对圆周七等分及作正七边形的计算

在工程施工和现场操作中总会遇到圆周七等分的问题。高等教育课程在几何作图这一节给出了圆周七等分的画法。但课本仅给出了作图方法，而对原理未作解答。在此利用对称原理、勾股定理、余弦定理和切割线定理，推算出教材中近似圆周七等分各弦长的解，并比较了各段弦的近似值与真实值的误差，对圆周七等分作图法进行了证明计算。

Calculationsfo r dividing seven equal parts of a circle and a construction method of an approximate reg ular heptagon

The problem of dividing a circle into seven equal parts is very common in engineering construction and on-site operations.A practical construction method of dividing seven equal parts of a circle is presented in descrip-tive geometry section of higher education courses, but the principle of the method has not been proved.In this pa-per, by applying symmetry principle, the pythagorean theorem, cosine theorem and the tangent-secant theory, the solutions of the approximate seven equal division chord length are deduced, and the errors between real values and approximate values of each chord are calculated to illustrate comparisons for researchers.