Projective Geometry

Projective Geometry

The elements of geometry are points, lines and planes, together with Space and Nothing. In Euclidian geometry, we observe these as if we are point-centered beings concerned with extensive measurement.

In non-Euclidian (projective) geometry, we are “planar” beings observing spatial relationships, free of measurement, as dynamic and transformational. This polar opposite vision of intensive space reveals remarkable secrets.

In this fascinating and useful book, expert Lawrence Edwards invites the reader to discover these secrets through practical exercises in creative geometry.

Topics include: the elements of geometry, duality, collineation, cross ratio, the circling and step measure, conics, and the nature of a curve.

C O N T E N T S:

Foreword

1. Introduction
2. Duality
3. Collineation
4. Cross Ration
5. Correspondences
6. The Conic
7. Growth Measure
8. Circling and Step Measure
9. Involution
10. Pole and Polar
11. Dual Properties of Curves
12. Pencils and Ranges of Conics
13. The Imaginary
14. The Nature of a Curve
15. The Imaginary Part of a Conic
16. Four-point Systems with Imaginary Elements
17. The Projective Idea of a Circle
18. The Imaginary Circle
19. Four-point Systems of Conics
20. Higher Order Curves
21. Path Curves
22. Osculating Conics
23. Fundamental Notions for Geometry in Space
24. The Quadric
25. The Imaginary Part of a Sphere
26. The Twisted Cubic
27. More Developables
28. The Linear Congruence and the Tetrahedron
29. Perspective

Index

About the Author

Lawrence Edwards (1912-2004) was a teacher of mathematics. He had pursued his unique research for over thirty years, focusing on the forms of living nature in relation to geometric analysis. He is the author of the acclaimed The Vortex of Life.