Happy π Day!
Saturday is March 14, or, as it’s written in the U.S., 3/14. That makes it Pi Day, because the mathematical constant π is roughly equal to 3.14. Nerds celebrate this date every year, because, well, we’re nerds. Duh.
But this year’s π Day is special: It’s the year 2015, so the date is 3/14/15, giving us two more decimal places of the famous constant. In fact, if you celebrate it at 9:26:53 today, you get π to nine decimals: 3.141592653. Since the next digit is a 5, you can even round up and celebrate π Day for an extra second. Woohoo!
Why is π special? Most of us learn it because it’s the ratio of a circle’s circumference to its diameter. That’s pretty handy in geometry, but it goes much, much further than that. π appears in mathematical formulae all over the place, even where you might not expect it to. For some reason it appears to be woven into the very fabric of the Universe, popping up every time you look deeper into mathematics and physics.
In honor of this ubiquitous number, here are 8 (or 2π if you round down) facts about it you may or may not know. If you already know them, congrats! You’re a nerd. If not, then yay! You learned something. I can’t think of a better way to celebrate π Day than that.
A Year of π
Did you know there are different kinds of years? I won’t go into details (you can read all about them here, and I do mean all about them), but for our calendar we use what’s called a tropical year, which is 31,556,941 seconds long.
By coincidence, that is very close to π x 10 million! In fact, it’s off by less than half a percent. So if you need to know how many seconds there are in a year—which happens surprisingly often in my career— π x 10 million is a handy number to remember.
There’s something of an urban legend that in 1897, Indiana tried to legislate the value of π to be exactly 3. That’s not precisely true. What happened was that an amateur mathematician had been working on a method to square the circle—to construct a square with the same area as a circle of given radius, using only a straightedge and a compass—and thought he found a solution (he hadn’t; there isn’t one). He submitted it to the Indiana Legislature, but it wasn’t ratified. His work didn’t even really say that π = 3; any value he found for π was incidental. But over the years, the story got warped, and now people think Indiana has that law in its books.
But that’s ridiculous. The government would never try to legislate a basic mathematical or scientific truth.
Anyway, there are other stories involved, like a joke story about Alabama redefining π, or the Bible stating it’s equal to 3. I find stories like this amusing. π is what it is, and humans trying to redefine it are, to coin an apropos phrase, trying to square the circle.
When I was a kid, there was a huge industry in “ancient mysteries.” There still is, sadly—because I mean made-up mysteries, not real ones. Aliens didn’t help Hannibal cross the Alps, there’s no black hole in the Bermuda Triangle (the Bermuda Triangle doesn’t even exist), and the Egyptians didn’t really know about π.
Yeah, I’ve read quite a few breathless websites claiming they did. It’s even, they say, built into the pyramids! Well, one pyramid. Well, kinda. Basically, if you measure the circumference of the base of the Great Pyramid of Khufu and divide it by the height, you get a close approximation of 2π.
The thing is, that’s true! But it almost certainly wasn’t on purpose. It’s more likely to do with the slope of the wall chosen by the builders, which would drive the relationship between circumference and height. Also, many other pyramids (which had similar slopes) don’t have that same ratio, making it less likely to be mysterious ancient knowledge, and more a case of cherry-picking.
Mmmmm, cherry π picking.
π in Your i
Leonhard Euler was one of the greatest mathematicians of all time. He found a very weird relationship, called an identity, that goes like this: eiπ + 1 = 0. It’s a special case of a more generalized formula, but it’s true. e is the base of the natural logarithm, and i is the square root of -1, called an imaginary number (I’ll note it exists, in the sense that it has meaning in math, so the term “imaginary” is misleading).
This one simple formula has five of the most basic numbers in all of math in it, and they have this relatively simple relationship. Why is π in there? Well, the general equation has sines and cosines in it, and those have to do with circles, which is all about π! But the way it works out is still simple and elegant and beautiful. Also a bit mind-twisty. Actually, it’s a lot mind-twisty. But there you go.
Click here to read more.
SOURCE: SLATE, Phil Plait