From 50097f94fc7f5c4ffdcfadaf88e249d6316a1172 Mon Sep 17 00:00:00 2001 From: Nick Coghlan Date: Tue, 28 Jun 2011 00:40:02 +1000 Subject: [PATCH] Take two, this time with the correct extension :) --- pep-0628.html | 149 -------------------------------------------------- pep-0628.txt | 100 +++++++++++++++++++++++++++++++++ 2 files changed, 100 insertions(+), 149 deletions(-) delete mode 100644 pep-0628.html create mode 100644 pep-0628.txt diff --git a/pep-0628.html b/pep-0628.html deleted file mode 100644 index 06ec88f2a..000000000 --- a/pep-0628.html +++ /dev/null @@ -1,149 +0,0 @@ - - --- - - - - - - - - - - - - - - - - - - - - - - - - - -
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
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Contents

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Abstract

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In honour of Tau Day 2011, this PEP proposes the addition of the circle -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 -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).

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PEP Deferral

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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.

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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.

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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.

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The Rationale for Tau

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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.

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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.

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Other Resources

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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:

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References

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[1]http://bugs.python.org/issue12345
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[2]http://tauday.com/
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[3]http://www.youtube.com/watch?v=jG7vhMMXagQ
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[4]http://www.youtube.com/watch?v=IF1zcRoOVN0
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[5]http://www.math.utah.edu/~palais/pi.html
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- - diff --git a/pep-0628.txt b/pep-0628.txt new file mode 100644 index 000000000..b03b64b21 --- /dev/null +++ b/pep-0628.txt @@ -0,0 +1,100 @@ +PEP: 628 +Title: Add ``math.tau`` +Version: $Revision$ +Last-Modified: $Date$ +Author: Nick Coghlan +Status: Deferred +Type: Standards Track +Content-Type: text/x-rst +Created: 2011-06-28 +Python-Version: 3.x +Post-History: 2011-06-28 +Resolution: TBD + + +Abstract +======== + +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``). + + +PEP Deferral +============ + +The idea in this PEP was first proposed in the auspiciously named +`issue 12345`_. 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``. + +.. _issue 12345: http://bugs.python.org/issue12345 + + +The Rationale for Tau +===================== + +``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. + + +Other Resources +=============== + +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`_ + * Bob Palais, the author of the original mathematics journal article + highlighting the problems with ``pi`` has `a page of resources`_ on the + topic + * For those that prefer videos to written text, `Pi is wrong!`_ and + `Pi is (still) wrong`_ are available on YouTube + +.. _Tau Manifesto: http://tauday.com/ +.. _Pi is (still) wrong: http://www.youtube.com/watch?v=jG7vhMMXagQ +.. _Pi is wrong!: http://www.youtube.com/watch?v=IF1zcRoOVN0 +.. _a page of resources: http://www.math.utah.edu/~palais/pi.html + + +Copyright +========= + +This document has been placed in the public domain. + +.. + Local Variables: + mode: indented-text + indent-tabs-mode: nil + sentence-end-double-space: t + fill-column: 70 + coding: utf-8 + End: