A short proof of the Hairy Ball theorem (2016) [pdf]

Re:A short proof of the Hairy Ball theorem (2016) [pdf] by orlandpm on Monday August 25, 2025 @07:18PM (#45020379)

Heard a mathematician friend call this the “hairy sphere theorem” once. At first I thought he was being a prude, but now I appreciate that the theorem is about spheres, as opposed to balls.

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Re:A short proof of the Hairy Ball theorem (2016) [pdf] by IAmBroom on Tuesday August 26, 2025 @12:52PM (#45029153)

It's not. It's about closed surfaces, which include the surface of spheres, oblate spheres, footballs, pencils, and airplanes.

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Re:A short proof of the Hairy Ball theorem (2016) [pdf] by orlandpm on Wednesday September 03, 2025 @12:24AM (#45112234)

Well, all these closed surfaces you mention are (topologically) spheres. The theorem doesn’t apply to some other closed surfaces, like the torus, which does admit a continuous non-vanishing vector field.

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