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UnivHypGeom28: The Cross law in Universal Hyperbolic Geometry

The Cross law is the fourth of the four main laws of trigonometry in the hyperbolic setting. It is also the most complicated, and the most powerful law. This video shows how we can prove it with the help of a remarkable polynomial identity. We also give an application to the relation between the quadrance and spread of an equilateral triangle.CONTENT SUMMARY: pg 1: @00:11 Cross law in Euclidean R.T. review; Cross law in UHG; Cross Dual lawpg 2: @06:43 Reluctant exposure to classical hyperbolic geometry; exercise [email protected]:25 ; observation - Euclidean cross law as a limiting case @11:02pg? 3: @12:46 Cross law (hyperbolic version); proof; heavenly assistance 16:06pg 4: @16:21 proof continued; using a computer (Scientific Workplace) to verify an identity @21:41 ; proof complete? @26:47pg 5: @28:22 A pleasant consequence of the cross law; Equilateral triangle theorem; proof; exercise 28-2 @31:24pg 6: @31:48 exercises 28.3-5 (THANKS to EmptySpaceEnterprise)
Length: 35:26

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