Class Central is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

YouTube

Orthocenters Exist - Universal Hyperbolic Geometry

Insights into Mathematics via YouTube

Overview

Save Big on Coursera Plus. 7,000+ courses at $160 off. Limited Time Only!
Explore the fascinating world of universal hyperbolic geometry in this 44-minute lecture that challenges classical notions and introduces crucial concepts for triangle geometry. Learn about the existence of orthocenters in hyperbolic triangles, a concept not found in classical hyperbolic geometry. Discover key definitions such as side, vertex, couple, triangle, and trilateral. Delve into important theorems including the Altitude line theorem, Orthocenter theorem, and Desargues theorem. Investigate the polar of a point with respect to a triangle and explore the orthic line, orthostar, and ortho-axis - the most significant line in hyperbolic triangle geometry. Gain valuable insights into this advanced mathematical topic through clear explanations and visual aids.

Syllabus

Introduction
Definitions: couple, triangle, trilateral
Altitude line theorem
Altitude point theorem
Orthocenter theorem
Proof of Orthocenter theorem
Ortholine theorem
Desargues' theorem
Cevians and Desargues' polars
Orthic axis, orthostar and ortho-axis

Taught by

Insights into Mathematics

Reviews

Start your review of Orthocenters Exist - Universal Hyperbolic Geometry

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Someone learning on their laptop while sitting on the floor.