Mathematicians in ancient Greece showed that ruler and compass constructions could be used in a wide variety of geometrical operations. Some elementary examples are: drawing a line (or ray) through two points, drawing a circle (or arc) of arbitrary radius centered at a point, creating a point at the intersection of two nonparallel lines and drawing a perpendicular to a line at a given point. Three geometric constructions sought from antiquity are squaring a circle, doubling a cube and trisecting an arbitrary angle. These have since been shown to be impossible using only a ruler and compass.