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Index
Read Chapter 3 of Yaglom.
In addition read, pages 102 - 106 of Plane Algebraic Curves by Egbert Brieskorn and Horst Knorrer.
While reading, please keep in mind these key terms. Be sure you can define each upon completion of your readings.
- projective geometry
- projective plane
- parallel projection
- central projection
- projective property
- affine geometry
- point at infinity
- line at infinity
- duality principle
- cross ratio
After completing these readings, please answer the following questions:
19 (a) When was the golden age of geometry? Why?
19 (b) Who were the major characters in the development of projective geometry? (In addition to the many mathematicians, don't forget to include the artists!)
19 (c) What is the main distinction between descriptive geometry and projective geometry? Between affine and projective geometry?
19 (d) What is a projective property?
19 (e) Is it possible to speak of circles in projective geometry? Explain.
19 (f) Why does the projective plane need a "line at infinity"? Include in your discussion, the topics of disappearing line, vanishing point, and vanishing line.
19 (g) Are the "points of infinity" in the real projective plane distinguishable from the other points in the real projective plane? Explain.
19 (h) What is the duality principle?
19 (i) What is analytic projective geometry?
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