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Geometry and Number Theory on Clovers
"... (x 2 + y 2) 2 = x 2 − y 2 pictured in Figure 1, can be divided into n arcs of equal length by straightedge and compass if and only if n is a power of 2 times a product of distinct Fermat primes [1, p. 314]. By an earlier theorem of Gauss, these are exactly the values of n for which a regular n-gon i ..."
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(x 2 + y 2) 2 = x 2 − y 2 pictured in Figure 1, can be divided into n arcs of equal length by straightedge and compass if and only if n is a power of 2 times a product of distinct Fermat primes [1, p. 314]. By an earlier theorem of Gauss, these are exactly the values of n for which a regular n-gon is constructible by straightedge
