Editing 1292: Pi vs. Tau
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==Explanation== | ==Explanation== | ||
− | This is yet another of | + | {{incomplete|octal expansion has to be explained. Please be serious on removing this tag. This explain needs a proper review.}} |
+ | This is yet another of Randall's [[:Category:Comics presenting a compromise|compromise comics]]. 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. Most of you will know pi by the approximation 3.14, and tau is twice as large as pi. 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 (or 0.75 tau). | ||
− | Some consider pi | + | 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. |
− | + | ===Mathematical jargon=== | |
− | + | The title text for the comic is incorrect. The first 200 digits of 'pau' in octal are: | |
− | The title text | + | <pre> |
− | + | 4.5545743763144164432362345144750501224254715730156503147633545270030431677126116550546747570313312523403514716576464333172731124310201076447270723624573721640220437652155065544220143116155742515634462 | |
− | The | + | </pre> |
− | + | The sequence '666' does not occur at all in it. | |
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Possibly, [[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]). | Possibly, [[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, | + | 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. In the first 200 digits of the octal expansion, the sequences 666 and 6666 do occur, | + | This gives a periodically repeating number. In the first 200 digits of the octal expansion, the sequences 666 and 6666 do occur, but each only once. There are 4 occurrences, however, in the first 300 digits: |
<pre> | <pre> | ||
4.554574376314416445676661714336617116240444076666510533533077631151350452060436452476274022621206136310000177621674175071262255702044274154476005744176002676623042402346036604733130522524127534777714554305412763636566643022106616734723661726160312772574551366370203115523402704104015532221722772357666</pre> | 4.554574376314416445676661714336617116240444076666510533533077631151350452060436452476274022621206136310000177621674175071262255702044274154476005744176002676623042402346036604733130522524127534777714554305412763636566643022106616734723661726160312772574551366370203115523402704104015532221722772357666</pre> | ||
Expansion that long 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. | Expansion that long 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. | |
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− | {{w|Mathematical coincidence|Coincidentally}}, e+2 is also very similar to 1. | ||
<pre> | <pre> | ||
1.5π = 4.71238898038... | 1.5π = 4.71238898038... | ||
e+2 = 4.71828182845... | e+2 = 4.71828182845... | ||
</pre> | </pre> | ||
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+ | 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}}". | ||
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+ | ==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 | ||
==Trivia== | ==Trivia== | ||
− | *For Pi | + | *For Pi the sequence '666' occurs for the first time at position 2440. Many more occurrences can be found here: [http://www.angio.net/pi/ The Pi-Search Page]. |
− | *Note that | + | * Note that pau is Catalan for peace, which is a good solution for the pi/tau dispute. |
− | + | * In the discussion it has been theorized that Randall used [[356: Nerd Sniping|Nerd Sniping]]. In which case he was aware of the mistake in Wolfram! | |
− | *In the discussion it has been theorized that Randall used [[356: Nerd Sniping|Nerd Sniping]]. In which case he was aware of the mistake in Wolfram! | + | *For an entertaining introduction to the concept, see this [https://www.khanacademy.org/math/recreational-math/vi-hart/pi-tau/v/pi-is--still--wrong Vi Hart video]. |
− | *For an entertaining introduction to the concept | ||
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{{comic discussion}} | {{comic discussion}} | ||
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[[Category:Comics with color]] | [[Category:Comics with color]] | ||
[[Category:Math]] | [[Category:Math]] | ||
− | [[Category: | + | [[Category:Comics presenting a compromise]] |