Quote Originally Posted by BillJ View Post
Phil also once set a problem for his students - assuming a conical hill and all things equal, if you are to get from one side to the other, is it quicker to go over the top, around it, or somewhere in between?

Interestingly the answer is always somewhere in between - how far up the shoulder of the hill depends on how steep it is.

We've done a handful of mountain marathons together and discussed mathematics on the way. Happy Days!
I've also done some work on the conical hill problem. If you're really interested in the maths, I can send you a copy of what I've done.