March 14, or 3/14, is known as “Pi Day” because of its resemblance to the first three digits in the decimal expansion of $\pi$ (pi), which is defined as the ratio of a circle’s circumference to its diameter: \[ \pi = \frac{C}{D} = 3.14\ldots \] As “the circle constant”, $\pi$ is the object of virtually unlimited adulation, so you are probably under the impression that $\pi$ is a particularly important number. I am sorry to report that you have been misinformed.

The true circle constant is the ratio of a circle’s circumference to its *radius*, not to its diameter. This number, called $\tau$ (tau), is equal to $2\pi$, so $\pi$ is $\frac{1}{2}\tau$—and March 14 is thus **Half Tau Day**. (Of course, June 28, or 6/28, is **Tau Day** itself.) Although it is of great *historical* importance, the mathematical significance of $\pi$ is simply that it is one-half $\tau$.

But how can this be? What about trigonometry? What about Euler’s identity? What about

$\pi r^2$? Can $\pi$ really be wrong? All your questions and more are answered here, in an article called
*The Tau Manifesto*.