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
Content
INTRODUCTION 1
PREPARATIONS 4
TEN BASIC ENTITIES 6
Form and Forming 7
The Harmonic Net and the Harmonic Four Points 11
The Infinitely Distant Point of a Line 23
The Theorem of Pappus 27
A Triangle Transformation 36Sections of the Point Field 38
The Projective versus the Euclidean Point Field 47
The Theorem of Desargues 49
The Line at Infinity 61
Desargues’ Theorem in Three-dimensional Space 64
Shadows, Projections, and Linear Perspective 78
Homologies 89
The Plane at Infinity 96
PRELUDE
CHAPTER 1
INTERLUDE
CHAPTER 2
INTERLUDE
CHAPTER 3
INTERLUDE
CHAPTER 4
INTERLUDE
CHAPTER 5
CHAPTER 6
CHAPTER 7
INTERLUDE
CLOSING
ACKNOWLEDGMENTS 101
BIBLIOGRAPH Y 103
