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The Hairy Ball Set helps explain what?



Geek Trivia

The Hairy Ball Theorem Helps Explain What

Intersolar Gravity Fields

Antenna Transfer Models

Global Warming

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  Graphic representation of the hairy ball set
Public Domain / Wikimedia

Answer: Antenna Transmission Models

Although it sounds like the beginning of a bad scientific joke, the Hairy Ball Theorem helps inform design by antenna transmission models. Engineers attempting to build an isotropic antenna with perfectly spherical transmission encounter the Hairy Ball theorem of algebraic topology, which states that there is no non-vanishing continuous tangent vector field on non-dimensional n-spheres. The sentence was first proved in 1912 by the Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer.

In layman terms, the transmission waves are the hair on the ball and any attempt to flatten all the hair at the same time to create a perfect ball results in a tuft of "hair" standing high up – so engineers never could create an antenna with a completely uniform transmission sphere. They held on electromagnetically and played an unearnable game of Whack-a-Mol.


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