# Why does convention not recognize $2\pi$ as the fundamental quantity? [duplicate]

This question already has an answer here:

It looks as though my question might turn out to be a duplicate. If so, it does not need an answer, after all, thanks.

ORIGINAL QUESTION

Why does convention recognize $\pi\approx 3.14$, rather than $2\pi\approx 6.28$, as the fundamental quantity?

You have some contour integrals that come out to $\sqrt{\pi}$ or $1/\sqrt{\pi}$, so that's kind of neat; but I don't know that that arises more often than, say, $1/\sqrt{2\pi}$, as in the Fourier transform. Anyway, all that special-function action is so advanced that it misses what might seem to some to be the main point: $2\pi$ is a circle. How much more fundamental can you get than that?

But mathematicians are smart people (and I am just a building-construction engineer), so I do not doubt that a good reason exists. I just do not know what the reason is. Hence the question.

Why wasn't some other symbol defined, $\kappa\approx 6.28$?

## marked as duplicate by Pedro Tamaroff♦May 27 '16 at 0:47

• Some people call this tau: tauday.com – Alex R. May 27 '16 at 0:19
• People don't care. Tradition gave a name to $3.1415\ldots$ and we kept it. – Pedro Tamaroff May 27 '16 at 0:23
• @AlexR.: Perhaps you have so much reputation on this site that it does not really matter to you; but, of course, if you made your interesting comment an answer, I would like to upvote it. – thb May 27 '16 at 0:34
• Wow, it's funny to hear this question asked by someone who hasn't heard of $\tau$. – littleO May 27 '16 at 0:40
• According to Wikipedia, in 2001 Robert Palais suggested $2\pi$ as the fundamental circle constant, and in 2010 Michael Hartl wrote The Tau Manifesto and suggested the letter $\tau$ for $2\pi$. Since then it's been discussed a lot on online forums. Vi Hart made a video called "Pi is (still) wrong" that currently has over 2 million views on youtube. – littleO May 27 '16 at 5:10

The short answer to your question is that there is another symbol for $2\pi$, namely $\tau$. Some people promote that notation, but it hasn't caught on in the mainstream of mathematics, at least yet (and I don't think it will).
The longer answer to your question comes from history. The reason that $3.1415...$ got its own symbol $\pi$ before $6.28...$ did is that $\pi=3.14...$ is the ratio of the circumference of a circle to the diameter of the circle. Finding that ratio was a question that Babylonian, Chinese and Greek mathematicians/geometers in antiquity would quickly encounter while studying geometric shapes. Measuring/approximating that constant became an interesting problem for them. Mathematics had to develop much further before the value $2\pi$ would begin to show up often enough to conceivably merit its own symbol. The value $2\pi$ started showing up frequently only after the idea of the radian measure was invented in the 18th century, because then it became natural to think of a full $360^\circ$ rotation as a rotation of $2\pi$ radians. Then as complex analysis, fourier analysis, etc developed, it would show up more often.
I have no definite answer as to why people have not started using $\tau$ or some other symbol instead of $2\pi$. I suspect that simply there is no real need for it; $2\pi$ is easy enough to write as it is.