用尺规三等分一角渐近作法的探索

A New Exploration on an Asymptotic Method about Trisecting an Angle with Ruler and Compasses

尺规作图求三等分一角,已经被证明是不可解的,但是人们对三等分角的探索从未停止过。用取极限的思想对任意角多次作角平分线,可以找出近似的任意角三等分线。通过逼近速率和误差分析,作角平分线5~6次,能够达到1/1 000的精度。

Though it has been proved that it is impossible to trisect an angle with ruler and compasses in finitely many times,people have never stopped the exploration on trisecting an angle.Recently.By approximation rate and error analysis,Using the idea of taking the limit,the method constructs an arbitrary angle's angular bisectors repeatedly,and finally gets the approximate trisector of an arbitrary angle.upto one thousandth.