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]?").