To the Infinite and Back Again, Part II, is an introduction to projective geometry and begins where Part I ended. In Part I, the concepts of point, line, and plane at infinity were introduced and tested within certain contexts. The goal was to show that they are meaningful and not arbitrarily conceived. This volume works with these concepts from the outset.

The principal of duality (or polarity), which was discovered in the 19th century, is central to projective geometry and is the main focus of this volume. Learning to think in polarities can facilitate a significant and beneficial expansion of modern thought and modern consciousness. 

The book provides numerous exercises that foster capacities of precise geometric imagination, thinking in transformations, and thinking in polarities. In a careful step-by-step fashion, the book shows how ideas form, grow, weave, and metamorphose. Richly illustrated, this workbook is intended for self-study by the layperson, and as a resource for teaching projective geometry in high school or college.

TABLE OF CONTENTS

Form and Forming

The Harmonic Net and the Harmonic Four Points

The Infinitely Distant Point of a Line

The Theorem of Pappus

A Triangle Transformation

Sections of the Point Field

The Projective Versus the Euclidean Point Field

The Theorem of Desargues

The Line at Infinity

Desargues’ Theorem in Three-dimensional Space

Shadows, Projections, and Linear Perspective

Homologies

The Plane at Infinity