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If you think that math isn’t a part of day to day life, think again while reading these amusing colloquial statements that encode math facts.
Can you hear the shape of a drum?
Take a map of wherever you are and lay it on the ground. There will be
exactly one point on the map that is directly above the point it
represents on the ground.Complete disorder is impossible.
All primes are odd except 2, which is the oddest of all.
If it walks like a sphere and it quacks like a sphere then it is a sphere.
If you are walking between two policemen going to the same station, you will end up there, too.
A brain tangled enough to tackle itself must be too tangled to tackle.
After stirring a cup of coffee, at least one point will end up in the exact same position as it was before.
Is your brain thirsty for more? Go to mathoverflow.net
Anyone point me to the theorem for the last one? I don’t believe it.
WLOG, Assume coffee mug is cylindrical for descriptive purposes. Rotate all contents 90° clockwise, and for the atom-thick-pillar in the middle that only rotates, but doesn’t actually change position, shift up by 1 inch. Any coffee that goes above the top is “wrapped” around to the bottom. Hence, no coffee is in the same place as where is started. Your statement is false.
The last one is probably a reference to the Brouwer fixed-point theorem, which requires the function to be continuous.
http://en.wikipedia.org/wiki/Brouwer_fixed-point_theorem
Uhm… sorry for not having seen the other comment below 😉
The last one is called Brouwer’s fixed-point theorem
http://en.wikipedia.org/wiki/Brouwer_fixed-point_theorem
I see, they assumed stirring coffee was a continuous function. In general, it is not, as the spoon is often lifted from the liquid, however small, creating a discontinuity. Blah, a better analogy would be nice.