Randall Munroe’s xkcd has a table of slightly wrong equations and identities.

The table gives that the number of seconds in a year is 75^{4} = 31640625 or (using the “*RENT* method”) 525,600 × 60 = 31536000. (This refers to the song Seasons of Love, which features the number of minutes in a year prominently in its lyrics.) I’ve always been partial to “pi seconds is a nanocentury” (attributed to Tom Duff), which gives π × 10^{7} for the number of seconds in a year, but you have to know π for this to be useful.

Also, while I’m on the subject: it’s easy to remember that the circumference of the Earth is 4 × 10^{7} meters, or 40,000 kilometers; the meter was originally defined to be one ten-millionth of the distance from the North Pole to the equator through Paris. Call this C, or 2πr. The surface area of the Earth is therefore 4πr^{2} = C^{2}/π, which works out to (1.6/π) × 10^{14} square meters; may as well let π = 3.2 for the moment and call that 5 × 10^{13}. Munroe gives 69^{8}, which I suppose has some amusement value.

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I’m pretty sure I’ve previously told you my favourite of these: π” = 8 cm (correct to .25%), which turns out to mean that metric hat sizes (where the granularity is centimetres of circumference) move in exact lock step with English hat sizes (where the granularity is eights of an inch of diameter).

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