To the Infinite and Back Again

by Henrike Holdrege


The Evolving Science Association, 2019
spiral bound workbook, 103 pages; $22 


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

DesarguesTheorem 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