# Happy Pi Day!

In the United States, today is the nerdiest of unofficial holidays: Pi Day (or really, π Day), because as we write dates here, today is 3/14, the first three digits of the eponymous number.

Pi is one of the most important of mathematical numbers, popping up *everywhere* in physics. Most people know it because it’s how you get the circumference of a circle:π x the diameter (or 2 x π x the radius).

It’s also how you get the surface area of a sphere: 4 x π x radius^{2}. In honor of that, NASA released a photo showing half the surface area of our planet today, about 255,032,236 square kilometers (98,034,392 square miles) worth of it:

Pretty, isn’t it? To be fair, this is slightly less than half the Earth, since the satellite is about 36,000 kilometers (22,000 miles) above the Earth, and you'd need to be infinitely far away to see exactly half (due to the horizon problem). Still, close enough.

I like how they chose an image taken today by GOES 13, an Earth-observing weather satellite, which looks down upon the western hemisphere, including the U.S. In other parts of the world, dates are written in the form DAY-MONTH-YEAR, so to them today is (ignoring the year) 14-3, which doesn’t help. I guess for everyone else, π Day would be on the 31^{st} of April.

Um.

π really is amazing. It's irrational, which means it cannot be exactly represented as the ratio of two other numbers. It goes on forever after the decimal point, never ending and never repeating (some numbers, like 1/9, are just repeating numerals when expressed as a decimal). That seems so counterintuitive, but it’s just the way numbers are. The Universe is under no obligation to conform to our common sense. More likely, our brains didn’t evolve to grasp such things easily. Good thing we invented math to figure this stuff out!

Otherwise, we might never have discovered the elegance that is the greatest equation of all time:

e^{i}^{π} + 1 = 0

where **e** is the base of the natural logarithm, and **i** is the square root of -1. This is called the Euler Identity, and the more you think about it the more your brain will twist into a Möbius strip.

Anyway, π really is amazing. Did you know it pops up in an equation that describes how the Universe itself behaves as it expands? It’s related to prime numbers. It appears in so many integrals it would be impossible to list them all (here are a few). You can add up an infinite series of numbers to get π.

It’s so important that Carl Sagan wove it into the very fabric of his fantastic book *Contact* (the movie was based on it, and while very good, the book’s even better). I won’t spoil how, but you have to read to the very last page.

So π may be the most important single number in the entire cosmos. Take a moment today to contemplate any or all of this information; you’ll be the better for it. Pondering such things expands the brain, renews our sense of wonder, and adds to the joy of life.

C’mon! Who doesn’t want a slice of π?