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 2021-10-29, 15:47 #1 Xyzzy     Aug 2002 840810 Posts Where Transcendental Numbers Hide in Everyday Math
2021-10-29, 18:23   #2
Dr Sardonicus

Feb 2017
Nowhere

23·233 Posts

Quote:
 Originally Posted by Xyzzy https://www.quantamagazine.org/where...math-20211027/
Quote:
 More than thirty years ago I had a friend, now long gone, who was a mathematician, but not of the higher branches: he was, inter alia, thoroughly up in all that relates to mortality, life assurance, &c. One day, explaining to him how it should be ascertained what the chance is of the survivors of a large number of persons now alive lying between given limits of number at the end of a certain time, I came, of course upon the introduction of π, which I could only describe as the ratio of the circumference of a circle to its diameter. "Oh, my dear friend! that must be a delusion; what can the circle have to do with the numbers alive at the end of a given time?"
-- Augustus de Morgan, Budget of Paradoxes (On Curiosities of π)

 2021-10-29, 21:06 #3 Nick     Dec 2012 The Netherlands 33418 Posts It's a pity they didn't mention the continued fraction for e
 2021-10-30, 15:32 #4 Dr Sardonicus     Feb 2017 Nowhere 14EF16 Posts If n > 1 is an integer, a permutation $\sigma\;\in\;S_{n}$ - the group of permutations of the set of integers from 1 to n - is called a derangement if it has no fixed points; that is, $\sigma(k)\;\ne\;k$ for k = 1 to n. The number of derangements in Sn may be determined by "inclusion-exclusion." The proportion of elements in Sn which are derangements is $\sum_{i=0}^{n}\frac{(-1)^{i}}{i!}$ which is a partial sum of the Taylor series for 1/e. Last fiddled with by Dr Sardonicus on 2021-10-30 at 15:33 Reason: xignif topsy
 2021-11-26, 16:56 #5 Xyzzy     Aug 2002 203308 Posts

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