PEP: 628 Title: Add math.tau Version: $Revision$ Last-Modified: $Date$
Author: Alyssa Coghlan <ncoghlan@gmail.com> Status: Final Type:
Standards Track Content-Type: text/x-rst Created: 28-Jun-2011
Python-Version: 3.6 Post-History: 28-Jun-2011

Abstract

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).

PEP Acceptance

This PEP is now accepted and math.tau will be a part of Python 3.6.
Happy birthday Alyssa!

The idea in this PEP has been implemented in the auspiciously named
issue 12345.

The Rationale for Tau

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.

Other Resources

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 persuasive, 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

Copyright

This document has been placed in the public domain.