To the Infinite and Back Again

A Workbook in Projective Geometry

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Description

To the Infinite and Back Again provides numerous exercises that foster clarity of thought and precision in imagination. This richly illustrated book is a practice-oriented introduction to projective geometry. In working through the exercises we learn to think transformatively and to experience a beautiful thought world in which ideas weave, grow, and metamorphose.

The book leads in a careful step-by-step fashion to the challenging idea of the infinite. We learn to think this mind-expanding concept, a concept that opens up whole new ways of understanding. We begin to see that everything finite gains wholeness and coherence when we conceive of the infinite.

As a fruit of the author’s many years of teaching, this workbook is intended for self-study by the lay-person and is a unique resource for high school and college math teachers. (From the back cover)

Contents:

  • INTRODUCTION
  • PREPARATIONS
  • TEN BASIC ENTITIES
  • PRELUDE: Form and Forming
  • CHAPTER 1: The Harmonic Net and the Harmonic Four Points
  • INTERLUDE: The Infinitely Distant Point of a Line
  • CHAPTER 2: The Theorem of Pappus
  • INTERLUDE: A Triangle Transformation
  • CHAPTER 3: Sections of the Point Field
  • INTERLUDE: The Projective versus the Euclidean Point Field
  • CHAPTER 4: The Theorem of Desargues
  • INTERLUDE: The Line at Infinity
  • CHAPTER 5: Desargues’ Theorem in Three-dimensional Space
  • CHAPTER 6: Shadows, Projections, and Linear Perspective
  • CHAPTER 7: Homologies
  • INTERLUDE: The Plane at Infinity
  • CLOSING
  • ACKNOWLEDGMENTS
  • BIBLIOGRAPHY

Additional information

Weight 19 oz
Dimensions 8 × 0.5 × 11 in
Author

ISBN13

9780974490656

Published

May 2019

Format

Spiralbound

Pages

103

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