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Bugs' Traffic
after Martin Gardner

Four bugs, the Green, the Yellow, the Red, and the Blue occupy the corners of a square as shown in the illustration. The side of the square is 10 units long. Simultaneously the Green bug starts to crawl directly toward the Yellow one, the Yellow toward the Red, the Red toward the Blue and the Blue toward the Green.

Since all four bugs crawl at the same constant rate, they will describe four congruent logarithmic spirals which meet at the center of the square.

Thus the question is: how far does each bug travel before they meet?

 

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Last Update
February 1, 2004

 
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