Solution: Let a line segment have a length of 1 and a small line segment with a length of x, which is equal to the ratio of this line segment with a length of 1 to other line segments, so it is the golden section.

X/ 1=( 1-x)/x can be obtained.

x？ = 1-x

x？ +x- 1=0

x=((- 1) (√( 1？ -4× 1×(- 1)))/(2× 1)

x=((- 1) (√5))/2

∴x 1=((√5)- 1)/2, x2=((- 1)-(√5))/2 (not practical, omitted).

The length of the line segment is (√5)- 1)/2,