Editing 1292: Pi vs. Tau
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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 | + | This is yet another of [[Randall]]'s [[:Category: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. |
| − | 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 | + | 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. 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. |
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. | 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. | ||
| − | 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. | + | 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). 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. |
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==Transcript== | ==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". Between these is 1.5π, captioned "Pau".] | :[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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:A compromise solution to the Pi/Tau dispute | :A compromise solution to the Pi/Tau dispute | ||
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<pre> | <pre> | ||
4.55457437631441644323623451447505012242547157301565031476335452700304316771261165505467475703133125234035147165764643331727311243102010764472707236245737216402204376521550655442201431161557425156344621363625174410110777026111560241174471252241762037163367420573533032164702576626667446275343255043345060027305171025475041452166612112500275317166412767657355633417212140135534536541060452450664011414377406267077573054507036064406511117752700327100355213521015136220621644573043264505244325316526666260</pre> | 4.55457437631441644323623451447505012242547157301565031476335452700304316771261165505467475703133125234035147165764643331727311243102010764472707236245737216402204376521550655442201431161557425156344621363625174410110777026111560241174471252241762037163367420573533032164702576626667446275343255043345060027305171025475041452166612112500275317166412767657355633417212140135534536541060452450664011414377406267077573054507036064406511117752700327100355213521015136220621644573043264505244325316526666260</pre> | ||
| − | (Note that this contains 500 digits after the | + | (Note that this contains 500 digits after the decimal 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, 43, 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. |
{{w|Mathematical coincidence|Coincidentally}}, e+2 is also very similar to 1.5 pi, although only to a few digits. | {{w|Mathematical coincidence|Coincidentally}}, e+2 is also very similar to 1.5 pi, although only to a few digits. | ||
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==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. |
| − | *Also, note that "pau" is the | + | *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 humour (although childishly) for portuguese-speaking readers, though it is fair to presume that it was not Randall's intention to do so. |
*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 of tau, 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 of tau, see this [https://www.khanacademy.org/math/recreational-math/vi-hart/pi-tau/v/pi-is--still--wrong Vi Hart video]. | ||
*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". | *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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{{comic discussion}} | {{comic discussion}} | ||
