Mice problem
In mathematics, the mice problem is a problem in which a number of mice (or bugs, dogs, missiles, etc.), starting from the corners of a regular polygon, follow each other and it must be determined when they meet.
The most common version has the mice starting at the corners of a unit square, moving at unit speed. In this case they meet after a time of one unit, because the distance between two neighboring mice always decreases at a speed of one unit. More generally, for a regular polygon of n sides, the distance between neighboring mice decreases at a speed of 1 − cos(2π/n), so they meet after a time of 1/(1 − cos(2π/n)).[1] [2]
For all regular polygons, the mice trace out a logarithmic spiral, which meets in the center of the polygon (as shown on the right). [3]
References
- ^ George Gamow, Stern, Marvin (1958), Puzzle math, New York: Viking press, pp. 112–114
- ^ Édouard Lucas, (1877), "Problem of the Three Dogs", Nouv. Corresp. Math. 3: 175–176
- ^ "Mice Problem". MathWorld. Retrieved 16 April 2013.
See also
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