In case you’re not familiar with the holiday, today is Pi Day, which falls on 3/14 since π ≈ 3.14159 etc. Generally the feast is observed with pies (for some strange reason), be they fruit, meat, or pizza. Other round foods are also permissible, though not as clever. Sometimes people even bother measuring their radius and circumference before chowing down, but that part is optional.
In honor of the day, I’m doing a quick post on what some think of as pi’s greatest rival—tau. The relationship between the two numbers is a simple τ = 2π (∼6.28318), and there are some good arguments for teaching geometry and trigonometry in terms of tau rather than pi.
This idea was brought into general consciousness apparently by an opinion piece published in 2001 in The Mathematical Intelligencer, which suggested redefining pi to be twice its current value. Bob Palais argued that this redefined pi would make learning angles more intuitive (since a full circle would then be π radians rather than 2π) and would simplify many equations that currently use 2π or multiples thereof.
Redefining pi, while a promising idea to some, seems a little confusing, so the letter tau is more popularly used these days. Here’s what it would do for some of the basic formulas for circles and spheres:
Admittedly, the equation for a circle’s area now has a fraction it didn’t before, but as Palais points out, this is a form that’s very similar to other simple expressions in physics and math, like kinetic energy (½mv²). In general, thinking of a single quantity where we often have to think of “2π” seems very sensible.
Why do we even have pi, then? A Scientific American article on the pi vs. tau controversy explains a common-sense reason: In the early civilizations that tried to come up with values for pi, measuring the diameter of a circle was much easier than measuring the radius. Logically, the number they came up with was one that related the circumference and diameter of a circle. This number then became ingrained in the way we think about angles, although pi itself wasn’t associated with it until Leonhard Euler used it in the eighteenth century.
There are many traditions worth keeping, whether because they’re still the best way we have of doing something or because it would be more trouble than it’s worth to change. It’s hard to go against convention, especially for such a universally used idea. Will my children someday learn their sines and cosines with tau instead of pi? Only time will tell.
One thing I can say about the battle of tradition and innovation—6/28 may be just as good a day to celebrate, but there’s no substitute for the hallowed tradition of some mathematical pie.