Happy Pi Day

For Pi day today we explored the amazing near integer

I started by showing the boys the numbers as well as just how close it was to being an integer. I measured the closeness both in terms of the decimal expansion and in terms of the continued fraction expansion of the number:

Next I asked the boys to each take a turn finding another number relating to that was either nearly an integer or nearly a rational number. It turned out – especially with my younger son – to be a really nice way to discuss properties of powers of numbers.

The number my younger son found was

The number my older son found was

So – obviously just for fun – but still a neat way to talk about numbers and continued fractions. And a pretty fun number at the start, too 🙂