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python-peps / pep-0628.txt

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PEP: 628
Title: Add ``math.tau``
Version: $Revision$
Last-Modified: $Date$
Author: Nick Coghlan <ncoghlan@gmail.com>
Status: Deferred
Type: Standards Track
Content-Type: text/x-rst
Created: 2011-06-28
Python-Version: 3.x
Post-History: 2011-06-28
Resolution: TBD


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 Deferral
============

The idea in this PEP was first proposed in the auspiciously named
`issue 12345`_. The immediate negative reactions I received from other core
developers on that issue made it clear to me that there wasn't likely to be
much collective interest in being part of a movement towards greater clarity
in the explanation of profound mathematical concepts that are unnecessarily
obscured by a historical quirk of notation.

Accordingly, this PEP is being submitted in a Deferred state, in the hope
that it may someday be revisited if the mathematical and educational
establishment choose to adopt a more enlightened and informative notation
for dealing with radians.

Converts to the merits of ``tau`` as the more fundamental circle constant
should feel free to start their mathematical code with ``tau = 2 * math.pi``.

.. _issue 12345: http://bugs.python.org/issue12345


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 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

.. _Tau Manifesto: http://tauday.com/
.. _Pi is (still) wrong: http://www.youtube.com/watch?v=jG7vhMMXagQ
.. _Pi is wrong!: http://www.youtube.com/watch?v=IF1zcRoOVN0
.. _a page of resources: http://www.math.utah.edu/~palais/pi.html


Copyright
=========

This document has been placed in the public domain.

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