Скачать или смотреть Theorems using perpendicularity | Universal Hyperbolic Geometry 11 | NJ Wildberger

We review how perpendicularity in hyperbolic geometry comes from duality, and then introduce duality for triangles and trilaterals. Then we discuss the orthic triangle and its dual, defining the important Base center point, which lies on the ortho-axis of a triangle, and is also somewhat remarkably the orthocenter of a triangle of orthocenters formed from the bases of the triangle.

We introduce a general strategy for approaching theorems in the subject, and introduce our Standard Triangle 1: which will be used to algebraically illustrate many concepts and as an arena for numerical investigations.

Video Content:
00:00 Introduction
4:37 Dual triangle
13:38 Base ortho-axis theorem
9:30 orthocenter and orthic triangle
15:15 Three steps to understanding theorems
19:28 Standard Triangle #1:(ST1)
23:42 Altitudes with standard triangle #1
31:34 Base triple orthocenter theorem

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