My first thought was "well of course it is, since pi is a little larger than 3" but it was cool to see an actual derivation of how much pi squared differs from 10 as a nice, closed form series.

The author wants tau=2*pi, but in the Greek alphabet, tau has one vertical stroke, and pi has two.

So, visually in Greek, pi=2*tau would seem an improvement.

Oh, well.

The second fact, pi^2 ~= g, is famous enough that it has a separate section in Wikipedia [1].

[1] https://en.wikipedia.org/wiki/Mathematical_coincidence#Gravi...

I remember discovering that pi x 10^7 is very close to the number of seconds in a year while at uni.

One of my tutors was convinced this had to be more than coincidence, but I always figured it was just chance and a nice but sometimes useful shortcut...