Pi appears in many more places than in ratio of circumferences to their diameter. For example, if you flip a coin n times, the probability of getting exactly n

Pi appears in many more places than in ratio of circumferences to their diameter. For example, if you flip a coin n times, the probability of getting exactly n heads and n tails asymptotically tends towards 1 / sqrt(π*n). The probability that two randomly chosen integers are coprime is 6/π^2. Etc. There is a list of formulae where π appears (some related to circles, some not) here: https://en.wikipedia.org/wiki/List_of_formulae_involving_π https://en.wikipedia.org/wiki/List_of_formulae_involving_π