Recently, I’ve heard a lot about the number τ, and I find the whole thing a bit odd.
Here’s how it goes:
The number π is the ratio of a circle’s circumference to its diameter. It’s been known about for thousands of years and is an extremely useful number which appears in all sorts of unusual and unexpected places. It’s not only irrational but also trancendental, which means you can’t write it down exactly using fractions or even square roots. Its decimal expansion begins 3.14159… and a not-too-bad approximation using fractions is 22/7.
People are so enamoured with π that they celebrate π day (14th of March), and π approximation day (22nd of July) — in fact, I will be celebrating π approximation day by writing the digits of π on the street in Adelaide.
But here’s the thing: some people claim that π is not the best number to use as your fundamental circle constant. This is because, if you represent angles as distances around circles (which is what mathematicians do), then π only represents half of the circle. Therefore, these people claim that you should use instead 2π — which they call τ. Vi Heart gives a very impassioned talk on this on YouTube: http://www.youtube.com/watch?v=jG7vhMMXagQ, and others have launched τ day (28th of June) as an alternative to π day.
Included in their reasoning to throw out π and embrace τ is a claim that it’s pedagogically more sound — that it’s confusing for the fundamental constant to only represent half a circle, and that many more formulas are easier to work with and easier to remember with τ rather than π. For example, they cite the trig functions and how they repeat themselves every τ as opposed to every π.
But this is my main bug-bear: of course it’s not easier! The switch in people’s minds from degrees to radians is such a huge jump that whether you use π or τ is really not going to make all that much of a difference! And while many formulas are nicer with τ, others are just uglier (in my mind!).
It just says to me that you can be passionate about something loudly enough and lots of people are likely to agree with you.
But I have one more thing to add: If you were going to work with a new circle constant, I think you should use not 2π, but π/2 — let’s call it η. You see, η represents a right angle, which to me is an extremely fundamental thing in our modern lives. And moreover, it represents the ratio of a semicircle to its diameter. That is, if you want to go from A to B, it’s how many times further you go if you go around a circular path as opposed to in a straight line. That makes a lot more sense to me than either the circumference/diameter, or the circumference/radius. Finally, the trig functions repeat their shape (if not their orientation) every η so the very constant you use would remind you of this simple fact. Yes, if you were going to define a new constant, I reckon η makes heaps more sense than τ.
But of course, I don’t care quite enough about this to make an empassioned speech about it on YouTube, so it’s unlikely anyone will listen. 😉
[NOTE: I do actually respect Vi Hart very much and wholeheartedly support her work in the physical and musical representation of maths, and also her use of YouTube to encourage play in maths rather than rote learning. I just don’t agree with her opinions about π.]