|Author:||Nick Coghlan <ncoghlan at gmail.com>|
In honour of Tau Day 2011, this PEP proposes the addition of the circle constant math.tau to the Python standard library.
The concept of tau (τ) is based on the observation that the ratio of a circle's circumference to its radius is far more fundamental and interesting than the ratio between its circumference and diameter. It is simply a matter of assigning a name to the value 2 * pi (2π).
This PEP is now accepted and math.tau will be a part of Python 3.6. Happy birthday Nick!
pi is defined as the ratio of a circle's circumference to its diameter. However, a circle is defined by its centre point and its radius. This is shown clearly when we note that the parameter of integration to go from a circle's circumference to its area is the radius, not the diameter. If we use the diameter instead we have to divide by four to get rid of the extraneous multiplier.
When working with radians, it is trivial to convert any given fraction of a circle to a value in radians in terms of tau. A quarter circle is tau/4, a half circle is tau/2, seven 25ths is 7*tau/25, etc. In contrast with the equivalent expressions in terms of pi (pi/2, pi, 14*pi/25), the unnecessary and needlessly confusing multiplication by two is gone.
I've barely skimmed the surface of the many examples put forward to point out just how much easier and more sensible many aspects of mathematics become when conceived in terms of tau rather than pi. If you don't find my specific examples sufficiently persausive, here are some more resources that may be of interest:
- Michael Hartl is the primary instigator of Tau Day in his Tau Manifesto 
- Bob Palais, the author of the original mathematics journal article highlighting the problems with pi has a page of resources  on the topic
- For those that prefer videos to written text, Pi is wrong!  and Pi is (still) wrong  are available on YouTube
This document has been placed in the public domain.