Quote:
Originally posted by MrL_JaKiri
Four insects, A, B, C and D, occupy the corners of a square of sides 10cm.
A crawls towards B, B crawls towards C, C crawls towards D and D towards A, so their paths make a logarithmic spiral towards the centre.
How far do they crawl before they meet?
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Lets assume the bugs crawn with the speed V
If you draw a square ABCD this square's diagonal will decrease at the speed of V/sqr(2) (since the insects direction of travel is always 45 degrees from the diagonal), and thus take sqr(200)*cm*sqr(2)/V=20cm/V time to reach 0. Since the insects travel at speed V, they will of course crawl 20 centimeters.
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