已知AB等于18cm,点P和点Q是线段AB的两个黄金分割点,则PQ=

取AB为a,PB为AP和PB中较短的一段,设长为x,AB :AP = AP :PB
a :(a - x) = (a - x) :x
(a-x)(a-x) = ax
x² - 3ax + a² = 0
x = (3 - √5)a/2 (另一解为负,舍去)
类似地,AQ = PB = (3 - √5)a/2
PQ = AB - AQ - PB = a - 2*(3 - √5)a/2 = (√5 -2)a
= 18(√5 - 2) cm