For thousands of years, scientists from around the world have tried to understand how the Egyptians designed and built the Great Pyramid of Giza – the last remaining of the seven wonders of the ancient world.
Now, an architect and researcher at the Norwegian University of Science and Technology (NTNU) says he has the answer to this ancient puzzle.
According to Ole Bryn, the Great Pyramid’s building grid was developed based on the prime number seven – and the core of Khufu’s 146.6 meters high monument is likely a step pyramid.
Khufu’s Great Pyramid, located on the Giza Plateau, was constructed around 2600 BC. It was the tallest man-made structure in the world for over 3,800 years, making it what is likely the most studied build in the history of mankind. Over time, many theories have been put forward – some more plausible (although still not accepted by the mainstream) than others – as to how the Egyptians constructed the ‘true’ pyramids.
Ole J Bryn, an architect and associate professor in NTNU’s Faculty of Architecture and Fine Art, argues that modern day scholars have been so preoccupied by the weight of the estimated 2.3 million limestone blocks – which weight roughly 7 million tons – that they tend to overlook the other major problems the pyramid builders would have faced.
In his paper, Bryn does not touch on how the ancient Egyptians would have put those enormously heavy building blocks in place – there are numerous theories about ramps and other suggestions already out there. Rather, the Norwegian scholar examined how the builders would have known where to put them.
“The need for precision is the same, whatever means one applies to get the masonry to the top,” he writes. And once it was decided where the blocks would have to go, then how was the master architect able to communicate these detailed, highly precise plans to a workforce of 10,000 illiterate men?
Bryn says that studying the plans from the thirty oldest Egyptian pyramids whilst keeping these two questions in mind, he discovered a precision system that made it possible for the Egyptians to reach the pyramid’s last and highest point – the apex point – with an impressive degree of accuracy.
“The Egyptians invented the modern building grid, by separating the structure’s measuring system from the physical building itself, thus introducing tolerance, as it is called in today’s engineering and architectural professions,” says Bryn.
In the 3rd millennium BC, the unit of measurement used to construct religious and royal structures was the Egyptian royal cubit (Rc). It represented the forearm of the Pharaoh, and was divided in 7 palms (p). The latter was then divided in four fingers, or digits. It wasn’t until the late 19th century, when Flinders Petrie was the first to accurately survey the Giza Plateau and the Great Pyramid, that a precise number for the length of an Egyptian royal cubit (Rc) was established: 52.355 cm – Khufu’s pyramid was 280 Rc hight.
Yet, 7 being a prime number, is problematic for a building grid. So how did the Egyptians solve this? “The Egyptians divided the pyramid in 7, which produced a 6-stepped core structure, with the seventh step replaced by the apex point,” writes Bryn. To produce a 3D building grid for this structure, one would need to divide 280 Rc by 7. As the Rc are divided into 7 palms, one can just change the units – from Rc to p. One palm is 4 fingers – the building grid becomes easily divisible.
Bryn points to the section of Khufu’s pyramid as the strongest evidence for the division of the pyramid into 7 parts – or six mastabas (the part of the pyramid between to steps) and the apex point. “The Queen’s chamber is placed precisely on top of the first mastaba, the King’s chamber is on the second mastaba, and the Great Gallery forms a ramp between the first and second mastabas.”
These 6 mastabas would make up the core of the pyramid, and “the accreditation walls forming the stepped core of a true pyramid are made with horizontal laid masonry” – which would allow to transfer the building’s grid vertically between the six steps, using nothing but a plumb line.
In ‘Retracing Khufu’s Great Pyramid: The ‘diamond matrix’ and the number 7‘, published May 2010 in the Nordic Journal of Architectural Research, Bryn further discusses how the use of a 6-square grid master plan would have influenced the main building grid, and thereby the geometry of the Great Pyramid. It wasn’t until the 1920s, when aerial photographs of the area were taken, that it was revealed that Khufu’s pyramid is not set on a square base. Rather, as Bryn explains, “the centre line on each face is moved inwards by a short distance at the base.” (Surprised? Look for yourself, this is clearly visible in these satellite images of the Giza Plateau.)
Ole J. Bryn’s findings will be presented and explained at the exhibition The Apex Point in Trondheim, Norway from September 13 to October 1, and in a forthcoming book to be published in the spring of 2011.