... 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.
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
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.
... 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.
That tells me you haven't memorized the first ten or twelve terms of the Fibonacci sequence.
1 km = 5 furlong, with < 1% error.