Pi appears in many more places than in ratio of circumferences to their diameter... | Hacker News

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Al-Khwarizmi on March 19, 2016 | parent | context | favorite | on: How Many Decimals of Pi Do We Really Need?

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

ikeboy on March 19, 2016 [–]

But how many coins can you flip before the heat death of the universe, and does using 43 digits make your expectation off by more than say 1/1000000?

In other words, if you were trying to calculate pi by checking the actual probabilities, how many digits can you get?

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