Monday, March 14, 2011

In Defense of Pi

I don't often do this, but, in honor of Pi Day, today I shall take up my words in the defense of traditional values. The traditional value in question is Pi itself. Much fuss has been made by proponents of a new circle constant, Tau, which would be equal to two times Pi. As much as it pains me to argue against the enigmatic and engaging Vi Hart, Pi is very much right.

While all concerned, except perhaps politicians and Biblical literalists, agree that Pi is an irrational value which is about 3.14, the argument is whether Pi is the value that we should consider important. Tau proponents argue that Tau is more sound pedagogically. Instead of half a circle being Pi radians, it would instead be half Tau radians. A quarter circle, a quarter Tau.

I cannot argue against this claim, it seems that high school mathematics would be made slightly simpler if we were to switch our focus from 3.14 to 6.28, however, arguing that we ought do this ignores a wealth of mathematical history. Humans have been seeking the decimal value of Pi as long as there has been civilization. The use of the Pi symbol to represent the value is over 300 years old, and was popularized by the mathematical great Euler. To cast Pi aside for slight notational clarity would be to show a remarkable disrespect for the historic foundations of mathematics.

Make no mistake, a slight notational clarity is the only true advantage of "Tau." Because "Tau" is just 2 times Pi, moving from one notation to the other is a trivial computation. If you have a value which is c*Pi, it will be (c/2)*Tau, if you have a value k*Tau, it will be 2k*Pi, easy as pie! Whatever notational clarity is gained by making the change, I would imagine more confusion would be created as we introduce a second, unnecessary, symbol for a concept that is already well represented.

Despite my nostalgia, I understand the systematic logic behind revoking Pluto's status as a planet. Despite my upbringing, I envy the computational clarity of the metric system. So please believe me when I say that I see no significant computational advantages to "Tau" over Pi!


elfarmy17 said...

I guess it's a toss-up: Do you make it easier for trig students, or keep things simple for the kids in pre-algebra?
I like how your main argument is a historical/traditional one, rather than a mathematical one. It ties things together nicely.
(Have you seen ViHart's video on the subject? It's very good.)

Kenny said...

The video I linked? ;) Yeah, I saw it, her videos are pretty much awesome in general!

My main argument is non-mathematical mostly because there is almost no mathematical argument to make, they are about the same thing. The other, smaller, reason is that on purely mathematical ground Tau actually does make a bit more sense.

elfarmy17 said...


Frank said...

I believe, Kenny!


I believe Kenny!