### UnivHypGeom22: Pythagoras' theorem in Universal Hyperbolic Geometry

Pythagoras' theorem in the Euclidean plane is easily the most important theorem in geometry, and indeed in all of mathematics. The hyperbolic version, stated in terms of hyperbolic quadrances, is a deformation of the Euclidean result, and is also the most important theorem of hyperbolic geometry. We review the basic measurement of quadrance (not distance!) between points.CONTENT SUMMARY: pg 1: @00:11 Pythagoras' theorem in UHG; points, point/line incidence, quadrance/cross ratiopg 2: @05:25 projecting 3-dim onto 'viewing plane'pg 3: @11:03 quadrance in planar coordinates; GSP illustrations of different quadrances in the plane? @13:22pg 4: @13:58 quadrance planar formula; note - null point restriction; zero denominator convention; examplepg 5: @17:22 Pythagoras' theorem (hyperbolic version); the importance of the theorem @18:04 ; examplepg 6: @22:42 exercises 22.1,2pg 7: @24:22 The proof of Pythagoras' theorem; a small miracle @27:04 ; suggested exercise @28:21pg 8: @29:03 The proof of Pythagoras' theorem continued from (pg 7); "That's a proof" @33:06?pg 9: @34:31 exercises 22-(3:5) (THANKS to EmptySpaceEnterprise)

Length:
36:14