1正多边形定义的推广———“分数”多边形图1将圆周五等分,画出正五边形和五角星.而五角星也是“五条边相等、五个顶角相等”的几何图形,它“符合”正多边形的定义中各边相等,各角相等的条件,但不是凸多边形.易求出它的顶角为36°.将36°代入正多边形内角公式:36°=(n-2)n×18 1 Generalization of the Definition of a Regular Polygon - “Score” Polygon Figure 1 The circle is divided into five equal parts to draw a regular pentagon and a pentagonal star. The pentagram is also a geometric figure with “five edges equal and five apexes equal”. It “conforms” to the definition of a regular polygon where all sides are equal and each corner is equal, but not a convex polygon. It is easy to find its apex angle of 36°. Substituting 36° into a regular polygon interior angle: 36° = (n -2)n×18