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| | {{comic | | {{comic |
| | | number = 1292 | | | number = 1292 |
| − | | date = November 18, 2013 | + | | date = November 17, 2013 |
| | | title = Pi vs. Tau | | | title = Pi vs. Tau |
| | | image = pi vs tau.png | | | image = pi vs tau.png |
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| | ==Explanation== | | ==Explanation== |
| − | This is yet another of [[Randall]]'s [[:Category:Compromise|compromise comics]]. A few mathematicians argue as to whether to use {{w|pi}}, which is the ratio between a circle's circumference and its diameter, or {{w|Turn (angle)#Proposals for a single letter to represent 2π|tau}}, which is the ratio between a circle's circumference and its radius.
| + | {{incomplete}} |
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| − | Some consider pi to be 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 and [https://www.youtube.com/watch?v=5iUh_CSjaSw publicized by Vi Hart]. 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 change is merely in notation — the underlying mathematics remains unaltered. Still, the choice of pi vs. tau can affect the clarity of equations, analogies between different equations, and how easy various subjects are to teach.
| + | This is yet another of Randall's 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. Randall is suggesting using pau, which is a portmanteau between pi and tau, and is a number situated halfway between pi and tau. This number would be effectively useless, as there are currently no commonly used formulas that involve 1.5 pi or 0.75 tau. |
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| − | Most people know π (pi) by the approximation 3.14, but do not know τ (tau) which, by definition, is twice as large as pi. Randall is suggesting using "pau", which is a {{w|portmanteau}} of "pi" and "tau", as a number situated, appropriately enough, halfway between pi and tau, i.e. 1.5 pi or 0.75 tau. But of course his number would be inconvenient, as this value does not naturally turn up when working with circles or other mathematical constructs, so there are no commonly used formulas that would use pau.
| + | Some consider pi has being the wrong convention in favor of tau (see the [http://tauday.com/tau-manifesto Tau Manifesto]). Some consider proponents of tau to be foolish and remain loyal to pi (see the [http://www.thepimanifesto.com Pi Manifesto]). Occasionally, the argument is that the food, pi(e), is the whole thing, not half and have made a [http://www.piday.org/ day about it]. Others say on tau day you get twice as much pi(e). |
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| − | The title text claims that pau can be approximated by e+2, as both values are roughly 4.71 — a similarity that holds little since it requires another irrational constant, {{w|E (mathematical constant)|e}} (although knowing the value of pau is somewhat more helpful in remembering e to 2 digits.){{Citation needed}} It also attributes the nickname "Devil's Ratio" to pau, due to the sequence {{w|Number of the Beast|666}} supposedly appearing four times in the first 200 digits of pau when expressed in the {{w|octal}} base. However, this is not the case, and was likely due to an error in the computer system used by WolframAlpha; for more details see below. | + | The inspiration for pi is wrong is found [http://www.math.utah.edu/~palais/pi.html here]. |
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| − | The tau vs. pi controversy was later mentioned in [[2520: Symbols]]. | + | The trivial nature of the argument is made plain in this comic. Regardless of which convention is used, the fundamental mathematics will remain unaltered |
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| − | ==Transcript==
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| − | :[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". Between these is 1.5π, captioned "Pau".]
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| − | :[Caption below the panel:]
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| − | :A compromise solution to the Pi/Tau dispute
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| − | ==Math details==
| + | The title text for the comic is also incorrect. The first 200 digits of 'pau' in octal are: |
| − | 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]).
| + | <pre> |
| − | However, when the comic was published, there was 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.
| + | 4.5545743763144164432362345144750501224254715730156503147633545270030431677126116550546747570313312523403514716576464333172731124310201076447270723624573721640220437652155065544220143116155742515634462 |
| | + | </pre> |
| | + | The sequence '666' does not occur at all. |
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| − | This gives a periodically repeating number. In the first 200 digits of the octal expansion, the sequences 666 and 6666 do occur, twice and once, respectively. There are 4 occurrences, however, in the first three hundred and ten (310 in base 8 equals 200 in base 10) digits:
| + | 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/ here] and [http://what-if.xkcd.com/62/ here]). |
| − | <pre>
| + | However, as of 2013-11-18, 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. |
| − | 4.554574376314416445676661714336617116240444076666510533533077631151350452060436452476274022621206136310000177621674175071262255702044274154476005744176002676623042402346036604733130522524127534777714554305412763636566643022106616734723661726160312772574551366370203115523402704104015532221722772357666</pre>
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| − | 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.
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| − | In the first 500 digits of the actual octal expansion of pau, we also find that 6666 occurs once, and 666 occurs two other times:
| + | 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> | | <pre> |
| − | 4.55457437631441644323623451447505012242547157301565031476335452700304316771261165505467475703133125234035147165764643331727311243102010764472707236245737216402204376521550655442201431161557425156344621363625174410110777026111560241174471252241762037163367420573533032164702576626667446275343255043345060027305171025475041452166612112500275317166412767657355633417212140135534536541060452450664011414377406267077573054507036064406511117752700327100355213521015136220621644573043264505244325316526666260</pre> | + | 4.5545743763144164456766617143366171162404440766665105335330776311513504520604364524762740226212061363100001776216741750712622557020442741544760057441760026766230424023460366047331305225241275347777145543054127636365666430221066167347236617261603127725745513663702031155234027041040155322217227723576660045156156</pre> |
| − | (Note that this contains 500 digits after the octal point.) No other run of 3 or more repeated digits (e.g. 111) occurs as many times, although 1111 occurs once, 111 occurs once elsewhere, and 333 and 777 also occur once each. 9 other strings of 3 digits occur 4 times, namely 164, 362, 521, 644, 432, 730, 043, 216, and 450, and only 573 occurs more often, as it occurs 6 times. Therefore, if 6666 is counted as two occurrences of 666, it is actually the joint second most common string of three numbers in the first 500 digits. | + | This number indeed does contain 666 four times (with one instance as 6666). It also contains 0000, 222, 444, and 7777, but they only appear once in a run. |
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| − | {{w|Mathematical coincidence|Coincidentally}}, e+2 is also very similar to 1.5 pi, although only to a few digits.
| + | [http://en.wikipedia.org/wiki/Mathematical_coincidence Coincidentally], e+2 is also very similar to 1.5pi, although only to a few digits. |
| | <pre> | | <pre> |
| − | 1.5π = 4.71238898038... | + | 1.5π = 4.71238898038 |
| − | e+2 = 4.71828182845... | + | e+2 = 4.71828182846 |
| | </pre> | | </pre> |
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| − | ==Trivia==
| + | The "Devil's Ratio" may be an allusion to the "[http://en.wikipedia.org/wiki/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 "[http://en.wikipedia.org/wiki/Golden_ratio Golden Ratio]". |
| − | *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].
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| − | *Note that "pau" is Catalan for peace, which might be a good solution for the pi/tau dispute.
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| − | *Also, note that "pau" is the Portuguese word for "stick", as well as, in Brazilian Portuguese, a very common slang for "penis". This may add to the humor (although childishly) for Portuguese-speaking readers, though it is fair to presume that it was not Randall's intention to do so.
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| − | *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!
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| − | *For an entertaining introduction to the concept of tau, see this [https://www.khanacademy.org/math/recreational-math/vi-hart/pi-tau/v/pi-is--still--wrong Vi Hart video].
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| − | *In March 2018 the video [https://www.youtube.com/watch?v=bcPTiiiYDs8 How pi was almost 6.283185...] was released on why Pi could just as well have been Tau (6.28), since {{w|Leonhard Euler|Euler}}, who used the letter Pi in his books, used it for both what we call Pi and Tau today... This very comic is also briefly shown in a segment regarding the controversy about these two versions of "Pi".
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| − | *Pau is a Chinese dish, a filled bun which is round and yummy{{Citation needed}}, just like pie.{{actual citation needed}}
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| − | *[https://en.wikipedia.org/wiki/Pau,_Pyr%C3%A9n%C3%A9es-Atlantiques Pau] is also a city of south-western France.
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| − | *Finally, "pau" means "finished" in Hawaiian.
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| | + | ==Transcript== |
| | + | {{incomplete transcript}} |
| | + | :(π, 'Pi', crossed out) (1.5 π, 'Pau') (2 π, 'Tau', also crossed out) |
| | + | :A compromise solution to the Pi/Tau dispute |
| | {{comic discussion}} | | {{comic discussion}} |
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| | [[Category:Comics with color]] | | [[Category:Comics with color]] |
| | [[Category:Math]] | | [[Category:Math]] |
| − | [[Category:Compromise]]
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