Angle trisection

Common card · No. 407579

Angle trisection is the construction of an angle equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge and a compass. It is a classical problem of straightedge and compass construction of ancient Greek mathematics. In 1837, Pierre Wantzel proved that the problem, as stated, is impossible to solve for arbitrary angles. However, some special angles can be trisected: for example, it is trivial to trisect a right angle or an angle of 135 degrees, because a 30-60-90 triangle and an isosceles right triangle are constructible, respectively. It is possible to trisect an arbitrary angle by using tools other than straightedge and compass. For example, neusis construction, also known to ancient Greeks, involves simultaneous sliding and rotation of a marked straightedge, which cannot be achieved with the original tools. Other techniques were developed by mathematicians over the centuries. Because it is defined in simple terms, but complex to prove unsolvable...

Read on Wikipedia · Image Neusis-trisection.png: Dr Andrew Kepert derivative work: Skrzeczu (talk), CC BY-SA 3.0