Constructible

A real number is said to be constructible if a [line segment]? that number of units long can be construct?ed with a compass? and unruled straight edge, given a line segment of length unity?.

Constructibe numbers comprise a field. It is a proved fact that constructible numbers do not include [cube root]?s (hence the impossibility of "[duplicating the cube]?"), general expressions of the form sine(x/3) for arbitrary x (hence the impossibility of "[trisecting the angle]?"), or the constant? pi (hence the impossibility of "[squaring the circle]?").