Here are some mathematical coincidences I quite like. There are more at the references below.
- – this leads to such approximations as a doubling corresponding to a 3dB increase, or a kilobit of data being represented by 10 bits.
- (= 365, the number of days in a year)
- , so now you know the doubling time for investments at 8% or 2% return.
- to 0.04% or to six decimal places
- , so
This was found by Ramanujan, who knows how he came up with it!
- 1 year is approximately seconds to 0.45% (1 year = 31,556,926 seconds)
- Some involving 666: , 666 is the sum of the squares of the first 7 primes,
- , where the difference only occurs after the 42nd decimal place!