#euler characteristic

[Eugenio Calabi, 1954 | Shing-Tung Yau, 1978]

I’m creating some images through Geogebra to help myself in studying some geometry. These were used to prove Euler’s polyhedron formula. A general polyhedron in blown into a circumscribing sphere (and rotated so that the north pole doesn’t lie on an edge. Afterwards, all faces but the one including the pole are projected from the north pole to the equatorial plane, giving the last picture. (This proof is by Cauchy and I won’t write it down here for now.)

To some people, it must seem like the whole point of maths is to fuck with non-mathematicians.