
Mathematical coincidence - ColinWright
http://en.wikipedia.org/wiki/Mathematical_coincidence
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ColinWright
Repeating here the relevant section from my comment earlier[2]:

The idea is that there are only so many small numbers, and there are lots of
ways of combining things together. The Pigeonhole Principle then says that if
you stuff too many things into a small enough space, some of them will be
close together. Although apparently obvious, this is more widely applicable
than people generally realize. It's used, for example, in one of the proofs
that that every prime of the form 4k+1 is expressible as the sum of two
squares (Examples: 29=4x7+1=5^2+2^2, 181=4x45+1=10^2+9^2).

Combine this with the birthday problem/paradox[0][1], and you end up with more
coincidences than you might expect.

[0]
[https://news.ycombinator.com/item?id=1312636](https://news.ycombinator.com/item?id=1312636)

[1]
[https://news.ycombinator.com/item?id=4753014](https://news.ycombinator.com/item?id=4753014)

[2]
[https://news.ycombinator.com/item?id=7892425](https://news.ycombinator.com/item?id=7892425)

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dalke
Also, [http://xkcd.com/1047/](http://xkcd.com/1047/) .

