Angle trisection is the classical problem of constructing an angle equal to exactly one third of a given arbitrary angle, using only an unmarked straightedge and a compass. It was one of the three famous construction problems of ancient Greek geometry. In 1837 the mathematician Pierre Wantzel proved that trisecting an arbitrary angle with only these two tools is impossible in general, although certain special angles, such as a right angle, can be trisected this way. The problem can be solved if tools beyond the straightedge and compass are allowed, such as the neusis construction already known to the ancient Greeks, which permits a marked straightedge to slide and rotate at the same time. Because the problem is easy to state but its impossibility is difficult to prove, it has long attracted amateur mathematicians who mistakenly claim to have solved it within the original rules.
Facts
StatementAn arbitrary angle cannot be trisected using only an unmarked straightedge and compass. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Angle trisection (Wikipedia)
Lead section
In 1837, Pierre Wantzel proved that the problem, as stated, is impossible to solve for arbitrary angles.
Section: Proof of impossibility
Pierre Wantzel published a proof of the impossibility of classically trisecting an arbitrary angle in 1837.
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