## hairy ball theorem
Does the same apply to a torus? Is there a hairy donut theorem? No! The number of "problem points," where the
hair would stick up on a surface, is related to a quantity called the Euler
characteristic of that surface. Basically, every point on a surface
has an index that describes how many times the vector field rotates in a
neighborhood of the problem point. The sum of the indices of all the vector
fields is the Euler characteristic. Since the torus has Euler number 0,
it is possible to have a covering of hair – a vector field –
on it that lies flat at every point. ## Related category• TOPOLOGY | |||||||

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