2010/02/19

road path problem

February 19th 2010 Posted to Uncategorized

Suppose there is a straight road, infinitely long at both ends, located 1 unit from your starting location. Find the most efficient path to reach the road, and the worst-case total length of this path.

The trivial but wrong way is to go for 1 unit in some direction, then trace the circumference of a unit-radius circle. The road will surely be found this way, but the path length is \(1+2\pi\), which can be improved upon.
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2008/10/3

triangular pursuit

October 03rd 2008 Posted to Uncategorized

Here’s a problem posed to me by a friend:

Consider an equilateral triangle ABC with edge length 1. At each vertex is an object that is capable of movement at exactly speed 1. Beginning at time 0, each of the three objects moves toward its initial adjacent neighbor object, as in a game of pursuit. Of course, by symmetry, the objects will meet at the incenter of ABC. The question: how far will they have traveled?
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