Pappus' theorem and the cross ratio | Universal Hyperbolic Geometry 3 | NJ Wildberger

Pappus' theorem is the first and foremost result in projective geometry. Another of his significant contributions was the notion of cross ratio of four points on a line, or of four lines through a point.

We discuss various important results: such as the Cross ratio theorem, asserting the invariance of the cross ratio under a projection, and Chasles theorem for four points on a conic. We show that the notion of cross ratio also works for four concurrent lines.

CONTENT SUMMARY: Pappus' theorem @00:52 cross ratio @02:46 cross ratio transformation theorem @11:08 cross ratio theorem @13:54 Chasles theorem @16:19 The cross ratio is the most important invariant in projective geometry 9:09

Video Contents:
00:00 Hyperbolic geometry as based on projective geometry
00:30 Pappus of Alexandria
02:45 Exercise - Verify Pappus' theorem for special cases
03:55 Cross ratio
08:41 Experience with cross ratio
11:03 Cross ratio transformation theorem
13:49 Cross ratio theorem
16:13 Chasles' theorem
19:07 Projective geometry and Desargues

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