Mathematicians define the golden section as a relation in which the smaller unit is to te larger unit as the larger is to the sum. In other words, a:b = b:(a+b). The name for this relation is phi. Its numeric value is 1.618034. Phi is an interesting number. If you add 1 to it you get its square. If you subtract 1 from it, you get its reciprocal (1/phi). If you keep multiplying it by itself you get an infinite series that retains the phi proportion.
The thirteen-century Italian mathematician Leonardo Fibonacci discovered that the phi proportion often manifests itself in nature as a spiral of increase found in snails, seashells, pinecones, and so forth. And so, it is said, did Maya mathematicians.
One element contributing to the beauty of Maya architecture may be its use of the golden section. (In the image above, I have drawn an approximate golden section over the opening atop the east court at the Maya ruins of Copan in Honduras.) Of course, we must beware of what a professor of mine called “the blueberry principle” — if you are out gathering blueberries you tend not to notice anything else, and you tend to see blueberries wherever you look. If we go looking for the golden section, we are likely to find it. But does this mean the Maya consciously employed it?
A researcher named Christopher Powell concluded that the answer to this question is “yes.” He says that the fundamental shape of Maya geometry is the golden section, and that the Maya composed such sections using a procedure that is brilliant in its simplicity. Using a cord, it is easy to construct a square. If the cord is doubled back on itself it obviously becomes half the length, and that halved cord can be used to find the midpoint of one of the sides of the square. Next, if the cord is placed on the midpoint and extended to one of the opposite corners, it can be swung like a compass in an arc that will define the length of a golden section, from which the final rectangle can be constructed.
Powell observed modern Yucatec Maya using this very technique. He was told that the use of the cord makes houses that are like flowers because of the relations of their proportions. His theory appears to have been confirmed by red marks that remain on some structures at Copan and Tikal and suggest sizing via this cord method.
In the Popul Vuh it is written that gods used the following method to lay out the cosmos:
Its four sides
Its four cornerings
Its four stakings
Its doubling-over cord measurement
Its stretching cord measurement
Its womb sky
Its womb earth
Four corners as it is said
- Linda Schele and Peter Mathews, The Code of Kings (Scribner)
- Alan Christenson, tr., The Popul Vuh, translation adapted by Schele and Mathews
- See also the Dennis Tedlock version of the Popul Vuh with his comment on this section in which he says that it is based on the cord approach to layout, and he reports that a source informed him that the passage “describes the measuring out of the sky and earth as if a cornfield were being laid out for cultivation.”
- Christopher Powell