Consider four cities, each is located at a corner of a square.

Find the shortest possible way to join the cities by segments of straight roads.

One possible (non-optimum) solution is just lines along three sides of the square.

Allow for more than one possible optimum solution.

Does your solution maintain the four-fold symmetry of the original square?

I use this example (which I first heard from my Ph.D advisor, Jim Sauls, in his first lecture in a graduate class on condensed matter).

I now give it in an undergraduate course on thermodynamics of condensed matter. Here is a draft of the lecture for monday.

It is one of my favourite because it also discusses space shuttle experiments and shows some cool videos involving broken symmetry in soap films.

Hmm. I just tried looking at the solution to the four city problem, but the Google Docs version of the presentation doesn't show the lines :(

ReplyDeleteJust by intuition, I'd assume the solution looks like a letter Y above an upside down letter Y.