We all know about Pi Day, that tasty holiday on March 14 where celebrations include reciting digits of Pi and eating pie. At MIT, we ate pizza pie, pine nuts, and dined on dozens of types of sugary and fruity pies. Today, on what’s usually called “2 Pi Day” (do you bake twice as many pies as you usually would?) we’re seeing headlines about “pi being under attack” and the movement to replace pi with another constant... tau?
Why tau instead of pi? We all know that pi (p) is the circumference (C) of a circle divided by its diameter (D):
Pi (p) is used constantly (no pun intended) in math, and shows up everywhere in nature. It’s irrational, meaning you can’t get it from a fraction of whole numbers, and it’s also transcendental, meaning that it’s not the root of a non-constant polynomial equation. Pi, however, isn’t the most fundamental constant that could be used in geometric and mathematical expressions: it’s actually “a confusing and unnatural choice” to be used as a circle constant, according to Dr. Michael Hartl of TauDay.com and author of the Tau Manifesto.
A more fundamental ratio for the circle constant is that of a circle’s circumference (C) to its radius (r):
This number is numerically equal to 2p (since the diameter is equal to 2r), and is called tau, or t, and like p, is also irrational and transcendental. Tau makes much more sense in mathematical formulas, especially in trigonometry: its value relates the full turn of a circle, not just half as with p, to a constant. Tau describes 360°, not just 180°. In this context, t is the more natural choice to use not just when talking about angles on a circle, but in general mathematics and beyond.
Dr. Kevin Houston of the University of Leeds (a recent convert to the tau camp from the pi contingent) provides an explanation of how t is more “natural” than p on YouTube:
The value 2p, or t, shows up almost everywhere that p does in mathematics: it appears in polar coordinates, quantum mechanics (h = h/2p), statistical distributions, Fourier transforms, and Riemann zeta function. It’s a lot less confusing to think of angles in terms of t rather than p---almost all trigonometric formulae use 2p rather than p, so why think about half of a circle with p when you could consider a whole circle and t? Using t in lieu of p would give you much more comprehensible special angles when dividing up a circle; rather than expressing angles in terms of fractions of p, it makes more sense to express them in fractions of t.
With all this background on t versus p, are you a follower of t or p? Is p “wrong” and “unnatural”, or would you rather see p retain its place as the most fundamental and tasty constant in circle mathematics? How are you celebrating 2 Pi or Tau Day? Let us know in the comments!