This strangely - name theorem has a rarefied theoretic background signal , get up from a perfectly round ball covered with perfectly fine fuzz . Despite that , it has actual - world applications , including the ability to construct gold nanowires — and finding the one slur on earth where there is no wind .
Top prototype : BryceGuy72 on Deviant Art .
The Hairy Ball Theorem bounce from an other 20th century mathematician ’s sentiment about transmitter fields applied to ideal shapes . I love , it voice fascinating . But Luitzen Brouwer took that preposterously abstract idea and gave it an easy understood variety – especially since Koosh balls were invented .
agree to Brouwer , to understand this , mass should render a perfectly pear-shaped ball covered with dead ok haircloth all over . Next , imagine take a brush and brushing the hair on the testicle in uninterrupted strokes , trying to flatten it to the body of the lump . After the brushing , the hair is essentially a vector field . Each hairsbreadth establish the motion of the brush , since each hairsbreadth has been tugged in whatever direction the brush was run as it drive the pilus into place . From the point of view of someone standing on the aerofoil of the ball , the tomentum drawn perpendicular to the airfoil of the Lucille Ball receive the most vigorous motion , while those standing up and down , just the fashion they were before the clash move through , show no motion at all . They are ‘ zero vector . ’
Well , fine , but what does this narrate us ? Brouwer figured out that , with the brush be active continuously over the surface of the ball , there was always one power point with a ‘ zero vector . ’ In other words , there was no way to brush all the hair’s-breadth so that it lie flavorless on a domain . One point will always have a hair standing up , vertical to the surface . This is not so on other build , like a square or a donut shape .
That sounds mathematically interesting , but not the least lilliputian flake useful to anyone . Amazingly , though , The Hairy Ball Theorem can be go for to nanotechnology . The Hairy Ball Theorem in 2007 was employed by an technology team . Using a gold nanoparticle as the ball , they covered it in acerb ‘ hairs ’ that stood out and created flaw in the surface of the ball that could be used to attach it to other Lucille Ball . Because of the theorem , they knew that some hairsbreadth would stomach out from the aerofoil of the ball , no matter what . Even under the most ideal condition , one hairsbreadth at least could be used to attach one nanoparticle to another , and build up a chain of them that would make a amber wire .
The Hairy Ball Theorem also secernate us something about the solid ground that seems almost orphic . Winds move in continuous stroke over the aerofoil of the terra firma . They could be turn over as a vector field . Since the ground is essentially a sphere , and the winds move over it , there has to be one power point at which the transmitter is zero . There has to be one breaker point on earth , all the time , where there is no wind , even though there is air flow all around it . That spot wo n’t stick in topographic point all the time . It would be interesting though , to see if there were a way of finding that one spot , at one point in time . The Hairy Ball theorem could , then , be an aspiration for multitude wishing to chase a dream . As well as for people interested in the automobile mechanic of having their orchis brushed . ( I ’m dismal . I had to . )
ViaMath Fun Facts , Wolfram Mathworld , andThe Math Book .
ikon : K Tempest Bradford
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