Beautiful theorems with short proofs

This question was asked on mathoverflow, and closed because it was judged to be subjective (are judgements of beauty really subjective??)  Luckily a few answers were posted before the question was shut off.  You can judge for yourself:

Feel free to post your reactions (which won’t be closed!) below.

About manyapajama

Associate Professor in Mathematics Education, and part-time poet.
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