What a kid learning math can look like -> working through a pretty challenging geometry problem

My older son had a really neat geometry problem on his enrichment math homework. The problem is this:

Let A_1, A_2, \ldots, A_n be the vertices of a regular n-gon, and let B be a point outside of the n-gon such that A_1, A_2, B form an equilateral triangle. What is the largest value of n for which A_n, A_1, and B are consecutive sides of a regular polygon?

His solution to this problem this morning surprised me because his starting point was “what happens if n is infinite?”

I asked him to present his solution tonight. It certainly isn’t a completely polished solution, but it is a great example of how a kid thinks about math

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