Lesson plan
Mice problem
In mathematics, the mice problem is a continuous pursuit–evasion problem in which a number of mice (or insects, dogs, missiles, etc.) are considered to be placed at the corners of a regular polygon. In the classic setup, each then begins to move towards its immediate neighbour (clockwise or anticlockwise). The goal is often to find out at what time the mice 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 unit-length sides, the distance between neighboring mice decreases at a speed of 1 - \cos(2\pi/n) , so they meet after a time of 1/\bigl(1 - \cos(2\pi/n)\bigr) .
Article summary
In mathematics, the mice problem is a continuous pursuit–evasion problem in which a number of mice (or insects, dogs, missiles, etc.) are considered to be placed at the corners of a regular polygon. In the classic setup, each then begins to move towards its immediate neighbour (clockwise or anticlockwise). The goal is often to find out at what time the mice 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 unit-length sides, the distance between neighboring mice decreases at a speed of 1 - \cos(2\pi/n) , so they meet after a time of 1/\bigl(1 - \cos(2\pi/n)\bigr) .
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.