# Why is Pi Pi?

In other words, why was the letter Pi chosen to symbolize the ratio of a circle’s circumference to its diameter? As opposed to say Omicron or Rho?

It stands for “perimeter”.

But then why is perimeter (circumference) a multiple of 2pi?

Yeah, probably, but nitpick: periphery.

compared to the radius. It’s only 1pi as big as the diameter.

O_o

I knew that.

Fuggin pi…how does it work?

It has been pointed out that radius is a much more natural measure of a circle than diameter, anyway, and so the number that we ought to care about is 6.28…, now sometimes known as tau.

In George O. Smith’s Lost Art, a story from his Venus Equilateral series, he says that the lost ancient Martian civilization represented Pi as a circle with a double dot. A single dot would make more sense, to me.

To answer great Sun Jester, all linear measures of a figure scale at the same rate, so what’s really important are the ratios, since those will be the same at any scale. Pi is the ratio between the circumference and the diameter, and shows up in surprising and (at first) unexpected mathematical relations, such as the results of infinite sums, the results of Cauchy integrals, relations with imaginary numbers, as well as in engineering problems like relations of the bending of simply supported beams, resistances measured between points on an infinite network grid of resistors, and similar such stuff. I’m sure people here will tell you more than you wish to know about any of these.

Or we can just send them to this portion of the relevant Wikipedia article.

Here we go.

I found a lot of things in my college trig course much easier once I started beginning all of my homework with Let τ = 2π.

Okay, I guess I should have done more research. I knew the Greek word for circle (κύκλος) started with a K so I wrongly assumed that whatever the Greek word for circumference was, it would have the same root and also start with a K. But the Greek word for circumference is περιφέρεια, which starts with a π.

I think tau and pi are backwards. The larger number should have 2 stems.

Seems a superstitious concept and a cause of needless confusion to me.
Tau will be a fleeting fad, forget it.

Superstitious? How, exactly?

If anything is needlessly confusing, it’s using 2pi to represent 1 turn of the unit circle. Yeah, let’s measure angles in terms of the radius but base the constant on the diameter. That’s a good idea.

Since Pi is a Greek letter, and since much of geometry traces back to the ancient Greeks (Euclid, Archimedes, etc.), who certainly knew about the number, it’s natural to assume that pi is what the Greeks themselves called it. It’s surprising (or at least it was to me when I first learned it) that the use of the symbol is relatively recent compared to the knowledge of the number itself. As bup’s link notes, it was popularized by Euler, as were many other bits of mathematical notation that we now take for granted (such as e, i, f(x), Sigma).

Nerdfight!!

[chuckles]