Well you could argue that it is just a corollary of the Poincaré-Hopf theorem, but I would not consider that the easiest proof. Correspondingly there are several approaches but you don't absolutely have to introduce simplicial complexes. ^^
Lengthy image sources are in the list at the bottom 👍

Nice links, by the way. I did not know "Uncyclopedia" before, although there is a conceptually similar page called "Stupidedia" in Germany :D