Why did the ancient Greeks give so much importance to the construction of regular polygons with $n$-sides using only ruler and compass and tried to study for what $n$ was such a construction possible? ...
I entered 2^63 as a stand alone value at WolframAlpha. Among the responses was a factoid that 'A regular 9223372036854775808-gon is constructible with a straightedge and compass.' What is such a ...