must be a power of 2. The field extension generated by , however, is of degree 3.

Proof of impossibility

We begin with the unit line segment defined by points (0,0) and (1,0) in the plane. We are required to construct a line segment defined by two points separated by a distance of . It is easily shown that compass and straightedge constructions would allow such a line segment to be freely moved to touch the origin,

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