CentralNotice From Wikipedia, the free encyclopedia Jump to: navigation , search For numbers "constructible" in the sense of set theory , see Constructible universe . For example, the square root of 2 is constructible : from the length unit, we can construct a line segment of length with straightedge and compass. A point in the Euclidean plane is a constructible point if, given a fixed coordinate system (or a fixed line segment of unit length ), the point can be constructed with unruled straightedge and compass . A complex number is a constructible number if its corresponding point in the Euclidean plane is constructible from the usual x - and y -coordinate axes. It can then be shown that a real number r is constructible if and only if , given a line segment of unit length, a line segment of length | r | can be constructed with compass and straightedge. [ 1 ] It...