Knowra Straightedge and compass construction Straightedge and compass construction A geometric construction using an unmarked straightedge and a compass to draw lines and circles and locate their intersections. It formalizes which geometric objects can be obtained from given points using these tools.
Line–line intersection : The unique point shared by two distinct nonparallel lines. Two constructed lines yield a new point whenever they cross.
Euclidean geometry : The geometry of points, lines, angles, and distances governed by Euclid's parallel postulate. The classical construction rules are formulated within this geometric framework.
Marked ruler construction : A geometric construction that permits placing a ruler with marks at prescribed points. A marked ruler enables constructions, such as general angle trisection, forbidden by the classical tools.
Euclid : An ancient Greek mathematician traditionally dated to around 300 BCE, author of the Elements. The Elements organized geometric propositions and constructions into an axiomatic system.
Pierre Wantzel : A French mathematician who proved in 1837 that angle trisection and cube doubling are generally impossible by classical construction. His algebraic criterion settled two major ancient construction problems.
Line–circle intersection : The point or points shared by a line and a circle. A line and circle can produce up to two new constructed points.
Compass : A drawing instrument used to draw circles or transfer distances between points. It creates circles centered at known points with radii set by known distances.
Origami mathematics : The study of geometric constructions performed by folding paper according to specified axioms. Some origami folds solve cubic equations that straightedge and compass cannot.
Euclid's Elements : A mathematical treatise presenting geometry and number theory through definitions, postulates, and proofs. Its first book sets out basic constructions using a straightedge and compass.
Carl Friedrich Gauss : A German mathematician whose work established deep links among number theory, algebra, and geometry. His criterion for constructible regular polygons transformed the study of classical constructions.
Show all 26