The Hairy Ball Theorem
Ever tried to comb a hairy ball? Math says you failed! Trying out a new feature: English Transcript! Let me know how it works Tweet it - http://bit.ly/sKAjpS Facebook it - http://on.fb.me/uj...
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Suppose you have a ball covered entirely with hair and you're trying to comb the hair sothat it lies flat everywhere along the surface. If the ball were a donut, or it existed intwo dimensions, this would be easy! But in three dimensions? Well, you're going to runinto trouble. A lot of trouble. A big hairy ball of trouble.That's because of a theorem in algebraic topology called the "Hairy Ball Theorem" (and yes,that's it's real name) which unequivocally proves that at some point, the hair must stickup. Now don't go wasting your time playing around with a hairy ball trying to prove thetheorem wrong - this is math we're talking about. It's proven - done - QED!Technically speaking, what the ...
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Suppose you have a ball covered entirely with hair and you're trying to comb the hair sothat it lies flat everywhere along the surface. If the ball were a donut, or it existed intwo dimensions, this would be easy! But in three dimensions? Well, you're going to runinto trouble. A lot of trouble. A big hairy ball of trouble.That's because of a theorem in algebraic topology called the "Hairy Ball Theorem" (and yes,that's it's real name) which unequivocally proves that at some point, the hair must stickup. Now don't go wasting your time playing around with a hairy ball trying to prove thetheorem wrong - this is math we're talking about. It's proven - done - QED!Technically speaking, what the ...
