Happy Tau Day, the day when you’re supposed to eat two pies. As an avid Pi Day enthusiast, June 28th provides the perfect opportunity to celebrate twice! All the major festivities you see on Pi Day, from memorizing digits to making music to baking fruit manifolds with crust boundaries, it’s all there on Tau Day. Ultimate Tau Day (6/28/31) is only eight years away, so start preparing before it’s too late.
Part of the beauty of Tau (τ) is that it has a life outside of being the ratio of a circle’s circumference to its radius. π has been featured in too many blockbuster equations and gets recognized everywhere. While τ is a lesser known celebrity, it can explore other fields, like particle physics and neuroscience and programming languages.
Pi and Tau day are wonderful, but they’re not alone. Mathematically wonderful dates are everywhere. Other than just being Tau Day, the numbers in today’s date (6/28/23) provide a beautiful equation—
$$\Gamma(6) = (28 - 23)!$$
—with ! denoting factorial, but also excitement because this is exciting. Tomorrow gives us an even simpler equation:
$$6 = 29 - 23$$
And yesterday worked out quite nicely as well:
$$6 = \Gamma(27 - 23)$$
For years, I’ve played this little game with the date, trying to insert non-digit symbols around and between the numbers, creating a valid equation while preserving their order from left to right. I recommend you try it too, it’s a nice way to spend a few minutes. Today, I built a toy programming language (thanks τ) whose programs are valid date equations. Then I wrote a script that searched through a finite space of potential programs to find valid ones for the given date. It generated the solutions for the dates I just listed.
After playing this game for years, I’ve realized that finding an equation for the date is always possible. In fact, there are universal solutions, though they’re not always very exciting. For example, by taking advantage of properties of the sine function:
$$ \forall m, d, y \in \mathbb{N}, \sin((m + d)\tau) = \sin(y\tau) $$
Strangely, celebrating τ allows us to celebrate other days of the year rather mathematically. Yes, τ is a superstar, but it allows us to celebrate others through its mere presence.
The Tau Manifesto was written in 2010, spreading the voices of those who carried τ on their backs for years in relative silence. While the Tau Day community has certainly come a far way since then, τ is far from the spotlight it deserves. Until that moment, celebrate each day mathematically. This is just the beginning.