Sometimes called the divine proportion, the golden ratio (phi) is a mathematical manifestation of alternation in which each new length grows out of the old in unchanged proportion, thereby mirroring itself. Phi defines the point at which the ratio of the smaller part of a line to the larger part is the same as the ratio of the larger part to the whole line. Sprinkled throughout the universe, phi weaves patterns in the fabric of nature and sets the standard for cohesion, beauty and symmetry.
Very few proportions are self-referential; those that are, like pi (the ratio of a circle’s circumference to its diameter) and the golden ratio, phi, are irrational numbers — they cannot be expressed as fractions and have decimal expansions that never repeat or terminate. Irrational numbers keep popping up in nature because they are self-referential, open ended and indeterminate — properties associated with alternation, creativity and evolution. They appear mysteriously within the building blocks of nature, which alternate between diversity and unity, creation and destruction, chaos and order.