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<h1 class="page-title">PEP 628 – Add <code class="docutils literal notranslate"><span class="pre">math.tau</span></code></h1>
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<dl class="rfc2822 field-list simple">
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<dt class="field-odd">Author<span class="colon">:</span></dt>
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<dd class="field-odd">Alyssa Coghlan <ncoghlan at gmail.com></dd>
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<dt class="field-even">Status<span class="colon">:</span></dt>
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<dd class="field-even"><abbr title="Accepted and implementation complete, or no longer active">Final</abbr></dd>
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<dt class="field-odd">Type<span class="colon">:</span></dt>
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<dd class="field-odd"><abbr title="Normative PEP with a new feature for Python, implementation change for CPython or interoperability standard for the ecosystem">Standards Track</abbr></dd>
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<dt class="field-even">Created<span class="colon">:</span></dt>
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<dd class="field-even">28-Jun-2011</dd>
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<dt class="field-odd">Python-Version<span class="colon">:</span></dt>
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<dd class="field-odd">3.6</dd>
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<dt class="field-even">Post-History<span class="colon">:</span></dt>
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<dd class="field-even">28-Jun-2011</dd>
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<details><summary>Table of Contents</summary><ul class="simple">
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<li><a class="reference internal" href="#abstract">Abstract</a></li>
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<li><a class="reference internal" href="#pep-acceptance">PEP Acceptance</a></li>
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<li><a class="reference internal" href="#the-rationale-for-tau">The Rationale for Tau</a></li>
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<li><a class="reference internal" href="#other-resources">Other Resources</a></li>
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<li><a class="reference internal" href="#copyright">Copyright</a></li>
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</ul>
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</details></section>
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<section id="abstract">
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<h2><a class="toc-backref" href="#abstract" role="doc-backlink">Abstract</a></h2>
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<p>In honour of Tau Day 2011, this PEP proposes the addition of the circle
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constant <code class="docutils literal notranslate"><span class="pre">math.tau</span></code> to the Python standard library.</p>
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<p>The concept of <code class="docutils literal notranslate"><span class="pre">tau</span></code> (<code class="docutils literal notranslate"><span class="pre">τ</span></code>) 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 <code class="docutils literal notranslate"><span class="pre">2</span> <span class="pre">*</span> <span class="pre">pi</span></code> (<code class="docutils literal notranslate"><span class="pre">2π</span></code>).</p>
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</section>
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<section id="pep-acceptance">
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<h2><a class="toc-backref" href="#pep-acceptance" role="doc-backlink">PEP Acceptance</a></h2>
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<p>This PEP is now <a class="reference external" href="https://bugs.python.org/issue12345#msg272287">accepted</a> and <code class="docutils literal notranslate"><span class="pre">math.tau</span></code> will be a part of Python 3.6.
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Happy birthday Alyssa!</p>
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<p>The idea in this PEP has been implemented in the auspiciously named
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<a class="reference external" href="http://bugs.python.org/issue12345">issue 12345</a>.</p>
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</section>
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<section id="the-rationale-for-tau">
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<h2><a class="toc-backref" href="#the-rationale-for-tau" role="doc-backlink">The Rationale for Tau</a></h2>
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<p><code class="docutils literal notranslate"><span class="pre">pi</span></code> 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 <code class="docutils literal notranslate"><span class="pre">tau</span></code>. A quarter circle is
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<code class="docutils literal notranslate"><span class="pre">tau/4</span></code>, a half circle is <code class="docutils literal notranslate"><span class="pre">tau/2</span></code>, seven 25ths is <code class="docutils literal notranslate"><span class="pre">7*tau/25</span></code>, etc. In
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contrast with the equivalent expressions in terms of <code class="docutils literal notranslate"><span class="pre">pi</span></code> (<code class="docutils literal notranslate"><span class="pre">pi/2</span></code>, <code class="docutils literal notranslate"><span class="pre">pi</span></code>,
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<code class="docutils literal notranslate"><span class="pre">14*pi/25</span></code>), the unnecessary and needlessly confusing multiplication by
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two is gone.</p>
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</section>
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<section id="other-resources">
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<h2><a class="toc-backref" href="#other-resources" role="doc-backlink">Other Resources</a></h2>
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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 <code class="docutils literal notranslate"><span class="pre">tau</span></code> rather than <code class="docutils literal notranslate"><span class="pre">pi</span></code>. If you don’t find my
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specific examples sufficiently persuasive, here are some more resources that
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may be of interest:</p>
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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></li>
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<li>Bob Palais, the author of the original mathematics journal article
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highlighting the problems with <code class="docutils literal notranslate"><span class="pre">pi</span></code> has <a class="reference external" href="http://www.math.utah.edu/~palais/pi.html">a page of resources</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> and
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<a class="reference external" href="http://www.youtube.com/watch?v=jG7vhMMXagQ">Pi is (still) wrong</a> are available on YouTube</li>
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</ul>
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</section>
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<section id="copyright">
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<h2><a class="toc-backref" href="#copyright" role="doc-backlink">Copyright</a></h2>
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<p>This document has been placed in the public domain.</p>
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</section>
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</section>
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<hr class="docutils" />
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<p>Source: <a class="reference external" href="https://github.com/python/peps/blob/main/peps/pep-0628.rst">https://github.com/python/peps/blob/main/peps/pep-0628.rst</a></p>
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<p>Last modified: <a class="reference external" href="https://github.com/python/peps/commits/main/peps/pep-0628.rst">2023-10-11 12:05:51 GMT</a></p>
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<nav id="pep-sidebar">
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<h2>Contents</h2>
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<ul>
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<li><a class="reference internal" href="#abstract">Abstract</a></li>
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<li><a class="reference internal" href="#pep-acceptance">PEP Acceptance</a></li>
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<li><a class="reference internal" href="#the-rationale-for-tau">The Rationale for Tau</a></li>
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<li><a class="reference internal" href="#other-resources">Other Resources</a></li>
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<li><a class="reference internal" href="#copyright">Copyright</a></li>
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</ul>
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