已知線段AB=2+√5，C為AB的黃金分割點(AC＞BC)，D為AC的黃金分割點(AD＞CD)，則CD為_________.

熱心網友

解:根據黃金分割原理，AC = AB(√5 - 1)/2AD = AC(√5 - 1)/2 = AB[(√5 - 1)/2]^2那么CD = AC - AD = AB(√5 - 1)/2 - AB[(√5 - 1)/2]^2 = AB[(√5 - 1)/2][1 - (√5 - 1)/2 ] = (√5 + 2)[(√5 - 1)/2][1 - (√5 - 1)/2 ] = (2 + √5)(3 - √5)(√5 - 1)/4 = (√5 + 1)(√5 - 1)/4 = 1