Happy Tau Day folks! :)
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Nick Coghlan
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<table class="rfc2822 docutils field-list" frame="void" rules="none">
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<tr class="field"><th class="field-name">PEP:</th><td class="field-body">628</td>
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<tr class="field"><th class="field-name">Title:</th><td class="field-body">Add <tt class="docutils literal">math.tau</tt></td>
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<tr class="field"><th class="field-name">Version:</th><td class="field-body">$Revision$</td>
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<tr class="field"><th class="field-name">Last-Modified:</th><td class="field-body"><a class="reference external" href="http://svn.python.org/view/*checkout*/peps/trunk/pep-0628.txt">$Date$</a></td>
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<tr class="field"><th class="field-name">Author:</th><td class="field-body">Nick Coghlan <ncoghlan at gmail.com></td>
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</tr>
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<tr class="field"><th class="field-name">Status:</th><td class="field-body">Deferred</td>
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</tr>
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<tr class="field"><th class="field-name">Type:</th><td class="field-body">Standards Track</td>
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</tr>
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<tr class="field"><th class="field-name">Content-Type:</th><td class="field-body"><a class="reference external" href="/dev/peps/pep-0012">text/x-rst</a></td>
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<tr class="field"><th class="field-name">Created:</th><td class="field-body">2011-06-28</td>
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<tr class="field"><th class="field-name">Python-Version:</th><td class="field-body">3.3</td>
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</tr>
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<tr class="field"><th class="field-name">Post-History:</th><td class="field-body">2011-06-28</td>
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</tr>
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<tr class="field"><th class="field-name">Resolution:</th><td class="field-body">TBD</td>
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</tr>
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</tbody>
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</table>
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<hr />
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<div class="contents topic" id="contents">
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<p class="topic-title first">Contents</p>
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<ul class="simple">
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<li><a class="reference internal" href="#abstract" id="id12">Abstract</a></li>
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<li><a class="reference internal" href="#pep-deferral" id="id13">PEP Deferral</a></li>
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<li><a class="reference internal" href="#the-rationale-for-tau" id="id14">The Rationale for Tau</a></li>
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<li><a class="reference internal" href="#other-resources" id="id15">Other Resources</a></li>
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<li><a class="reference internal" href="#id1" id="id16">References</a></li>
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<li><a class="reference internal" href="#copyright" id="id17">Copyright</a></li>
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</ul>
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</div>
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<div class="section" id="abstract">
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<h1><a class="toc-backref" href="#id12">Abstract</a></h1>
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<p>In honour of Tau Day 2011, this PEP proposes the addition of the circle
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constant <tt class="docutils literal">math.tau</tt> to the Python standard library.</p>
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<p>The concept of <tt class="docutils literal">tau</tt> (<tt class="docutils literal">τ</tt>) 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 <tt class="docutils literal">2 * pi</tt> (<tt class="docutils literal">2π</tt>).</p>
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</div>
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<div class="section" id="pep-deferral">
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<h1><a class="toc-backref" href="#id13">PEP Deferral</a></h1>
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<p>The idea in this PEP was first proposed in the auspiciously named
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<a class="reference external" href="http://bugs.python.org/issue12345">issue 12345</a> <a class="footnote-reference" href="#id2" id="id3">[1]</a>. 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.</p>
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<p>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.</p>
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<p>Converts to the merits of <tt class="docutils literal">tau</tt> as the more fundamental circle constant
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should feel free to start their mathematical code with <tt class="docutils literal">tau = 2 * math.pi</tt>.</p>
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</div>
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<div class="section" id="the-rationale-for-tau">
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<h1><a class="toc-backref" href="#id14">The Rationale for Tau</a></h1>
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<p><tt class="docutils literal">pi</tt> 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 <em>radius</em>. 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.</p>
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<p>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 <tt class="docutils literal">tau</tt>. A quarter circle is
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<tt class="docutils literal">tau/4</tt>, a half circle is <tt class="docutils literal">tau/2</tt>, seven 25ths is <tt class="docutils literal">7*tau/25</tt>, etc. In
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contrast with the equivalent expressions in terms of <tt class="docutils literal">pi</tt> (<tt class="docutils literal">pi/2</tt>, <tt class="docutils literal">pi</tt>,
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<tt class="docutils literal">14*pi/25</tt>), the unnecessary and needlessly confusing multiplication by
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two is gone.</p>
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</div>
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<div class="section" id="other-resources">
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<h1><a class="toc-backref" href="#id15">Other Resources</a></h1>
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<p>I've barely skimmed the surface of the many examples put forward to point out
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just how much <em>easier</em> and more <em>sensible</em> many aspects of mathematics become
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when conceived in terms of <tt class="docutils literal">tau</tt> rather than <tt class="docutils literal">pi</tt>. 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:</p>
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<blockquote>
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<ul class="simple">
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<li>Michael Hartl is the primary instigator of Tau Day in his <a class="reference external" href="http://tauday.com/">Tau Manifesto</a> <a class="footnote-reference" href="#id4" id="id5">[2]</a></li>
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<li>Bob Palais, the author of the original mathematics journal article
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highlighting the problems with <tt class="docutils literal">pi</tt> has <a class="reference external" href="http://www.math.utah.edu/~palais/pi.html">a page of resources</a> <a class="footnote-reference" href="#id10" id="id11">[5]</a> on the
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topic</li>
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<li>For those that prefer videos to written text, <a class="reference external" href="http://www.youtube.com/watch?v=IF1zcRoOVN0">Pi is wrong!</a> <a class="footnote-reference" href="#id8" id="id9">[4]</a> and
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<a class="reference external" href="http://www.youtube.com/watch?v=jG7vhMMXagQ">Pi is (still) wrong</a> <a class="footnote-reference" href="#id6" id="id7">[3]</a> are available on YouTube</li>
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</ul>
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</blockquote>
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</div>
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<div class="section" id="id1">
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<h1><a class="toc-backref" href="#id16">References</a></h1>
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<table class="docutils footnote" frame="void" id="id2" rules="none">
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<colgroup><col class="label" /><col /></colgroup>
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<tbody valign="top">
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<tr><td class="label"><a class="fn-backref" href="#id3">[1]</a></td><td><a class="reference external" href="http://bugs.python.org/issue12345">http://bugs.python.org/issue12345</a></td></tr>
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</tbody>
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</table>
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<table class="docutils footnote" frame="void" id="id4" rules="none">
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<colgroup><col class="label" /><col /></colgroup>
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<tbody valign="top">
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<tr><td class="label"><a class="fn-backref" href="#id5">[2]</a></td><td><a class="reference external" href="http://tauday.com/">http://tauday.com/</a></td></tr>
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</tbody>
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</table>
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<table class="docutils footnote" frame="void" id="id6" rules="none">
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<colgroup><col class="label" /><col /></colgroup>
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<tbody valign="top">
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<tr><td class="label"><a class="fn-backref" href="#id7">[3]</a></td><td><a class="reference external" href="http://www.youtube.com/watch?v=jG7vhMMXagQ">http://www.youtube.com/watch?v=jG7vhMMXagQ</a></td></tr>
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</tbody>
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</table>
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<table class="docutils footnote" frame="void" id="id8" rules="none">
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<colgroup><col class="label" /><col /></colgroup>
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<tbody valign="top">
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<tr><td class="label"><a class="fn-backref" href="#id9">[4]</a></td><td><a class="reference external" href="http://www.youtube.com/watch?v=IF1zcRoOVN0">http://www.youtube.com/watch?v=IF1zcRoOVN0</a></td></tr>
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</tbody>
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</table>
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<table class="docutils footnote" frame="void" id="id10" rules="none">
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<colgroup><col class="label" /><col /></colgroup>
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<tbody valign="top">
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<tr><td class="label"><a class="fn-backref" href="#id11">[5]</a></td><td><a class="reference external" href="http://www.math.utah.edu/~palais/pi.html">http://www.math.utah.edu/~palais/pi.html</a></td></tr>
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</tbody>
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</table>
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</div>
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<div class="section" id="copyright">
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<h1><a class="toc-backref" href="#id17">Copyright</a></h1>
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<p>This document has been placed in the public domain.</p>
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