SACRED GEOMETRY -- WHAT IS IT?
The term "sacred geometry" is used by archaeologists, anthropologists, and geometrician's to encompass the religious, philosophical, and spiritual beliefs that have sprung up around geometry in various cultures during the course of human history. It is a catch-all term covering Pythagorean geometry and neo-Platonic geometry, as well as the perceived relationships between organic curves and logarithmic curves.
Here are a few examples of how the "sacred" has entered into geometry in different eras and cultures:
1) The ancient Greeks assigned various attributes to the Platonic solids and to certain geometrically-derived ratios, investing them with "meaning." For example, the cube symbolized kingship and earthly foundations, while the Golden Section was seen as a dynamic principle embodying philosphy and wisdom. Thus a building dedicated to a god-king might bear traces of cubic geometry, while one dedicated to a heavenly god might have been constructed using Golden Section proportions.
2) When Hindus (ancient and modern) plan to erect any edifice for religious purposes, from a small wayside shrine to an elaborate temple, they first perform a simple geometric construction on the ground, establishing due East and West and constructing a square therefrom. (It's a simple, elegant piece of work, at about the level of high school geometry). Upon this diagram they lay out the entire building. The making of this geometric construction is accompanied by prayers and other religious observances.
3) The Christian religion uses the cross as its major religious emblem, and in geometric terms this was elaborated during the Medieval period to the form of an unfolded cube (reminiscent of example #1 above, where the cube was equated with kingship). Many Gothic cathedrals were built using proportions derived from the geometry inherent in the cube and double-cube; this tradition continues in modern Christian churches to the present time.
4) The ancient Egyptians discovered that regular polygons can be increased while still maintaining the ratio of their sides by the addition of a strictly constructed area (which was later named the "gnomon" by the Greeks); the Egyptians assigned the concept of the ratio-retaining expansion of a rectangular area to the god Osiris, who was, therefore, often shown in ancient Egyptian frescoes seated on a square throne (square= kingship again) in which the original square and its L-shaped gnomon are clearly delineated, but the geometrical construction used to create the gnomon is not shown. It is, in fact, the absense of the attendent arcs and extension lines used in the creation of geometric forms that has led art historians and iconographers such a merry chase through history. It often takes the eye of a geomterician to spot the tell-tale signs of construction.
5) One of the best-known pieces of detective work in this regard was the discovery by Jay Hambidge, an art historian at Yale University during the 1920s, that the spirals on the Ionic column capitals of ancient Greek temples were laid out by the so-called "whirling rectangle" method for creation of a logarithmic spiral. He realized this by examining numerous Ionic capitals in art museums until he located some in which the holes made by the placement of compass points had not been obliterated over time. (One of these capitals was an unfinished, broken piece, dug up from a rubbish heap near a temple -- it had apparently been damaged during manufacture and was discarded; its burial preserved it from the elements, and the marks of the geometric layout were remarkably clear upon it.) No "sacred meaning" for the log spiral form of the Ionic column capital has been determined from Greek writings, but the use of other log spirals in Greek temple architecture (for instance in floor-block proportions and their placement in relation to overall floor area) indicates that Greek architects, unlike the Romans who came after them, deliberately constructed their temples according to "whirling rectangle" geometric ratios.
By catherine yronwod
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