The problem of angle trisection is one of the three major geometric drawing problems put forward by the ancient Greeks 2400 years ago, that is, any angle is divided into three equal parts with compasses and rulers. The difficulty of the problem lies in the limitation of drawing tools. The ancient Greeks demanded that only rulers (rulers without scales, only straight lines) and compasses be used in geometric drawing. This problem attracted many people to study, but no one succeeded. In 1837, Fanzier (18 14- 1848) proved that this is an impossible proportional drawing problem by algebraic method.

In the process of studying angle trisection, special curves such as clam shell line, heart line and conic curve are found. It has also been found that as long as the subject of "drawing with a ruler" is abandoned, it is not a difficult problem to divide the angle into three parts. The ancient Greek mathematician Archimedes (287- 2 BC12) found that as long as a point was fixed on the ruler, the problem could be solved. The method is briefly introduced as follows: add a little p to the edge of the ruler, the foot tail is O, let the angle to be divided into three parts be ∠ACB, take C as the center and OP as the radius, and make a semicircle with intersecting edges at A and B; Make point o move along the straight line of CA and point p move on the circumference. When the ruler passes through B, connect OPB. Because OP = PC = CB, ∠ COB = ∠ ACB/3. The tools used here are not limited to rulers, and the drawing method does not conform to the postulate.