*Pi and the square root of 10

Continued fractions have really caught my younger son’s eye the last couple of days. The link below (plus the link inside of that link) give two examples of our recent discussions:

A Continued Fraction Experiment

Today we were playing around online with continued fraction calculators and other sites discussing continued fractions and found quite a surprise – there is a generalized continued fraction for \pi that looks very similar continued fraction for \sqrt{10}. I used this little coincidence to review some basics of calculating continued fractions:

Next up – a short discussion of the generalized continued fraction that we found for \pi. I think that kids will always find it surprising that there are relatively simple ways to describe \pi even though just about everything you hear about \pi is that it has no pattern.

Neat little morning – very fun to show a surprising way to see some structure in \pi. Also quite a surprise to see the seemingly small change that changes \pi into \sqrt{10}.