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<!DOCTYPE html> <html lang="en"> <head> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <meta name="color-scheme" content="light dark"> <title>PEP 628 – Add math.tau | peps.python.org</title> <link rel="shortcut icon" href="../_static/py.png"> <link rel="canonical" href="https://peps.python.org/pep-0628/"> <link rel="stylesheet" href="../_static/style.css" type="text/css"> <link rel="stylesheet" href="../_static/mq.css" type="text/css"> <link rel="stylesheet" href="../_static/pygments.css" type="text/css" media="(prefers-color-scheme: light)" id="pyg-light"> <link rel="stylesheet" href="../_static/pygments_dark.css" type="text/css" media="(prefers-color-scheme: dark)" id="pyg-dark"> <link rel="alternate" type="application/rss+xml" title="Latest PEPs" href="https://peps.python.org/peps.rss"> <meta property="og:title" content='PEP 628 – Add math.tau | peps.python.org'> <meta property="og:description" content="In honour of Tau Day 2011, this 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class="colour-scheme-icon-when-dark"><use href="#svg-moon"></use></svg> <svg aria-hidden="true" class="colour-scheme-icon-when-light"><use href="#svg-sun"></use></svg> <span class="visually-hidden">Toggle light / dark / auto colour theme</span> </button> </header> <article> <section id="pep-content"> <h1 class="page-title">PEP 628 – Add <code class="docutils literal notranslate"><span class="pre">math.tau</span></code></h1> <dl class="rfc2822 field-list simple"> <dt class="field-odd">Author<span class="colon">:</span></dt> <dd class="field-odd">Alyssa Coghlan <ncoghlan at gmail.com></dd> <dt class="field-even">Status<span class="colon">:</span></dt> <dd class="field-even"><abbr title="Accepted and implementation complete, or no longer active">Final</abbr></dd> <dt class="field-odd">Type<span class="colon">:</span></dt> <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> <dt class="field-even">Created<span class="colon">:</span></dt> <dd class="field-even">28-Jun-2011</dd> <dt class="field-odd">Python-Version<span class="colon">:</span></dt> <dd class="field-odd">3.6</dd> <dt class="field-even">Post-History<span class="colon">:</span></dt> <dd class="field-even">28-Jun-2011</dd> </dl> <hr class="docutils" /> <section id="contents"> <details><summary>Table of Contents</summary><ul class="simple"> <li><a class="reference internal" href="#abstract">Abstract</a></li> <li><a class="reference internal" href="#pep-acceptance">PEP Acceptance</a></li> <li><a class="reference internal" href="#the-rationale-for-tau">The Rationale for Tau</a></li> <li><a class="reference internal" href="#other-resources">Other Resources</a></li> <li><a class="reference internal" href="#copyright">Copyright</a></li> </ul> </details></section> <section id="abstract"> <h2><a class="toc-backref" href="#abstract" role="doc-backlink">Abstract</a></h2> <p>In honour of Tau Day 2011, this PEP proposes the addition of the circle constant <code class="docutils literal notranslate"><span class="pre">math.tau</span></code> to the Python standard library.</p> <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 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 <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> </section> <section id="pep-acceptance"> <h2><a class="toc-backref" href="#pep-acceptance" role="doc-backlink">PEP Acceptance</a></h2> <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. Happy birthday Alyssa!</p> <p>The idea in this PEP has been implemented in the auspiciously named <a class="reference external" href="http://bugs.python.org/issue12345">issue 12345</a>.</p> </section> <section id="the-rationale-for-tau"> <h2><a class="toc-backref" href="#the-rationale-for-tau" role="doc-backlink">The Rationale for Tau</a></h2> <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. However, a circle is defined by its centre point and its <em>radius</em>. 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.</p> <p>When working with radians, it is trivial to convert any given fraction of a circle to a value in radians in terms of <code class="docutils literal notranslate"><span class="pre">tau</span></code>. A quarter circle is <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 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>, <code class="docutils literal notranslate"><span class="pre">14*pi/25</span></code>), the unnecessary and needlessly confusing multiplication by two is gone.</p> </section> <section id="other-resources"> <h2><a class="toc-backref" href="#other-resources" role="doc-backlink">Other Resources</a></h2> <p>I’ve barely skimmed the surface of the many examples put forward to point out just how much <em>easier</em> and more <em>sensible</em> many aspects of mathematics become 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 specific examples sufficiently persuasive, here are some more resources that may be of interest:</p> <ul class="simple"> <li>Michael Hartl is the primary instigator of Tau Day in his <a class="reference external" href="http://tauday.com/">Tau Manifesto</a></li> <li>Bob Palais, the author of the original mathematics journal article 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 topic</li> <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 <a class="reference external" href="http://www.youtube.com/watch?v=jG7vhMMXagQ">Pi is (still) wrong</a> are available on YouTube</li> </ul> </section> <section id="copyright"> <h2><a class="toc-backref" href="#copyright" role="doc-backlink">Copyright</a></h2> <p>This document has been placed in the public domain.</p> </section> </section> <hr class="docutils" /> <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> <p>Last modified: <a class="reference external" href="https://github.com/python/peps/commits/main/peps/pep-0628.rst">2025-02-01 08:59:27 GMT</a></p> </article> <nav id="pep-sidebar"> <h2>Contents</h2> <ul> <li><a class="reference internal" href="#abstract">Abstract</a></li> <li><a class="reference internal" href="#pep-acceptance">PEP Acceptance</a></li> <li><a class="reference internal" href="#the-rationale-for-tau">The Rationale for Tau</a></li> <li><a class="reference internal" href="#other-resources">Other Resources</a></li> <li><a class="reference internal" href="#copyright">Copyright</a></li> </ul> <br> <a id="source" href="https://github.com/python/peps/blob/main/peps/pep-0628.rst">Page Source (GitHub)</a> </nav> </section> <script src="../_static/colour_scheme.js"></script> <script src="../_static/wrap_tables.js"></script> <script src="../_static/sticky_banner.js"></script> </body> </html>