https://www.explainxkcd.com/wiki/index.php?title=1292:_Pi_vs._Tau&feed=atom&action=history1292: Pi vs. Tau - Revision history2024-03-28T20:46:08ZRevision history for this page on the wikiMediaWiki 1.30.0https://www.explainxkcd.com/wiki/index.php?title=1292:_Pi_vs._Tau&diff=336169&oldid=prev42.book.addict at 18:36, 29 February 20242024-02-29T18:36:25Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>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{{<del class="diffchange diffchange-inline">citation </del>needed}}<del class="diffchange diffchange-inline">). </del>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.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>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<ins class="diffchange diffchange-inline">.)</ins>{{<ins class="diffchange diffchange-inline">Citation </ins>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.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The Tau/pi controversy was later mentioned in [[2520: Symbols]].</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The Tau/pi controversy was later mentioned in [[2520: Symbols]].</div></td></tr>
</table>42.book.addicthttps://www.explainxkcd.com/wiki/index.php?title=1292:_Pi_vs._Tau&diff=318157&oldid=prevChristmasGospel: Fixed capitalization2023-07-20T21:31:22Z<p>Fixed capitalization</p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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].</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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".</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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".</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Pau is a <del class="diffchange diffchange-inline">chinese </del>dish, a filled bun which is round and yummy{{Citation needed}}, just like pie.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Pau is a <ins class="diffchange diffchange-inline">Chinese </ins>dish, a filled bun which is round and yummy{{Citation needed}}, just like pie.<ins class="diffchange diffchange-inline">{{actual citation needed}}</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*[https://en.wikipedia.org/wiki/Pau,_Pyr%C3%A9n%C3%A9es-Atlantiques Pau] is also a city of south-western France.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*[https://en.wikipedia.org/wiki/Pau,_Pyr%C3%A9n%C3%A9es-Atlantiques Pau] is also a city of south-western France.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*Finally, "pau" means "finished" in Hawaiian.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*Finally, "pau" means "finished" in Hawaiian.</div></td></tr>
</table>ChristmasGospelhttps://www.explainxkcd.com/wiki/index.php?title=1292:_Pi_vs._Tau&diff=304699&oldid=prevColorfulGalaxy: Restored leading zero2023-01-12T21:35:52Z<p>Restored leading zero</p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>4.55457437631441644323623451447505012242547157301565031476335452700304316771261165505467475703133125234035147165764643331727311243102010764472707236245737216402204376521550655442201431161557425156344621363625174410110777026111560241174471252241762037163367420573533032164702576626667446275343255043345060027305171025475041452166612112500275317166412767657355633417212140135534536541060452450664011414377406267077573054507036064406511117752700327100355213521015136220621644573043264505244325316526666260</pre></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>4.55457437631441644323623451447505012242547157301565031476335452700304316771261165505467475703133125234035147165764643331727311243102010764472707236245737216402204376521550655442201431161557425156344621363625174410110777026111560241174471252241762037163367420573533032164702576626667446275343255043345060027305171025475041452166612112500275317166412767657355633417212140135534536541060452450664011414377406267077573054507036064406511117752700327100355213521015136220621644573043264505244325316526666260</pre></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>(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, <del class="diffchange diffchange-inline">43</del>, 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.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>(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, <ins class="diffchange diffchange-inline">043</ins>, 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.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{w|Mathematical coincidence|Coincidentally}}, e+2 is also very similar to 1.5 pi, although only to a few digits.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{w|Mathematical coincidence|Coincidentally}}, e+2 is also very similar to 1.5 pi, although only to a few digits.</div></td></tr>
</table>ColorfulGalaxyhttps://www.explainxkcd.com/wiki/index.php?title=1292:_Pi_vs._Tau&diff=301312&oldid=prevSilverTheTerribleMathematician: /* Trivia */2022-12-14T08:37:58Z<p><span dir="auto"><span class="autocomment">Trivia</span></span></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Trivia==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Trivia==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*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].</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*For Pi<ins class="diffchange diffchange-inline">, </ins>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].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*Note that "pau" is Catalan for peace, which might be a good solution for the pi/tau dispute.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*Note that "pau" is Catalan for peace, which might be a good solution for the pi/tau dispute.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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.</div></td></tr>
</table>SilverTheTerribleMathematicianhttps://www.explainxkcd.com/wiki/index.php?title=1292:_Pi_vs._Tau&diff=301311&oldid=prevSilverTheTerribleMathematician: /* Trivia */2022-12-14T08:37:25Z<p><span dir="auto"><span class="autocomment">Trivia</span></span></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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].</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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".</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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".</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Pau is a chinese dish, a filled bun which is round and yummy, just like pie.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Pau is a chinese dish, a filled bun which is round and yummy<ins class="diffchange diffchange-inline">{{Citation needed}}</ins>, just like pie.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*[https://en.wikipedia.org/wiki/Pau,_Pyr%C3%A9n%C3%A9es-Atlantiques Pau] is also a city of south-western France.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*[https://en.wikipedia.org/wiki/Pau,_Pyr%C3%A9n%C3%A9es-Atlantiques Pau] is also a city of south-western France.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*Finally, "pau" means "finished" in Hawaiian.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*Finally, "pau" means "finished" in Hawaiian.</div></td></tr>
</table>SilverTheTerribleMathematicianhttps://www.explainxkcd.com/wiki/index.php?title=1292:_Pi_vs._Tau&diff=299483&oldid=prevJLZ0kTC5 at 10:50, 20 November 20222022-11-20T10:50:06Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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].</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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].</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*Note that "pau" is Catalan for peace, which might be a good solution for the pi/tau dispute.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*Note that "pau" is Catalan for peace, which might be a good solution for the pi/tau dispute.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*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 <del class="diffchange diffchange-inline">humour </del>(although childishly) for Portuguese-speaking readers, though it is fair to presume that it was not Randall's intention to do so.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*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 <ins class="diffchange diffchange-inline">humor </ins>(although childishly) for Portuguese-speaking readers, though it is fair to presume that it was not Randall's intention to do so.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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!</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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!</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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].</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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].</div></td></tr>
</table>JLZ0kTC5https://www.explainxkcd.com/wiki/index.php?title=1292:_Pi_vs._Tau&diff=295506&oldid=prevGuyspy21: /* Explanation */ Citation needed (forth paragraph).2022-09-26T00:29:02Z<p><span dir="auto"><span class="autocomment">Explanation: </span> Citation needed (forth paragraph).</span></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>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.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>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<ins class="diffchange diffchange-inline">{{citation needed}}</ins>). 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.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The Tau/pi controversy was later mentioned in [[2520: Symbols]].</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The Tau/pi controversy was later mentioned in [[2520: Symbols]].</div></td></tr>
</table>Guyspy21https://www.explainxkcd.com/wiki/index.php?title=1292:_Pi_vs._Tau&diff=294139&oldid=prevWhoop whoop pull up: /* Trivia */2022-09-05T01:32:50Z<p><span dir="auto"><span class="autocomment">Trivia</span></span></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Trivia==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Trivia==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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].</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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].</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>*Note that "pau" is Catalan for peace, which might be a good solution for the pi/tau dispute</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>*Note that "pau" is Catalan for peace, which might be a good solution for the pi/tau dispute<ins class="diffchange diffchange-inline">.</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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!</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>*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!</div></td></tr>
</table>Whoop whoop pull uphttps://www.explainxkcd.com/wiki/index.php?title=1292:_Pi_vs._Tau&diff=294056&oldid=prev172.71.102.149 at 13:35, 3 September 20222022-09-03T13:35:18Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><pre></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><pre></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>4.55457437631441644323623451447505012242547157301565031476335452700304316771261165505467475703133125234035147165764643331727311243102010764472707236245737216402204376521550655442201431161557425156344621363625174410110777026111560241174471252241762037163367420573533032164702576626667446275343255043345060027305171025475041452166612112500275317166412767657355633417212140135534536541060452450664011414377406267077573054507036064406511117752700327100355213521015136220621644573043264505244325316526666260</pre></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>4.55457437631441644323623451447505012242547157301565031476335452700304316771261165505467475703133125234035147165764643331727311243102010764472707236245737216402204376521550655442201431161557425156344621363625174410110777026111560241174471252241762037163367420573533032164702576626667446275343255043345060027305171025475041452166612112500275317166412767657355633417212140135534536541060452450664011414377406267077573054507036064406511117752700327100355213521015136220621644573043264505244325316526666260</pre></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>(Note that this contains 500 digits after the <del class="diffchange diffchange-inline">decimal </del>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.</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>(Note that this contains 500 digits after the <ins class="diffchange diffchange-inline">octal </ins>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.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{w|Mathematical coincidence|Coincidentally}}, e+2 is also very similar to 1.5 pi, although only to a few digits.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>{{w|Mathematical coincidence|Coincidentally}}, e+2 is also very similar to 1.5 pi, although only to a few digits.</div></td></tr>
</table>172.71.102.149https://www.explainxkcd.com/wiki/index.php?title=1292:_Pi_vs._Tau&diff=266967&oldid=prev172.70.130.121: Undo revision 2667742022-05-11T17:53:06Z<p>Undo revision 266774</p>
<a href="//www.explainxkcd.com/wiki/index.php?title=1292:_Pi_vs._Tau&diff=266967&oldid=266774">Show changes</a>172.70.130.121