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What famous historical problems are there about regular polygons?

I am doing an essay and it has several titles. Overall title is: The history of mathematics. Group title: Famous problems. Individual title: Regular polygons. I have spent several hours reading through a lot of books and internet pages and cannot find anything very specific.

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One Response so far.

  1. silipan says:

    Well there’s the classical constructibility of a regular polygon with a given number of sides using only a ruler and compass. There’s a Wikipedia page on constructible polygons, which might be a starting point for your research. Gauss characterized constructible polygons around 1800, though only published half of it.This problem goes back to the Greeks, and Gauss’ solution gained him quite a bit of fame.