My favorite counter-example in math is https://en.wikipedia.org/wiki/Schwarz_lantern https://en.wikipedia.org/wiki/Schwarz_lantern Intuitively, you'd think tha

My favorite counter-example in math is https://en.wikipedia.org/wiki/Schwarz_lantern https://en.wikipedia.org/wiki/Schwarz_lantern Intuitively, you'd think that the surface area in 3D can be approximated by using a series of converging polyhedra, but that's not the case.