In 2010, physicist and educator Michael Hartl published something he called *The Tau Manifesto*, a piece of writing that makes a surprisingly controversial assertion: pi is wrong.

That’s not to say that our measurements of it are off; few things are easier to compute to high precision 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, and the argument for it is actually kind of mind-blowing.

Fun fact: If you know 50 digits of pi, you already know 50 digits of tau, if you’re really good at mental math. |

At first, this whole thing might seem unnecessary or trivial. After all, it’s not much harder to write out “2π” than “T”, and changing over would mean rewriting a lot of geometry textbooks. But there’s a certain elegance to Hartl’s line of thinking. To begin with: angles can be measured in *degrees* or *radians*—in degrees, a full circle is 360°, but in radians, it’s 2 pi. Wouldn’t it be nicer to have the circle constant correspond to a full revolution? Pi shows up everywhere in physics and mathematics, but practically everywhere that pi 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. The Coulomb constant, which relates the magnitude of an electric charge to the strength of the electric field it creates, includes a factor of 4π—two for each of the intersecting planes you need to indicate points a three-dimensional space.

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.

*time integral*of that equation. Integral calculus can be scary, but mathematically it’s pretty simple—you add one to the exponent of the variable, and divide the whole quantity by the number you get when you do that. So the integral of g*t is just:

^{1}. Adding 1 gets us t

^{2}, and then we divide the whole thing by the new exponent, 2.

*m*:

*dr*.

Image from The Tau Manifesto, by Michael Hartl |

*dr*is their width. The long “s” shape indicates that we’re integrating, and the 0 and r tell us that we’re looking at the sum of the areas of rings with circumferences between 0 and r—the total radius of the circle.

*r*. Fortunately, that’s what pi is for—relating the circumference of a circle to the radius:

*The Tau Manifesto*struck me as worth sharing. It reminded me that there are a million of those connections out there, some in plain sight, just waiting to be realized—and that’s an exciting feeling, because it means a lifetime experiencing the wonder of discovery.

*Thanks go out again to Michael Hartl for writing The Tau Manifesto, which provided the above mathematical argument and which you can read in its entirety here.*