It’s March 14, our annual homage to pi, whose decimal representation starts out 3.14… As I wrote last year, it’s a number God gives us, and we can’t have any opinion as to its value.

Despite being a mathematician of sorts and having a sense of humor, I was lost for a while on this problem on my math calendar:

In this calendar, the 14 of the date indicates the answer to the problem…except in this case. It’s one of the two annual jokes, no problem solving required. Translation?

i 8 [summation sign] pi = I ate some pie!

Most of us remember that pi is associated with circles. The circumference of any circle is 2 x pi x radius, and the circle’s area is pi x radius-squared. But pi pops up in other places as well. Watch this:

That’s not too hard to intuit. Starting with zero, each time, we’re advancing half the distance from where we are to 1. We will get as close to 1 as we like, and mathematicians say that this infinite series converges to 1.

Not all infinite fractional series do. For example, consider the harmonic series:

The harmonic series does NOT converge. It may take a while, but we can make the sum of this series as large as we want. I’ll spare you the proof even though it’s not difficult.

But consider this variation on the harmonic series:

Put this into a spreadsheet, and run it out a few thousand terms, and you’ll see it appears to converge to 1.6449… Which is…wait for it…pi-squared/6. Wow. Bet you didn’t see that coming. I know I didn’t until someone told me. It’s another example of things that are. Is mathematics invented or discovered? In this case, it’s discovered and was first observed by Euler in 1735 and formally proved in 1741.

So Happy Pi Day! We’ll get back to more serious topics tomorrow.

The secret things belong to the LORD our God, but the things that are revealed belong to us and to our children forever, that we may do all the words of this law. (Deuteronomy 29.29, ESV)