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From Eagle, Albert (1958), *The elliptic functions as they should be: an account, with applications, of the functions in a new canonical form*:

> Most mathematicians must have often wished that there was a single symbol that could be written instead of $\frac 1 2 π$ or $π/2$. When one thinks that for the elliptic functions we have the convenient symbols of $K$ and $K'$ for the two quarter periods, it is really too absurd that for the circular functions, which are employed millions of times as often as the elliptic functions, we have no symbol for the quarter period at all, and have to express it as "half the half period".
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> The letter $π$ *should* have been used to denote $\frac 1 2 π$; but the meaning of $π$ can obviously not be changed now. But the Greek letter $τ$, with its one leg instead of two, so closely resembles $π$ cut in two that I have appropriated that letter exclusively for $\frac 1 2 π$. Consequently I ask my readers every time they see it to say to themselves "half-pi" or "pi by two" instead of "tau" or "taw". If a shorter name is desired for it what could be more appropriate to imply <i>h</i>alf-p<i>i</i> than "hi"? How convenient it is to write $τ$ as the upper limit of a trig integral instead of $\frac 1 2 π$! And how convenient it is to say "the integral of $\sin^nθ\ dθ$ from nought to hi" since the integrand is zero at the lower limit, and the upper limit is its *high* point!
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> It is natural that the practical man, measuring the diameter and the circumference of a cylinder, should want a symbol for the ratio of the two lengths. But a pure mathematician, noting that a diameter of a circle divides the circumference into two halves, would think it more reasonable to introduce a symbol for the ratio of *half* the circumference to the diameter. And he, perhaps rather surprisingly, would be showing better common sense about the matter than the practical man did!
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> Seriously, who can want to have $e^{-\frac 1 2 π}$ or $e^{-π/2}$ printed instead of $e^{-τ}$? Or who won't much prefer to write $τ$ than $\frac 1 2 π$ for the upper limit of a trig integral?
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> Those who peruse the numerous formulae in my book will, I think come to see that the finding of a single Greek letter $τ$ to stand for $\frac 1 2 π$ was a necessity that was forced upon me. How immensely nicer books on Fourier's Theorem would look!

Thu, 05 Oct 2017 03:43 GMT