Consider the following problem: a dog runs at the speed of 1 and swims at the speed of $s<1$. A dog is at a point $A$ of a shoreline and tries to get to a ball which is in the water at point $B$. He wants to get there as soon as possible. What path should the dog take? This is a very classical problem of optimization that can be found, with different contexts, in virtually every elementary calculus book. In fact, this is related to Snellâ€™s law of refraction. The author gives a ruler and compass construction of this and some other close related settings. This is a nice paper to be read by advanced high school students.

Reviewer:

Antonio M. Oller (Zaragoza)