The Beautiful Story of Non-Euclidean Geometry

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In this video we are going to explore the origins of non-Euclidean geometry. We look back to Euclid and his infamous book the Elements, where he outlined an axiomatic approach to Euclidean geometry using five postulates. The fifth, the parallel postulate, has always been controversial, a consistent system of geometry that accepted the first four postulates but rejected the parallel postulate wasn't discovered until the nineteen century by Janos Bolyai, Nikolai Lobachevsky, and Carl Gauss who independently worked towards something called hyperbolic geometry, one of multiple non-Euclidean geometries. We specifically will explore the Poincare disk, one model of hyperbolic geometry.

Play around with the Geogebra page I used in the video ► https://www.geogebra.org/classic/sxakwtrr

0:00 Euclidian Geometry and the Elements
2:12 The Five Postulates
3:21 Should the Parallel Postulate be a theorem?
4:29 Spherical Geometry
5:59 Janos Bolyai discovers Hyperbolic Geometry
6:48 Hyperbolic Geometry and the Poincare Disk
10:49 Resolving the Parallel Postulate Question
11:19 Angles and Triangles
13:44 Brilliant.org/TreforBazett

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Видео The Beautiful Story of Non-Euclidean Geometry канала Dr. Trefor Bazett