文[1]中将正三角形的一个性质推广到正n边形中,读后很受启发.下面尝试给出文[1]所得结论的简证并将这些结论再进一步加以推广.定理1设P为正n边形A1A2…An的可控区域内任一点,过P点分别作各边A1A2,A2A3,…,An-1An,AnA1的垂线,垂足分别为B1,B2,…,Bn,则∑n(i=1)|AiBi|=∑n(i=1)|BiA(i+1)|(其中A(n+1)=A1).说明:正多边形的可控区域是满足下列要求 In [1], we generalize a property of an equilateral triangle into a positive n-polygon, which is inspired by reading. The following is an attempt to give a brief introduction of the conclusion obtained in [1] and further extend these conclusions. Theorem 1 P is any point in the controllable area of ​​the regular n-polygon A1A2 ... An, P is the vertical line of each side A1A2, A2A3, ..., An-1An, AnA1 respectively, , Then Σn (i = 1) | AiBi | = Σn (i = 1) | BiA (i + 1) | (where A (n + 1) = A1). NOTE The controllable area of ​​the regular polygon is The following requirements