The golden section was first mentioned by Euclid about 300 BC. Approximately the ratio of 8:5, this number is believed to have particular aesthetic balance and beauty. It is commonly used to explain the proportions of great works of architecture, writes Caroline Davis.
Even ancient Egyptian buildings many centuries before Euclid, such as the Great Pyramid of Cheops, have been attributed to the ratio. But researchers from Churchill College, Cambridge, claim that Egyptian builders used much simpler techniques.
Corinna Rossi, an architect and Egyptologist, said: "Modern interpretations of ancient buildings are based on our modern mathematics, but ancient Egyptian mathematics is enough to explain the contemporary architecture."
Dr Rossi says that the Egyptians had no notion of the golden section and has attempted to prove that any proportions that comply with it are following a modern tendency to see the golden section everywhere.
The golden section can be arrived at through complex geometric constructions or as the convergence of the ratios of consecutive terms in the Fibonacci series (1, 2, 3, 5, 8... where each term is the sum of the previous two).
Dr Rossi, with mathematician Christopher Tout, analysed the mathematics in the Rhind Mathematical Papyrus , written c. 1650BC and one of the most important surviving documents from the period. The problems discussed in the papyrus are regarded as lacking the theoretical content of the Greeks' mathematical constructions.
Dr Rossi found that although the Egyptians performed complex calculations with series of fractions, there was no evidence that they had the concept of convergence so could not have arrived at the golden section from the Fibonacci series.
Moreover, the Egyptians did not use scale drawings to plan their buildings. They sketched how the final building would look marking the actual lengths in cubits and would not have noticed a golden section pattern in their design. The findings, published in Historia Mathematica , could revolutionise the way Egyptian architecture and its reconstruction are approached.
Dr Rossi said: "We should stick to the way Egyptians used numbers and then we'd be more likely to be able to reconstruct their architecture."