Скачать или смотреть Orthocenters exist! | Universal Hyperbolic Geometry 10 | NJ Wildberger

In classical hyperbolic geometry, orthocenters of triangles do not in general exist. Here in universal hyperbolic geometry, they do. This is a crucial building block for triangle geometry in this subject. The dual of an orthocenter is called an ortholine---also not seen in classical hyperbolic geometry!

This lecture also introduces a number of basic important definitions: that of side, vertex, couple, triangle, trilateral. We also introduce Desargues theorem and use it to define the polar of a point with respect to a triangle. The lecture culminates in the definition of the orthic line, orthostar and ortho-axis of a triangle. The ortho-axis will prove to be the most important line in hyperbolic triangle geometry.

Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of each lecture. Great for review, study and summary.

Video Content

00:00 Introduction
3:47 Definitions: couple, triangle, trilateral
10:45 Altitude line theorem
12:46 Altitude point theorem
14:59 Orthocenter theorem
18:24 Proof of Orthocenter theorem
29:39 Ortholine theorem
32:26 Desargues' theorem
34:31 Cevians and Desargues' polars
39:05 Orthic axis, orthostar and ortho-axis

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