A golden rectangle has the interesting property that, if you create a new rectangle by swinging the long side around one of its ends to create a new long side, the new rectangle is also golden. Phi is the golden ratio. Dividing each number in the Fibonacci sequence by the number that precedes it stabilizes around the value of phi. Phi appears in nature in the arrangement of petals on a flower.
Plants seem to produce leaves, petals and seeds based upon the golden number.
The golden ratio that appears as a rectangle in human constructs often is expressed in nature forms as an elegant spiral. The Egyptians used the golden ratio when building temples and places for the dead. If the proportions of their buildings weren't according to the golden ratio, the deceased might not make it to the afterlife or the temple would not be pleasing to the gods. As well, the Egyptians found the golden ratio pleasing to the eye. They used it in their system of writing and in the arrangement of their temples.