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For questions in Mathematics Education as a scientific discipline. For more hands-on questions on teaching Mathematics, please use the tag teaching. There is also a Stack Exchange community http://matheducators.stackexchange.com/

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An example of a beautiful proof that would be accessible at the high school level?

If we're going for "beautiful" rather than just "neat", I'd vote for the Eckmann-Hilton argument. Although it's reasonably abstract for a high-schooler, it should still be quite accessible, and has a …