Updated 13 November 99
  [This includes all new material. 11/13/99 I added Figures 20.4 and 20.8 and a some other changes.]
• Appendix: Geometric Introduction to Differential Geometry. Updated 27 June 99
  [This is only slightly revised.]
• Bibliography. Updated 27 June 99.

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