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| The sometimes 'Beauty' of mathematics??? |
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| magic:
Yep. Even a cat would pass :D |
| TimFox:
You would be surprised how small a hole a standard household mouse can fit through. |
| mathsquid:
Yes. The rope is \$\frac{1}{2\pi}\$ meters above the ground because the additional length was 1 meter. |
| RJSV:
Thanks, phew that ALGEBRA is hard, for me. Seriously, I've come to realize: College level Calculus got built on foundation of 'crappy' high school Algebra. Heck, I've heard Einstein lamented, "...couldn't factor a polynomial, to save my life!..." Oh, and those smaller four legged 'Rodents' can run straight up a slightly roughened exterior wall. |
| CatalinaWOW:
Sometimes the beauty comes when an (almost) totally non-math explanation is available. The following is apparently related to a problem in topology, but has practical applications, and has delighted me ever since I came across it. It is the proof that you can place a square table on any uneven floor that meets a couple of simple criteria. The simple criteria: 1. No discontinuities in the floor. 2. Irregularities have to be a fair amount smaller than the length of the legs. 3. The legs are equal length. The proof. First, by inspection, you can get three legs to touch by putting two in contact with the floor and rotating the table about the line between the contact points until another leg touches. Now the pretty part. Since the table is symmetric for 90 degree rotations about its center there are three other rotational positions where three legs touch the same three points. But they aren't the same three legs. And if you keep the legs in contact with the surface as you rotate between the four positions there will be a point at which the current three legs transition to the next three. At that point four legs are touching the ground. |
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