Einstein and Pi

Sean Carroll in Preposterous Universe:

ScreenHunter_554 Mar. 15 19.50Each year, the 14th of March is celebrated by scientifically-minded folks for two good reasons. First, it’s Einstein’s birthday (happy 135th, Albert!). Second, it’s Pi Day, because 3/14 is the closest calendrical approximation we have to the decimal expansion of pi, π =3.1415927….

Both of these features — Einstein and pi — are loosely related by playing important roles in science and mathematics. But is there any closer connection?

Of course there is. We need look no further than Einstein’s equation. I mean Einstein’sreal equation — not E=mc2, which is perfectly fine as far as it goes, but a pretty straightforward consequence of special relativity rather than a world-foundational relationship in its own right. Einstein’s real equation is what you would find if you looked up “Einstein’s equation” in the index of any good GR textbook: the field equation relating the curvature of spacetime to energy sources, which serves as the bedrock principle of general relativity. It looks like this:


It can look intimidating if the notation is unfamiliar, but conceptually it’s quite simple; if you don’t know all the symbols, think of it as a little poem in a foreign language.

More here.