In 2010, physicist and educator Michael Hartl published something he called The Tau Manifesto, a piece of writing which put forth arguments for a surprisingly controversial assertion: π is wrong.
That’s not to say that our measurements of it are off, of course; few things are more readily calculable than the ratio of a circle’s circumference to its diameter. Instead, Hartl makes a compelling case for the idea that 2π, the ratio of a circle’s circumference to its radius, is a far more fundamentally significant and useful construct. He calls his new "circle constant" tau.
|Fun fact: If you know 50 digits of pi, you already know 50 digits of tau, if you're exceedingly good at mental math.|
At first, this might seem unnecessary or trivial. After all, it’s not much harder to write out “2π” than “T”, and changing over means that a lot of geometry textbooks would need rewriting. However, the line of thinking is not without its appeal; it’s intuitively pleasing that the circle constant should describe one full cycle of a sine wave, rather than half (as is the case with π). π shows up everywhere in physics and mathematics, but practically everywhere that π shows up, Hartl claims, tau would be simpler.
And indeed, when performing an angular integral, we integrate from zero to 2π. When reducing Planck’s constant h, we use a factor of 2π. Coulomb’s constant carries 4π, two for azimuth and two for altitude. Perhaps the only place where pi appears alone is in the formula for the area of a circle, a point which Hartl brings up and then proceeds to knock down with an argument so simple but striking that it bears repeating here, partly because it should be very familiar to anyone with a physics background.
|Image from The Tau Manifesto, by Michael Hartl|