Vinkeltrisering

Vinkeltrisering, or angle trisection, is the geometric process of dividing a given angle into three equal parts. It is a classic subject in the study of geometric constructions, traditionally performed with a straightedge and a compass.

Historically, angle trisection was one of the famous problems of ancient geometry. In 1837, Pierre Wantzel proved that, using only a straightedge and a compass, it is impossible to trisect every angle. This result established a fundamental limitation of Euclidean construction and clarified which construction tasks are doable with standard tools.

Despite the general impossibility, some angles can be trisected exactly with straightedge and compass, and particular methods exist for specific cases. Moreover, more powerful tools or methods outside the classical scope—such as a marked ruler (neusis), or algebraic approaches—can achieve angle trisection for arbitrary angles. These extended methods are not part of the classical Euclidean toolkit but are used in broader geometric contexts and in some design or engineering applications.

In practice, angle trisection remains a useful theoretical example in geometry, illustrating the limits of constructibility and the distinction between exact and approximate solutions. When exact trisection is not required, several approximate constructions exist that produce a close three-way division of any given angle using standard tools.

See also: angle trisection, classical problems of geometry, neusis construction, geometric constructibility.