| PEP: | 628 | +
|---|---|
| Title: | Add math.tau | +
| Version: | $Revision$ | +
| Last-Modified: | $Date$ | +
| Author: | Nick Coghlan <ncoghlan at gmail.com> | +
| Status: | Deferred | +
| Type: | Standards Track | +
| Content-Type: | text/x-rst | +
| Created: | 2011-06-28 | +
| Python-Version: | 3.3 | +
| Post-History: | 2011-06-28 | +
| Resolution: | TBD | +
Contents
+ +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).
+The idea in this PEP was first proposed in the auspiciously named +issue 12345 [1]. 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.
+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.
+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 [2]
+- Bob Palais, the author of the original mathematics journal article +highlighting the problems with pi has a page of resources [5] on the +topic
+- For those that prefer videos to written text, Pi is wrong! [4] and +Pi is (still) wrong [3] are available on YouTube
+
| [1] | http://bugs.python.org/issue12345 |
| [2] | http://tauday.com/ |
| [3] | http://www.youtube.com/watch?v=jG7vhMMXagQ |
| [4] | http://www.youtube.com/watch?v=IF1zcRoOVN0 |
| [5] | http://www.math.utah.edu/~palais/pi.html |
This document has been placed in the public domain.
+ +