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Old 2021-10-29, 15:47   #1
Xyzzy
 
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Default Where Transcendental Numbers Hide in Everyday Math

https://www.quantamagazine.org/where...math-20211027/

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Old 2021-10-29, 18:23   #2
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Quote:
Originally Posted by Xyzzy View Post
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)
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Old 2021-10-29, 21:06   #3
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It's a pity they didn't mention the continued fraction for e
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Old 2021-10-30, 15:32   #4
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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
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Old 2021-11-26, 16:56   #5
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https://www.quantamagazine.org/why-e...best-20211124/

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