[Book Cover]

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.
Cloth
ISBN 0-13-373770-5


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Summary

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 participation—including 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 open forum.

Features


reflects the latest teaching styles seen in today's classrooms, emphasizing activities like...

  • group learning
  • writing as assessment
provides a launching pad of inviting, challenging, open-ended problems.
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...
  • build student confidence
  • show students where their real difficulties lie
allows students to write their own proofs based upon a deeper, more experiential understanding of ideas.


Table of Contents
    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.
    18. Polyhedra.
    Appendix A. A Geometric Introduction to Differential Geometry.
    Bibliography.
    Index.


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