310 The golden section
10.1 The golden sectionφ
A segmentABis said to be divided into the golden ratio by a pointPif
AP^2 =AB·PB.
A B
M
P
1
φ
AB
AP
=φ=
√
5+1
2
.
Some basic properties ofφ
1.φ^2 =1+φ;φ^1 =φ− 1.
2.The diagonal and the side of a regular pentagon are in the golden
ratio.
3.The ratio of successive Fibonacci numbers tends toφ.
4.The simple continued fraction expansion ofφis