Experiencing Geometry: On Plane and Sphere, 1/e
David W. Henderson, Cornell University
Published July, 1995 by Prentice Hall Engineering/Science/Mathematics
Copyright 1996, 193 pp.
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In Experiencing Geometry on Plane and Sphere, Henderson invites
readers to explore the basic ideas of geometry beyond the formulation
of proofs. The text conveys a distinctive approach, stimulating
readers to develop a broader, deeper understanding of mathematics
through active participationincluding discovery, discussion, and
writing about fundamental ideas. It provides a series of interesting,
challenging problems, then encourages readers to gather their reasonings
and understandings of each problem and discuss their findings in an
reflects the latest teaching styles seen in today's classrooms,
emphasizing activities like...
provides a launching pad of inviting, challenging, open-ended
- group learning
- writing as assessment
places problems in a flexible, learn-by-doing context that
rewards exploration and encourages conjectures and experiments.
designs problems to be accessible to everyone, allowing
each student to pursue each problem to the best of their ability.
encourages students to express their thoughts even when
they can't solve a particular problem completely in an effort to...
allows students to write their own proofs based upon a deeper,
more experiential understanding of ideas.
- build student confidence
- show students where their real difficulties lie
1. Straightness and Symmetry.
2. Straightness on a Sphere.
3. What is an Angle?
4. Straightness on Cylinder and Cone.
5. SAS and ASA.
6. Area, Parallel Transport and Holonomy.
7. ITT, SSS and ASS.
8. Parallel Transport.
9. SAA and AAA.
10. Parallel Postulates.
11. 3-Spheres in 4-Space.
12. Dissection Theory.
13. Square Roots, Pythagoras and Similar Thoughts.
14. Geometric Solutions of Quadratic and Cubic Equations.
15. Projections of a Sphereonto a Plane.
16. Duality and Trigonometry.
17. Isometries and Patterns.
Appendix A. A Geometric Introduction to Differential Geometry.