[GoldenRacer]

My favorite is 1 mile = phi kilometers with <1% error

[baliex]

That one’s useful too. If you know a few Fibonacci numbers you can convert miles to kilometres and vice versa with ease.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55 …

21 km is ~13 miles, 13 km is ~8 miles, etc.

A 26 mile marathon? Must be ~42km.

Same for speed limits too; 34 mph is ~55 kmh

[eesmith]

I use that approximation, via the Fibonacci sequence, to translate between miles and km. 13 miles ~ 21 km (actually 20.921470).

My favorite approximation is π·E7 = 31415926.5... , which is a <1% error from the number of seconds in a year.

[saalweachter]

... you all realize that phi is barely a better approximation than 8/5, right? 1.6 vs 1.609 (km in a mile) vs 1.618?

(8/5)/(1 mile/1 km) = 0.9942; (1 mile/1 km)/phi = 0.9946. You're making things way harder on yourself for essentially no improvement in precision, especially when you're just rounding to the nearest whole number.

[eesmith]

That tells me you haven't memorized the first ten or twelve terms of the Fibonacci sequence.

[saalweachter]

1 km = 5 furlong, with < 1% error.