The Beautiful Story of Non-Euclidean Geometry

Visit https://brilliant.org/TreforBazett/ to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pages/trefor 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 COURSE PLAYLISTS: ►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa ►DIFFERENTIAL EQUATIONS: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxde-SlgmWlCmNHroIWtujBw ►LAPLACE TRANSFORM: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 ►GAME THEORY: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxdzD8KpTHz6_gsw9pPxRFlX OTHER PLAYLISTS: ► Learning Math Series https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Cool Math Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join SOCIALS: ►Twitter (math based): http://twitter.com/treforbazett ►Instagram (photography based): http://instagram.com/treforphotography