Applications of Euler's Formula and Graphs in Algebraic Topology

Applications of Euler's Formula and Graphs in Algebraic Topology

Explore the applications of Euler's formula and graphs in this lecture from the Algebraic Topology course. Discover how Euler's formula proves the existence of only five Platonic solids and learn about other polyhedra types, including deltahedra and Schafli's higher-dimensional generalizations. Examine the 120-cell, 600-cell, and 24-cell in four dimensions. Conclude with a discussion on Euler's formula for planar graphs. Gain insights into these fundamental concepts of algebraic topology through clear explanations and examples provided by Associate Professor N J Wildberger of UNSW.