To the Infinite and Back Again: A Workbook in Projective Geometry
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 transformative 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)
- 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
Robert Hamilton (verified owner) –
So far I have purchased 2 books. The service was great and so were the books. The content that interests me (space and counterspace) is not available elsewhere very easily.