Books: “Euler’s Gem The Polyhedron Formula and the Birth of Topology” by David S. Richeson
This book is a beautifully illustrated gem! It examines Euler’s famous formula: V-E+F=2 which holds for all polyhedra or surfaces which are topologically equivalent to the sphere. The formula is an example of a topological invariant, something which can be computed for any surface, and thus allows one to categorize surfaces. The book also covers the famous classification theorem which categorizes all surfaces as either homeomorphic (topologically equivalent) to a sphere, n-handled torus, or sphere with n cross-caps (projective plane). Next it dives into knot theory and Seifert surfaces, before moving on to the interplay between topology and geometry, and ends by mentioning homology and how topology is done in higher dimensions.
