### UnivHypGeom29: Thales' theorem, right triangles and Napier's rules

This video establishes important results for right triangles in universal hyperbolic geometry--these are triangles where at least two sides are perpendicular. Besides Pythagoras' theorem, there is a simple result called Thales' theorem, giving a formula for a spread as a ratio of two quadrances. Together these allow us to state a very simple form for Napier's rules in this algebraic setting.CONTENT SUMMARY: pg 1: @00:11 Review of the 4 main laws? of trigonometry; pg 2: @02:55 right triangles described; singly right, doubly right, triply rightpg 3: @06:16 Thales theorem; A kind of 'similarity' for right triangles @09:05 ; Inclassical hyperbolic geometry this result is obscured @11:48pg 4: @12:36 Thales theorem relationship to Euclidean RT; the spread as a crucial ratio @15:30pg 5: @17:41 Quadrea as the single most important number associated to a triangle; reminder on how to obtain an altitude @18:41 ; Quadrea are @22:11 pg 6: @22:42 Napier's rules; suggested exercise @24:38pg 7: @26:10 proof? of Napier's rules;pg 8: @30:02 proof continued; suggested algebra exercise @35:46pg 9: @36:49 When in doubt create some right? triangles; exercise 29.1 @37:37;pg 10: @39:35 exercise 29.2pg 11: @40:53 exercise 29.3,4(THANKS to EmptySpaceEnterprise)

Length:
42:35