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*So if you love ** pi**, you’ll really love

**, since it’s twice as much pie.**

*tau*(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

**? 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):**

*pi*“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

**. They call this new constant**

*pi***(**

*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

**in half you get**

*π***. As it turned out, no one else used half the**

*τ***; 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:**

*pi*Which brings us to Tau Day.

If ** pi** is 3.14159… then

**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*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!!*

June 28th, 2014 at 4:23 pm

Ha! Can’t fool me! Geometry = Math!

If you aren’t going to eat your slice of the pi, pass it over!

June 28th, 2014 at 5:00 pm

Well, yeah, but really pretty and fun math (and pretty fun math)! If you like

geology, ya gotta likegeometry, right? 🙂First come, first served: The pi is all yours!

June 28th, 2014 at 6:23 pm

Oh yes, good old Survey 101 and how to triangulate. But I can’t think of that now… I’ve got some pi to attend to! 😉

June 28th, 2014 at 9:21 pm

Enjoy! I’m still puzzling over the circle’s area formula:

pi r squared. I don’t get it; I thought pie are round! 😀August 18th, 2015 at 3:26 am

Down with pie. In agreement there. Cooked fruit plus lots of added sugar doesn’t appeal to me much either.

Continuing on in reading your post. Just felt the need to say that. 😉 Never heard of tau before tonight.

August 18th, 2015 at 7:07 am

Cake and cookies. And bread. Those are my downfall.

Tau is pretty geeky. You have to first be into good old π before you can be into its alternate! Tau does make some sense. You’d be surprised how often you find 2π or 4π or 8π in physics formulas.

November 30th, 2022 at 9:58 am

[…] say about either right now. In any event, I’m more inclined to celebrate Tau Day when we have double the pi(e). I do have something that’s maybe kind of vaguely of pi-ish. It’s something I was going […]