This might seem like another math post… but it’s not! It’s a geometry post! And geometry is fun, beautiful and easy. After all, it’s just circles and lines and angles. Well, mostly. Like anything, if you really want to get into it, then things can get complex (math pun; sorry). But considering it was invented thousands of years ago, can it really be that much harder than, say, the latest smart phone?
Even the dreaded trigonometry is fairly simple once you grasp the basic idea that the angles of a triangle are directly related to the length of its sides. (Okay, admittedly, that’s a bit of a simplification. The (other two) angles of a right-angle triangle are directly related to the ratios of the length of its sides, but still.)
However, this isn’t about trig; this is about tau!
What the heck is tau? I’m so glad you asked! Here’s the short answer: it’s two times pi.
(To be honest, I don’t actually like pie, because I don’t like cooked fruit. Cooking fruit, and then adding a bunch of sugar, seems to me like a horrible thing to do fresh fruit. It’s safe to say there is no form of cooked fruit I particularly like, even a little. And, no, I’m not really big on jams or jellies. So you can have my pie. Or twice my pie. I’ll have the cake!)
Why tau and not pi? It’s very simple, and it involves something that’s bugged me since I first saw the very simple equation for calculating the circumference (C) of a circle given its radius (R):
“What the heck is that ‘2’ doing in there,” I wondered? Why not use the circle’s diameter (D) — which is twice its radius? Then you get a much simpler formula:
And this version also makes it very clear how pi is simply the ratio of the diameter to the circumference. It makes one wonder why we use the radius instead of the diameter.
As it turns out, there’s actually a good reason for using the radius. In trigonometry (and other circular or sinuous geometry), it simplifies things enormously if we start with a circle where we assume the radius is one.
One what? Doesn’t matter. One inch, one foot, one mile, whatever size we happen to be dealing with, we assume the radius is one of them. Doing that creates what’s called the unit circle.
There is also that trigonometry (and geometry!) does care about the radius of a circle much more (like, all the time) than than the diameter. If you’re dealing with arcs (partial circles), for example, there really isn’t a diameter. And if you’re setting a compass to draw a circle, obviously you’re setting its radius.
So the radius is important and useful, but pi — which lies at the root of all of this — is the ratio of a circle’s diameter and circumference. Which means we’re stuck with the R and the 2.
In fact, that pesky 2 (or its friends 4 and 8) shows up in a lot of formulas that use pi, which has led many to imagine a new constant that’s twice the pi. They call this new constant tau (τ).
Using the Greek tau makes sense when you know that originally Albert Eagle wanted to define it as π/2, and if you chop π in half you get τ. As it turned out, no one else used half the pi; instead they decided they liked twice the pi. And it does make things simpler. Now the formula for a circle’s circumference (given its radius) is:
Which brings us to Tau Day.
If pi is 3.14159… then tau is 6.28318… (both of these go on forever without repeating). Many folks like to celebrate Pi Day, which is 3/14. They’ll be especially happy next year when Pi Day falls on 3/14/15.
Tau Day, therefore, is 6/28. Today! (Happy Tau Day!!) Unfortunately, fans of tau will have to wait until 2031 for the really big party (6/28/31).
It also turns out that Tau Day has some extra-special significance to me, but you’ll have to wait until tomorrow to find out why (I promise it has absolutely nothing to do with math — or geometry).
Meanwhile: Happy Tau Day! Eat twice the pie!!