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.
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 geometeric 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” geometeric ratios.