101 lines
3.5 KiB
Plaintext
101 lines
3.5 KiB
Plaintext
PEP: 628
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Title: Add ``math.tau``
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Version: $Revision$
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Last-Modified: $Date$
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Author: Nick Coghlan <ncoghlan@gmail.com>
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Status: Deferred
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Type: Standards Track
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Content-Type: text/x-rst
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Created: 2011-06-28
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Python-Version: 3.x
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Post-History: 2011-06-28
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Resolution: TBD
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Abstract
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========
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In honour of Tau Day 2011, this PEP proposes the addition of the circle
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constant ``math.tau`` to the Python standard library.
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The concept of ``tau`` (``τ``) is based on the observation that the ratio of a
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circle's circumference to its radius is far more fundamental and interesting
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than the ratio between its circumference and diameter. It is simply a matter
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of assigning a name to the value ``2 * pi`` (``2π``).
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PEP Deferral
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============
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The idea in this PEP was first proposed in the auspiciously named
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`issue 12345`_. The immediate negative reactions I received from other core
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developers on that issue made it clear to me that there wasn't likely to be
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much collective interest in being part of a movement towards greater clarity
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in the explanation of profound mathematical concepts that are unnecessarily
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obscured by a historical quirk of notation.
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Accordingly, this PEP is being submitted in a Deferred state, in the hope
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that it may someday be revisited if the mathematical and educational
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establishment choose to adopt a more enlightened and informative notation
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for dealing with radians.
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Converts to the merits of ``tau`` as the more fundamental circle constant
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should feel free to start their mathematical code with ``tau = 2 * math.pi``.
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.. _issue 12345: http://bugs.python.org/issue12345
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The Rationale for Tau
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=====================
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``pi`` is defined as the ratio of a circle's circumference to its diameter.
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However, a circle is defined by its centre point and its *radius*. This is
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shown clearly when we note that the parameter of integration to go from a
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circle's circumference to its area is the radius, not the diameter. If we
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use the diameter instead we have to divide by four to get rid of the
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extraneous multiplier.
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When working with radians, it is trivial to convert any given fraction of a
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circle to a value in radians in terms of ``tau``. A quarter circle is
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``tau/4``, a half circle is ``tau/2``, seven 25ths is ``7*tau/25``, etc. In
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contrast with the equivalent expressions in terms of ``pi`` (``pi/2``, ``pi``,
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``14*pi/25``), the unnecessary and needlessly confusing multiplication by
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two is gone.
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Other Resources
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===============
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I've barely skimmed the surface of the many examples put forward to point out
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just how much *easier* and more *sensible* many aspects of mathematics become
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when conceived in terms of ``tau`` rather than ``pi``. If you don't find my
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specific examples sufficiently persausive, here are some more resources that
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may be of interest:
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* Michael Hartl is the primary instigator of Tau Day in his `Tau Manifesto`_
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* Bob Palais, the author of the original mathematics journal article
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highlighting the problems with ``pi`` has `a page of resources`_ on the
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topic
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* For those that prefer videos to written text, `Pi is wrong!`_ and
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`Pi is (still) wrong`_ are available on YouTube
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.. _Tau Manifesto: http://tauday.com/
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.. _Pi is (still) wrong: http://www.youtube.com/watch?v=jG7vhMMXagQ
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.. _Pi is wrong!: http://www.youtube.com/watch?v=IF1zcRoOVN0
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.. _a page of resources: http://www.math.utah.edu/~palais/pi.html
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Copyright
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=========
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This document has been placed in the public domain.
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..
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Local Variables:
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mode: indented-text
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indent-tabs-mode: nil
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sentence-end-double-space: t
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fill-column: 70
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coding: utf-8
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End:
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