Numbers like $\pi$ and $\sqrt{2}$ are irrational. But does that mean they’re unreasonable or just that they lack a ratio?

The Ancient Greek ἄλογος is even more ambiguous. Λόγος is used by Euclid to mean ratio, but it could also mean word, speech, story, idea, or reason reason. So ἄλογος could also mean speechless, unspeakable, unexpected, or non-reasoning.

Modern Greek mathematicians now call $\mathbb{Q}$ the inexpressible (άρρητος) numbers.

In case you ever have need for a large-ish prime number, here are a few that are easy to remember:

• 314159 ($\lfloor \pi \cdot {10}^5\rfloor$)
• 8675309 (Jenny’s number)
• 1000000007 (a billion and seven)
• 2147483647 ($2^{31}-1$, i.e. INT_MAX)
• 11111111111111111111111 (twenty-three ones)
• 1000000000000066600000000000001 (Belphegor’s prime)

You can get a really good approximation of a sinusoidal curve from twelve equally-spaced line segments of slope 1/12, 2/12, 3/12, 3/12, 2/12, 1/12, -1/12, -2/12, -3/12, -3/12, -2/12, and -1/12, respectively.

This approximation, known as the rule of twelfths, rounds $\sqrt{3}\approx 5/3$ but otherwise uses exact values along the curve.

I learned this from a kayaking instructor, since it’s particularly handy for estimating tides.

According to dimensional analysis, the time it takes to properly roast a whole turkey is proportional to its weight to the ⅔ power. My old mathematical modelling textbook specifically recommends 45 minutes per lb^2/3 when cooked at 350℉.

A precise formula has been derived for a spherical turkey of uniform thermal conductivity and density, though this is somewhat less practical for chefs.