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For questions requesting examples of a certain structure or phenomenon

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.
3 votes

Fundamental Examples

Theorem on Friends and strangers in Ramsey Theory.