1292: Pi vs. Tau

2013-11-20T19:54:28Z

(Deal with it: /* Explanation */

{{comic
| number = 1292
| date = November 18, 2013
| title = Pi vs. Tau
| image = pi vs tau.png
| titletext = Conveniently approximated as e+2, Pau is commonly known as the Devil's Ratio (because in the octal expansion, '666' appears four times in the first 200 digits while no other run of 3+ digits appears more than once.)
}}

==Explanation==
{{incomplete}}
This is yet another of Randall's compromise comics (previous ones are [[690: Semicontrolled Demolition]], [[1167: Star Trek into Darkness]] and [[1285: Third Way]]). A few mathematicians argue as to whether to use pi, which is the ratio between a circle's circumference and its diameter, or tau, which is the ratio between a circle's circumference and its radius. Randall is suggesting using "pau", which is a portmanteau of "pi" and "tau", as a number situated, appropriately enough, halfway between pi and tau. But of course his number would be inconvenient, as there are currently no commonly used formulas that involve 1.5 pi (0.75 tau).

{{CompromiseComicSeries}}

Some consider pi as being the wrong convention and are in favor of using tau as ''the'' circle constant (see the [http://tauday.com/tau-manifesto Tau Manifesto], which was inspired by the article "[http://www.math.utah.edu/~palais/pi.html Pi is wrong!]" by mathematician Robert Palais). Others consider proponents of tau to be foolish and remain loyal to pi (see the [http://www.thepimanifesto.com Pi Manifesto]). Of course, regardless of which convention is used, the fundamental mathematics will remain unaltered. But the choice of pi vs tau can affect the clarity of equations, analogies between different equations, and how easy various subjects are to teach.

The title text for the comic is incorrect. The first 200 digits of 'pau' in octal are:
<pre>
4.5545743763144164432362345144750501224254715730156503147633545270030431677126116550546747570313312523403514716576464333172731124310201076447270723624573721640220437652155065544220143116155742515634462
</pre>
The sequence '666' does not occur at all in it.

Apparently, [[Randall]] used [http://www.wolframalpha.com/ Wolfram|Alpha] to calculate the result (he uses it a lot, for example [http://what-if.xkcd.com/70/ What-if 70: The Constant Groundskeeper] or [http://what-if.xkcd.com/62/ What-if 62: Falling With Helium]).
However, as of November 18, 2013, there's a bug in Wolfram|Alpha so that, when getting 200 octal digits from "pau", it just calculates the decimal value rounded to 15 significant digits (this is 4.71238898038469) and expands that as octal digits as far as needed.

This gives a periodically repeating number. The number of digits is also represented in octal, so instead of 200 digits it is actually 310 digits, finally giving:
<pre>
4.5545743763144164456766617143366171162404440766665105335330776311513504520604364524762740226212061363100001776216741750712622557020442741544760057441760026766230424023460366047331305225241275347777145543054127636365666430221066167347236617261603127725745513663702031155234027041040155322217227723576660045156156</pre>
This number indeed does contain 666 (the {{w|Number of the beast|number of the beast}}) four times (with one instance as 6666). It also contains 0000, 222, 444, and 7777, but they only appear once in a run.

{{w|Mathematical coincidence|Coincidentally}}, e+2 is also very similar to 1.5pi, although only to a few digits.
<pre>
1.5π = 4.71238898038...
e+2 = 4.71828182845...
</pre>

The "Devil's Ratio" may be an allusion to the "{{w|Tritone|Devil's Interval}}", aka the "Devil's Chord" or 'Diabolus in Musica' ('The Devil in music'), which is the name sometimes given to the harmony between a root note and its tritone/augmented fourth/diminished fifth. This note is situated halfway between octaves, and is named for its dissonant quality. It is possibly a cross-reference between this and the "{{w|golden ratio}}".

==Transcript==
:[On the left is a "forbidden"-style slashed circle with the π symbol, captioned "Pi". On the right is a "forbidden"-style slashed circle with 2π, captioned "Tau". In the middle it reads 1.5π, captioned "Pau".]
:A compromise solution to the Pi Tau dispute

{{comic discussion}}
[[Category:Comics with color]]
[[Category:Math]]

explain xkcd:Sandbox

2013-11-20T18:52:05Z

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__NOINDEX__
Make changes, try things out, or just have fun with the wiki here! Just leave everything above the line alone, please.
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{{#expr:1220+({{CURRENTWEEK}}-23)*3+{{#switch:{{CURRENTDOW}}|1|2=0|3|4=1|5|6|0=2}}}}

{{ComicSeries|29384|name="Test"}}

explain xkcd:Sandbox

2013-11-20T18:51:50Z

(Deal with it:

explain xkcd:Sandbox

2013-11-20T18:51:34Z

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User:(Deal with it

2013-11-15T16:27:51Z

(Deal with it:

{{comic
| number = 859
| date = February 11, 2011
| title = (
| image = (.png
| titletext = Brains aside, I wonder how many poorly-written xkcd.com-parsing scripts will break on this title (or ;;"'<nowiki/>'{<<[' this mouseover text."
}}

User:(Deal with it

2013-11-15T16:27:08Z

(Deal with it: Created page with "File:http://xkcd.com/859/"

[[File:http://xkcd.com/859/]]

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1292: Pi vs. Tau

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