I already knew about how dogs take the optimal path, running and swimming, to fetch a frisbee, a task we would use calculus for.

Of course, the plants and animals aren't doing what we do, but these stories get me shaking my head in wonder.

**What other examples do you know of?**

[Thanks, David Petersen, for tweeting this.]

Several years ago I went to a nice talk by Qinglan Xia that uses optimal transport calculations to simulate the formation of leaves. Varying certain parameters gives theoretical leaves that look an awful lot like oak and maple leaves!

ReplyDeletehttp://www.ma.utexas.edu/users/qlxia/Research/leaf.pdf

Nice! Maybe I'll see if I can read that while I'm on the plane on Wednesday.

ReplyDeleteWater goes down the hill in the (locally) optimized manner. The globally optimal path may be different, though.

ReplyDeletePlanets, moons and other celestial objects arrange themselves in breathtakingly organized ways. So does the rest of the physical universe, when you think about it.

However, I don't consider any of that math, because these activities lack shareable descriptions (or formalizations). I had to struggle with that one for my "baby algebra"! But babies, unlike plants, streams and planets, can use signs.