[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.