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文[1]探究了正n边形中三角形计数问题,受其启发笔者探究了正n边形中四边形计数问题.引理1圆内接四边形为平行四边形(矩形),当且仅当该四边形的两条对角线为该外接圆的两条直径.引理2圆内接四边形为菱形(正方形),当且仅当该四边形的两条对角线为该外接圆的两条互相垂直的直径.引
The paper [1] explores the problem of counting triangles in a positive n-gon. Inspired by this, the author explores the problem of counting quadrilaterals in positive n-gons. Lemma 1 inscribed quadrilateral is a parallelogram (rectangle) if and only if the quadrilateral The two diagonals are the two diameters of the circumscribed circle. The Lemma 2 inscribed in the quad is the diamond (square) if and only if the two diagonals of the quad are the two perpendicular to the circumcircle. Diameter.