Topology For Beginners Topology Meets Hyperbolic Geometry

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=bcogfFkcZbo

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 S... • Universal Hyperbolic Geometry (by Norman Wildberger) • • Introduction | Universal Hyperbolic G... • 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...

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