'On Pi is wrong, and the Tauist Movement'
$ \pi $ is perhaps the most well known mathematical constant in the world, and its significance in mathematics cannot be overstated. $ \pi $ has been thoroughly studied by the most brilliant minds in the history of mathematics, is part of the most elementary mathematics education for the young students, and now is under attack by growing number of scientists who think that this magnificent constant is wrong.
Well, not really- $ \pi $ is still a transcendental number with decimal value 3.14159…. What is wrong is its undeserved adulation and sanctity. The constant deserving the glory, according to Bob Palais, professor at University of Utah and the author of the much discussed paper “Pi is wrong”, is $ \tau $.
Tal: Why $ \pi $? Geometrically, $ \pi $ is ratio of circle’s circumference to its diameter. This is unnatural – it is with radius, not diameter, that we define circles with. Therefore, I think it is more natural to describe the ration of circumference to the radius of the circle, $ circumference/radius $ = $ 2\pi $ = $ \tau $. Then the equation for circumference is simpler, namely $ Circumference = r\tau $.
Ip: Your insight is shortsighted, young grasshopper. You simplify the formula for circumference by sacrificing the formula for the area. With $ \tau $, the area of the circle now becomes $ A = \frac{1}{2}\tau r^2 $.
What is so unnatural about diameter? Is the ratio of circumference, one full rotation around the circle, to radius, HALF across the circle, any more natural?
Tal: Perhaps not, but the area of the circle defined by $ \tau $, although a bit more bulky, serves an educational purpose. This comes in two fold: one is that it is now obvious that the area of the circle is the antiderivative of circumference, and the second is that the formula is not unfamiliar to us all. Where have you seen another formula bearing similar structure of 1/2*x*y^2? (think energy).
Ip: Well, that's a physicists' argument. They are strange.
Tal
