Points A and B are on a plane surface, 1 mile apart. Suppose you must walk in a path consisting of N straight lines from point A to point B, such that at all times your (Euclidean) distance to point B is decreasing. What is the longest possible route length (as a function of N)?

Maybe it would be instructive to hold a competition for, say N=10?

Posted by Steven Lord on 2019-01-16 00:40:52