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The Forbidden Geometry That Bends Reality

Ever wonder what would happen if the axioms of Euclidean Geometry were broken? Through the power of projections and intuition, we can step into the fascinating world of Non-Euclidean Geometry. Lines begin to diverge or converge, angles are altered, parallel lines become infinite or cease to exist and everything we know is flipped upside-down! But how is that we can understand the properties of curved space and portray it in Euclidean? In this video, we’ll answer all those questions and explore the properties and projections of the fascinating spherical and hyperbolic spaces! ___________________________________________________________________________ Music and SFX: Smoke - Lish Grooves Outreach - Go By Ocean _ Ryan McCaffrey Lazy Laura - Quincas Moreira Last Sunrise - Adam MacDougall Otros Hijos - Casa Rosa Moonlight Magic - Asher Fulero Exploring The Crystal Caves - Asher Fulero Tiburtina - Schwartzy ___________________________________________________________________________ 0:00 Introduction 0:42 What is Non-Euclidean Geometry? 1:00 Spherical Geometry 2:30 Spherical Projections 3:35 Stereographic Visualisation 4:28 Hyperbolic Geometry 6:00 Hyperbolic Projections 7:52 Poincare Visualisation 8:46 Conclusion 9:03 End Card Desmos: Graphing Calculator https://www.desmos.com/calculator Davinci Resolve: https://www.blackmagicdesign.com/prod… Blender: https://www.blender.org/download/