Topology For Beginners: Topology Meets Hyperbolic Geometry скачать в хорошем качестве

Topology For Beginners: Topology Meets Hyperbolic Geometry

https://sites.google.com/site/richard... In this video I will briefly introduce hyperbolic geometry and continue discussing the relationship between curvature, tilings, non-euclidean geometry and surfaces with boundary. Hyperbolic geometry is introduced using computer simulations of the Beltrami-Poincare disk, and Hyperbolic paper. In particular, I argue that surfaces with different genus (number of wholes) can have different types of geometry and hence admit different topologies. The Gauss-Bonnet formula is described at the end to concrete these ideas. Resources The Shape of Space (book by Jeffrey R. Weeks) Non Euclidean Geometry & Hyperbolic Social Networks (by Richard Southwell)    • Non Euclidean Geometry & Hyperbolic Social...   Universal Hyperbolic Geometry (by Norman Wildberger)    • Introduction | Universal Hyperbolic Geomet...   Wolfram Demonstrations Project: Tiling the Hyperbolic Plane with Regular Polygons (by Gašper Zadnik) http://demonstrations.wolfram.com/Til... Wolfram Demonstrations Project: Lines through Points in the Poincaré Disk (by Brett Champion) http://demonstrations.wolfram.com/Lin...