Geometric construction

A geometric construction creates points, lines, and figures through explicitly permitted operations. Classical constructions use an unmarked straightedge and compass.

Compass-and-straightedge construction: A geometric construction using only an unmarked straightedge and compass. It is the classical rule system that gives geometric construction its best-known form.
Straightedge: A ruler-like tool used to draw straight lines, without measuring distances in classical constructions. Its restriction to drawing lines distinguishes classical construction from measurement.
Angle trisection: The problem of dividing an arbitrary angle into three equal angles using specified geometric tools. Its impossibility with classical tools reveals a sharp limit of construction.
Euclidean geometry: The geometry of flat space developed from axioms associated with Euclid. Classical constructions developed within the geometric tradition formalized by Euclid.
Euclidean plane: The flat geometric space described by Euclidean geometry. Classical construction operations take place in this plane.
Compass (drawing instrument): An instrument with two legs used to draw circles or transfer distances. It supplies the circles and equal-radius comparisons allowed by the classical rules.
Doubling the cube: The problem of constructing a cube with twice the volume of a given cube. Its solution requires a length that classical constructions cannot produce.
Euclid: An ancient Greek mathematician traditionally associated with the foundational work Elements. Elements presents geometric propositions through constructions and proofs.
Line–line intersection: The point where two distinct, nonparallel lines meet. Constructing intersections of lines is one permitted way to create points.
Perpendicular lines: Lines that intersect at a right angle. Constructing perpendiculars is a basic task built from straightedge-and-compass operations.

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