To the Infinite and Back Again, Part II — A Workbook in Projective Geometry
To the Infinite and Back Again, Part II — A Workbook in Projective Geometry
Henrike Holdrege
Great Barrington, MA: The Evolving Science Association, 2021
(spiral bound workbook, 119 pages)
For orders of five or more copies for group or classroom use, we offer a wholesale price of $13 per book, plus shipping. Please order directly from us by email or telephone (518) 672-0116.
It is possible to purchase Part I & Part II together at a special price of $35
Also available to purchase as a digital PDF file here
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