In this answer, the person who answered used $\tau$ instead of $2\pi$, and I commented that he should probably use $2\pi$ instead to avoid confusion.

My question is:

Do we have any guidelines here on math.SE about $2\pi$ vs $\tau$?

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    $\begingroup$ If nothing else, it should be explained, since $\tau$ is not in common use. $\endgroup$ – user14972 Aug 2 '14 at 10:48
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    $\begingroup$ I just downvote every post that I view as advocating the use of $2\pi$ in favor of $\pi$ as the circle constant. Mind you, I concede that this policy is a partial win to the $2\pi$-pushers - they managed to get under my skin to this extent. $\endgroup$ – Jyrki Lahtonen Aug 2 '14 at 11:41
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    $\begingroup$ @JyrkiLahtonen I think the real problem here is not using $2\pi$ vs $\pi$ but $\tau$ vs $\pi$ as the $\tau$ symbol is not widely known. $\endgroup$ – Alice Ryhl Aug 2 '14 at 11:52
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    $\begingroup$ Using $\tau$ without explanation is what I'd call being smug and unhelpful. I understand the arguments for using $\tau$, but if a (non-scientist) American asks the outdoor temperature, and give him a Celsius answer without at least saying Celsius, you are not being helpful, you are being smug. $\endgroup$ – Thomas Andrews Aug 2 '14 at 13:05
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    $\begingroup$ When Jan 1, 2000 was coming around, i joked that the people who insisted on telling you that 2001 was the "real millennium" were "Smart enough to know, dumb enough to care." There is a certain kind of obsession with detail that seems designed to assert superiority, not to actually be useful. Some grammar police are like this, as well. $\endgroup$ – Thomas Andrews Aug 2 '14 at 13:17
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    $\begingroup$ @Darksonn, I just refuse to type that other Greek letter in this context :-) $\endgroup$ – Jyrki Lahtonen Aug 2 '14 at 15:46
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    $\begingroup$ Perhaps the controversy is common knowledge, but just in case: explainxkcd.com/wiki/index.php/1292:_Pi_vs._Tau $\endgroup$ – copper.hat Aug 2 '14 at 18:03
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    $\begingroup$ @ThomasAndrews, unhelpful, yes; smug, not necessarily. Not everyone thinks about the social context in which they're posting. As Napoleon said: "Never ascribe to malice that which is adequately explained by incompetence." $\endgroup$ – goblin GONE Aug 3 '14 at 2:19
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    $\begingroup$ $\tau = 2 \pi$. That took me 14 characters, and it could easily be 11 if I cut out the spacing. How many characters are we allowed for an answer? $\endgroup$ – Robert Soupe Aug 3 '14 at 2:50
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    $\begingroup$ @goblin, see shannonselin.com/2014/07/10-things-napoleon-never-said $\endgroup$ – Gerry Myerson Aug 3 '14 at 3:30
  • $\begingroup$ @GerryMyerson, fair enough! Anyway I've always disliked Napoleon, so this frees me to use the quote without ascribing it to him. $\endgroup$ – goblin GONE Aug 3 '14 at 3:32
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    $\begingroup$ Am I wrong in thinking that this edit should have been rejected? The editor commented his edit as "LaTeX-ified" but he needlessly removed units and explanations beside formulas. He also changed tau to 2pi. Why didn't he just write his own answer then? $\endgroup$ – William Aug 3 '14 at 12:24
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    $\begingroup$ There are formulae for which using $\tau$ simplifies them significantly, and also clarifies whether the powers of $2$ come from some circle phenomenon, or from another part of the context. But I would suggest that on this site, which is for all levels of mathematics, the notation definitely needs to be introduced whenever it is used - I would go with "and writing $\tau$ for $2\pi$ the formula is/becomes" and I would personally restrict it to contexts where it actually clarifies what is going on. $\endgroup$ – Mark Bennet Aug 3 '14 at 17:33
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    $\begingroup$ @ThomasAndrews, Hey, I tell Americans the temperature in Celsius all the time, not because I'm smug, but that I forget that they use Fahrenheit (and I'm not familiar enough with it to convert easily) $\endgroup$ – fhyve Aug 8 '14 at 20:54
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    $\begingroup$ $\tau~(x)~\sim~\dfrac{2x}{\ln x}~$ $\endgroup$ – Lucian Aug 15 '14 at 17:15

There's no formal guideline about using $\tau$ instead of $2\pi$. But anyone who uses $\tau$ should remember that it is not standard notation. In particular, the notation $\tau$ for $2\pi$ is not used in textbooks, and those with little mathematical knowledge are unlikely to know what $\tau$ is supposed to mean.

At the same time, if someone does use $\tau$ in an answer, I don't think anyone else should edit the answer just to remove it. A comment simply stating that $\tau$ is $2\pi$ should be enough.

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    $\begingroup$ I suppose '$\tau$, which is how some pedants choose to write $2\pi$' would be a bit snarky... $\endgroup$ – Steven Stadnicki Aug 2 '14 at 22:36
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    $\begingroup$ Also it's a silly notation, because by visual inspection π = τ + τ. $\endgroup$ – Simon Aug 9 '14 at 9:06
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    $\begingroup$ Yeah, but the vertical strokes are under the horizontal one like the denominator of a fraction. So, π is like 1/2, and τ is like 1/1 = 1. $\endgroup$ – Dan Aug 9 '14 at 17:21
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    $\begingroup$ @Simon: well I think it is a multiplicative notation instead of an additive one. So rather $\pi \approx \tau \tau = \tau^2$ $\endgroup$ – Gottfried Helms Aug 9 '14 at 20:41
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    $\begingroup$ @Dan so surely then π is like 1/11 and τ is like 1/1, so τ = 11π. $\endgroup$ – Simon Aug 10 '14 at 10:48
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    $\begingroup$ Also, have a care for the elliptic/modular form guys. The elliptic nome would look like $e^{i\tau\tau}$ (which, as per @GottfriedHelms, is $e^{i\pi} = -1$) $\endgroup$ – Balarka Sen Aug 12 '14 at 14:54
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    $\begingroup$ @GottfriedHelms: Actually, I sometimes think $\sqrt{\pi}$ might be a nicer constant than $\pi$. $\endgroup$ – David K Aug 13 '14 at 20:33

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