There’s an article on the BBC website celebrating the mathematical ratio:

The article also says:

Pi shows up everywhere. In mathematics, pi appears in many fundamental equations that have nothing to do with circles. In science, pi is inextricable from measuring everything from ocean waves to economic statistics.

Pi is found in the very measurements of the Great Pyramid at Giza. And if you divide the length of a river from source to mouth across a gently sloping plane by its direct length “as the crow flies”, you’ll find pi.

Does anyone have any more details on these non-circular applications of pi?

Well, anything with pi in it is related to circles since pi is related to circles. But in a lot of places the connection to circles is non-obvious.

My favorite is the Euler identity, which is e[sup]pi*i[/sup] = -1

I don’t quite understand what the article is trying to say about rivers. I think they’re talking about viewing a river as the hypotenuse of a right triangle. In that case, the ratio of the height of the river to the length can be found by trigonometry, and the trig functions are all functions of pi (and each other.)

Every October 23rd, my high school would celebrate Mole Day. My chemistry teacher’s preferred festivity was igniting small balloons filled with exactly one mole of H[sub]2[/sub].