Here is how history DID unfold:

1) People noticed that the ratio of the circumference to the diameter of ANY circle is always the same, it's a number between 3 and 4, roughly 3.14 or as my Dad would say, exactly 22/7 (see this blog post). On the web (see here) is a claim that Euler first used the symbol pi since it is the first letter of a Greek word for *Circumference*. I've seen other sites that claim someone less famous and its the first letter of a Greek work for *Perimeter*.

But in any case pi was known (though not called that) a LONG time ago.

2) MUCH LATER people noticed

1/1^2 + 1/2^2 + 1/3^2 + ... = pi^2/6 (Euler showed this in 1735, see here. That site says that it was Basel's problem to determine the sum. Yeah for Basel--- his name lives on even after his problem was solved! This did not happen for Baudet and Vazsonyi. If you don't know what they conjectured--- well, that proves my point. ADDED LATER: commenter Robert pointed out that Basel is NOT a person's name but a cities name. I am delighted to know that!)

1 - 1/3 + 1/5 - 1/7 + 1/9 ... = pi/4 (Leibniz showed this in 1676, see here. A good Quora site on that sum is here.)

(There are other series where pi comes up as well.)

3) People wonder *Why did pi, which has to do with CIRCLES, end up in INFINITE SERIES?*

What if history unfolded the other way:

1) People noticed

1/1^2 + 1/2^2 + 1/3^2 + ... =a^2/6 (Euler did that in 1735, see here.)

1 - 1/3 + 1/5 - 1/7 + 1/9 ... = b/4 (Leibniz showed this, see here. A good Quora site on that sum is here.)

and they noticce that a=b and is between 3 and 4, closer to 3. They decide to call it pi for no good reason.

(There are other series where pi comes up as well.)

2) MUCH LATER people noticed that this same funny constant pi was the ratio of circumference to diameter in any circle.

3) People wonder *Why did pi, which has to do with INFINITE SERIES, end up in CIRCLES?*

The following comic captures the dichotomy: here