Happy Half Tau Day!

The π is a lie…

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, since $\tau = 6.28\ldots$, 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.

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