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 spot, somewhere on the ball, where a cowlick is unavoidable?

Reveal the answer

Yes — there is no way to comb a hairy ball completely flat; at least one point must always have a hair sticking straight up (or no hair at all). Formally proven in topology as the "hairy ball theorem," it has a surprising real-world consequence: at any given moment, there must be at least one point on Earth with completely calm, windless air.

— Henri Poincaré (early work); Luitzen Brouwer (general proof, 1912), Hairy ball theorem — Topology, proven 1912

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