19 Totally Mind-Blowing Facts

There is a theory that a hairy sphere can never be combed perfectly flat.

Who knew that math could give you hair advice. The hairy ball theorem of algebraic topology (yes, that’s really what it’s called) was first discovered by Henri Poincare in the late 19th century. It states that given a ball with hairs all over it, it is impossible to comb the hair continuously and have all the hairs lay flat. You will always have at least one tuft of hair sticking out.

In other words “you can’t comb the hair on a coconut.” The formal statement of this theorem is that “there is no nonvanishing continuous tangent vector field on the sphere. Less briefly, if f is a continuous function that assigns a vectorin R3 to every point p on a sphere, and for all p the vectorf(p) is a tangent direction to the sphere at p, then there is at least one p such that f(p)= 0.”

Now, we know that the Earth is approximately a ball and that wind has direction on each point of the surface. Well according to this theorem, there is always a place where the air is perfectly still.

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