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For questions requesting examples of a certain structure or phenomenon
3
votes
Fundamental Examples
Theorem on Friends and strangers in Ramsey Theory.
155
votes
Proofs without words
This is elementary as well, but one of my favorite ones :)
$1^2 + 2^2 + \dots + n^2 = \frac13n(n+1)(n+\frac12)$
(Author: Man-Keung Siu)
31
votes
Proofs without words
As you probably already know — there are lots of these in Proofs without Words (and II) by Roger Nelson.