Constructible number

Number constructible via compass and straightedge

In geometry and algebra, a real number r {\displaystyle r} is constructible if and only if, given a line segment of unit length, a line segment of length | r | {\displaystyle |r|} can be constructed with compass and straightedge in a finite number of steps. Equivalently, r {\displaystyle r} is constructible if and only if there is a closed-form expression for r {\displaystyle r} using only integers and the operations for addition, subtraction, multiplication, division, and square roots. The geometric definition of constructible numbers motivates a corresponding definition of constructible points, which can again be described either geometrically or algebraically.

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