若P是正n边形A1A2······An的内心,则有向量PA1+向量PA2+向量PA3+······向量PAn=0?
问题描述:
若P是正n边形A1A2······An的内心,则有向量PA1+向量PA2+向量PA3+······向量PAn=0?
答
正2n边形,相对的向量两两抵消;正2n+1边形,可将PA1分解为A2A1+A3A1,类推,最后也是A2A1与A1A2这类,两两抵消