Mixed Speeds, Best Path
- John Golden
I was reading about some optimal ants this morning, that choose the fastest path as opposed to the shortest path. This is a classic problem in math, and that idea is known as Fermat's Principle. So I was curious about making an experiment in GeoGebra for this idea. How good are people at finding the best path? Ants: http://cab1729.tumblr.com/post/46932123377/ants-follow-fermats-principle-of-least-time-ants Fermat's Principle: http://en.wikipedia.org/wiki/Fermat%27s_principle Tim Pennings' dog, who also has studied Fermat: http://www.maa.org/features/elvisdog.pdf Can you find the best path? What about in general: which factors matter? How do they determine the best path?
More GeoGebra at mathhombre.blogspot.com.