Happy Pi Day

For Pi day today we explored the amazing near integer e^{ \pi \sqrt{163}}

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 \pi 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 100 * 314^{\pi}

The number my older son found was 3.4 * \pi^{\sqrt{2}}

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 🙂

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