这P就是线段AB的黄金分割点.
设PB=X,则AP=1-X,
∵AB/AP=AP/PB,
∴AP^2=AB*PB,
(1-X)^2=X
X^2-3X+1=0
X=(3±√5)/2,舍去X=(3+√5)/2(因为大于AB=1)
PB=X=(3-√5)/2
这P就是线段AB的黄金分割点.
设PB=X,则AP=1-X,
∵AB/AP=AP/PB,
∴AP^2=AB*PB,
(1-X)^2=X
X^2-3X+1=0
X=(3±√5)/2,舍去X=(3+√5)/2(因为大于AB=1)
PB=X=(3-√5)/2