The Tau Manifesto

Your Pi Day festivities may have been canceled this year, but get ready to celebrate Tau Day on June 28th!

The Tau Manifesto proposes that we should all consider — and
perhaps teach — the benefits of \(\tau = 6.283185\ldots\) over that in-hindsight-poorly-named \(\pi\).
For one thing, by virtue of being the *actual* circle constant, it simplifies the formula for the
circumference of a circle:

Then we can compute the area of a circle by summing the areas of an infinitude of infinitesimally thin triangular slices with height \(r\) and combined base lengths \(C\) to find

\[A = \frac{1}{2}Cr = \frac{1}{2}\tau r^2\]The measure of a full circle is \(\tau\) radians; the measure of one-third of a circle is \(\frac{1}{3}\tau\) radians. And of course \(e^{i\tau} = 1\).

Food for thought.