Golden Number

There are a lot of interesting recurrence sequences, but the most popular one is the Fibonacci sequence. Every number or term of this sequence is the sum of the two direct preceding terms:
Fn + Fn+1 = Fn+2
and lim.n to infinite: Fn / Fn-1 = 1.618... or Phi.
...-1, 1, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377...
which is a golden number.

THE GOLDEN RECTANGLE

One of the most interesting properties of the golden rectangle is that if you cut off a square section whose side is equal to the shortest side, the piece that remains is also a golden rectangle.

The golden rectangle R, constructed by the Greeks, has the property that when a square is removed a smaller rectangle of the same shape remains. Thus a smaller square can be removed, and so on, with a spiral pattern resulting. The sides are in the "golden proportion" (1 : 1.618034 which is the same as 0.618034 : 1) has been known since it occurs naturally in some of the proportions of the Five Platonic Solids .

Also,The golden rectangle was considered by the Greeks to be of the most pleasing proportions, and it was used in ancient architecture.