The University of New South Wales, , Prof. N J Wildberger
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Updated On 02 Feb, 19
Introduction to Algebraic Topology - One-dimensional objects - Homeomorphism and the group structure on a circle - Two-dimensional surfaces: the sphere - More on the sphere - Two-dimensional objects - the torus and genus - Non-orientable surfaces - the Mobius band - The Klein bottle and projective plane - Polyhedra and Euler's formula
Applications of Euler's formula and graphs - More on graphs and Euler's formula - Rational curvature, winding and turning - Duality for polygons and the Fundamental Theorem of Algebra - More applications of winding numbers - rational curvature of a polytope - Rational curvature of polytopes and the Euler number - The geometry of surfaces - The two-holed torus and 3-crosscaps surface - Knots and surfaces I
4.1 ( 11 )
We use Eulers formula to show that there are at most 5 Platonic, or regular, solids. We discuss other types of polyhedra, including deltahedra (made of equilateral triangles) and Schaflis generalizations to higher dimensions. In particular in 4 dimensions there is the 120-cell, the 600-cell and the 24-cell. Finally we state a version of Eulers formula valid for planar graphs.
This is the ninth lecture in this beginners course on Algebraic Topology, given by Assoc Prof N J Wildberger at UNSW. His other YouTube series are found at YouTube channel njwildberger.
Sep 12, 2018
Excellent course helped me understand topic that i couldn't while attendinfg my college.
March 29, 2019
Great course. Thank you very much.