Abstract

Angle trisection which involves dividing an angle into three equal parts is a classic problem in geometry However it s important to note that it s impossible to exactly trisect an arbitrary angle using only a compass and straightedge as proven by the ancient Greek mathematicians The classical geometric construction methods allow for the creation of angles that are multiples of a fixed angle using only a compass and straightedge The only angles that can be trisected exactly are those that can be constructed by repeatedly bisecting angles such as angles of 60 degrees since 60 2 2 3 5 The problem of angle trisection is closely related to the problem of angle duplication which involves constructing an angle that is twice a given angle This problem is similarly unsolvable with only a compass and straightedge for arbitrary angles If you re interested in an approximation of angle trisection one approach involves using numerical methods to approximate the trisected angle However this wouldn t involve a pure geometric construction and would likely require the use of calculators or computers to perform the calculations