Henri Poincaré: 2 ideas and puzzles worth knowing

2 ideas and puzzles from Henri Poincaré, each explained in a minute and credited to the original work. Free on Savvy.

Can you comb every hair flat on a coconut with no cowlick?
Imagine a ball completely covered in hair, and you try to comb every single hair so it lies flat against the surface with none sticking straight up. Is there always at least one sp…
— Henri Poincaré (early work); Luitzen Brouwer (general proof, 1912), Hairy ball theorem
Two orbiting bodies are perfectly predictable forever; add a third and chaos creeps in
Newton's laws give a clean, exact formula for how two bodies orbit each other under gravity, valid for all time. Add just one more body and the same equations have no general close…
— Henri Poincaré, Sur le problème des trois corps et les équations de la dynamique

Five ideas worth knowing, every week