A new place for activists: math
Published: Wednesday, March 14, 2012
Updated: Wednesday, March 14, 2012 09:03
Remember the unit circle? Of course you don’t. It’s a bunch of numbers lost in the fog of high school geometry. But it’s not your fault. It’s pi’s fault. Pi is wrong, and I want you to help make it right.
I don’t mean that pi is factually wrong; the ratio of a circle’s circumference to its diameter hasn’t changed. I mean that it’s the wrong choice of the circle constant because it leads to weird and unnatural situations. Let me explain.
Mathematicians don’t like to measure circles in degrees. They prefer radians, which are just a way of making every circle look like the unit circle, regardless of size. Because the unit circle has a radius of one, its diameter is two and its circumference is two−pi. Therefore, every circle has a circumference of two−pi radians. Pi radians is only half a circle. That’s all the math you need. I promise.
So, in classic textbook tradition, let’s apply math to a real−world situation where you would never actually need it. Say you’re cutting up your favorite circular fruit−filled pastry and your friend wants a mathematically precise amount. Where do you cut? The problem is that one pie isn’t one−pi — it’s two−pi. If you want an eighth of a pie, it’s a quarter pi, measured along the crust. It’s also really confusing, measured from anywhere.
The way to fix this is to make the circle constant the size of the whole circle, currently known only as two−pi. If I had a time machine, I’d go explain this to Leonard Euler and make pi twice as large, enough to cover the whole circle. Our beloved 3.14 would be known by a name that belies its semicircular nature — one pierogi, perhaps. But it turns out I don’t have a time machine (surprise!), so unless we want to change every math textbook and paper ever written, we’re stuck with pi meaning half a circle.
The next best thing is to give the true circle constant — around 6.28 — a name. We’re going to call it — drumroll please — tau. Tau is another Greek letter that looks kind of like pi, if you amputated one leg and moved the other to the middle. Tau is the ratio of a circle’s circumference to its radius (instead of to its diameter). Think of one tau as one turn. You want an eighth of a turn? That’s one−eighth tau. Half a pie? Half a tau — or as some people say, one−pi.
Contrary to what you might remember from calculus at 8:30 a.m. freshman year, math is supposed to be beautiful and simple. There are many other benefits of tau beyond making radians understandable to mere mortals, and arguments against tau that I could refute. We’re going to put them aside to address what I consider to be a great injustice: No university math department accepts tau. I want Tufts to be the first.
We’re a forward−thinking university full of activists. Tufts should accept all students, regardless of their numerical beliefs or angular orientation. Even though pi and tau are 180 degrees apart (literally), I think we can turn this thing around. All we need to do is show a few pi−ous administrators that they are, in fact, two pi−ous.
The effects will reach far beyond Tufts. The simplicity tau offers is not nearly as important for graduate students as it is for children first learning geometry. But since no one is going to teach nonstandard notation, tau will never catch on until higher education accepts it. Reducing math’s barrier to entry in middle school will lead to more scientists and engineers coming up with solutions for the world’s problems. It also means fewer people will be scared of math.
How can such a small bit of notation make people less scared of math? To revisit the unit circle, take the angle five−eighths tau. It’s immediately clear that it’s a little bit more than half a turn. But pi messes everything up. Substituting in, that’s ten−eighths pi, but the factors of two cancel, so it’s five−fourths pi. Scary mathematics, indeed. I want it out of our high schools and out of Tufts.
I’m not asking for much from our math department. I want the symbol tau to be officially accepted as an alternative way of writing two−pi on homework, exams and papers. Anyone who wants to continue to use pi can do so.
If you want to know more about tau, go to TauDay.com (if you’re an engineer or math major) or Google “Vi Hart tau” and feel lucky (if you’re not). They’re my sources for this op−ed, so consider them cited. If you want to know more about the movement to bring tau to Tufts, you’re going to have to make that news yourself.
Max Goldstein is a sophomore majoring in computer science.