本文介绍正n棱锥的几个有趣性质与应用,供读者参考.定理正n棱锥S-A1A2A3…An-1An的侧面等腰三角形的顶角为α,相邻两侧面所成二面角的平面角为β,侧棱与底面所成的角为θ,侧面与底面所成的角为φ,π是圆周率.则图1定理图(1)sin2βcos2α=cosπn;(2)tanθcotφ=cosπn;(3)sin2β This article describes several interesting properties and applications of positive n-pyramids, for the reader’s reference. Theorem positive pyramids S-A1A2A3... An-1An side isosceles triangle with apex angle α, adjacent two sides into a dihedral plane The angle is β, the angle formed by the side edge and the bottom surface is θ, the angle formed by the side surface and the bottom surface is φ, and π is the pi. The theorem of Fig. 1 (1) sin2βcos2α=cosπn; (2) tanθcotφ=cosπn; (3 )sin2β