# Using $\tau$ instead of $2\pi$?

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 $\tau$?

• If nothing else, it should be explained, since $\tau$ is not in common use. – Hurkyl Aug 2 '14 at 10:48
• 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. – Jyrki Lahtonen Aug 2 '14 at 11:41
• @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. – Alice Ryhl Aug 2 '14 at 11:52
• 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. – Thomas Andrews Aug 2 '14 at 13:05
• 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. – Thomas Andrews Aug 2 '14 at 13:17
• @Darksonn, I just refuse to type that other Greek letter in this context :-) – Jyrki Lahtonen Aug 2 '14 at 15:46
• Perhaps the controversy is common knowledge, but just in case: explainxkcd.com/wiki/index.php/1292:_Pi_vs._Tau – copper.hat Aug 2 '14 at 18:03
• @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." – goblin Aug 3 '14 at 2:19
• $\tau = 2 \pi$. 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? – Robert Soupe Aug 3 '14 at 2:50
• – Gerry Myerson Aug 3 '14 at 3:30
• @GerryMyerson, fair enough! Anyway I've always disliked Napoleon, so this frees me to use the quote without ascribing it to him. – goblin Aug 3 '14 at 3:32
• 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? – wil93 Aug 3 '14 at 12:24
• 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. – Mark Bennet Aug 3 '14 at 17:33
• @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) – fhyve Aug 8 '14 at 20:54
• $\tau~(x)~\sim~\dfrac{2x}{\ln x}~$ – 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.
• I suppose '$\tau$, which is how some pedants choose to write $2\pi$' would be a bit snarky... – Steven Stadnicki Aug 2 '14 at 22:36
• @Simon: well I think it is a multiplicative notation instead of an additive one. So rather $\pi \approx \tau \tau = \tau^2$ – Gottfried Helms Aug 9 '14 at 20:41
• 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 $e^{i\pi} = -1$) – Balarka Sen Aug 12 '14 at 14:54
• @GottfriedHelms: Actually, I sometimes think $\sqrt{\pi}$ might be a nicer constant than $\pi$. – David K Aug 13 '14 at 20:33