Some of Egypt's most magnificent pyramids were deliberately designed to follow a pattern of invisible diagonal lines, an Italian study has concluded.
According to Giulio Magli, professor of archaeoastronomy at Milan's Polytechnic University, these invisible lines would connect most of the funerary complexes raised by the kings of the Old Kingdom between 2630 and 2323 B.C.
"Following these diagonals, it appears clear that the arrangement of the monuments was carefully chosen in order to satisfy a number of criteria, which include dynastic lineage, religion and astronomical alignments," Magli told Discovery News.
Published on the Cornell University physics Web site arXiv.org, the study examined the chronology and geographical location of all the pyramids of the Fourth and Fifth Dynasties, from the Step Pyramid of Djoser (2630-2611 B.C.) to the now-collapsed pyramid of Unas (2356-2323 B.C.), both in Saqqara.
"Our starting point was the so-called 'Giza diagonal,' an ideal line which connects the southeast corners of the three main pyramids and points to Heliopolis. This was an important religious center sacred to the sun god," Magli said.
While the pyramids of Khufu, the second pharaoh of the Fourth Dynasty, and his son Khafre were easily aligned along the diagonal, the pyramid of Menkaure, Khufu's grandson, had to be built very far into the desert to sit on the line of sight toward Heliopolis.
"But there is more. As a consequence of this intentional alignment, the second smaller pyramid becomes invisible from Heliopolis, its mass being covered by Khufu's larger pyramid," Magli said.
Why would Khafre position his pyramid so that it becomes invisible from the city sacred to the sun god?
According to Magli, the illusion might indicate a sign of respect for the sun god, and it might also have also launched a "symbolic invisibility" model which governed the planning of the pyramids up to the end of the Fifth Dynasty.
"Under this model, the funerary monuments of the pharaohs stand one after another, marking the dynastic link with the preceding pharaoh," Magli said. "They are linked by a diagonal which points to Heliopolis."
Attaching new pyramids to the "Giza diagonal" became increasingly difficult as the line extended far into the desert.
"It wasn't by chance that a new pyramid field rose in Abu Sir. This is the first available location in the south from which Heliopolis is not visible, although a diagonal can be drawn to link it to the city of the sun," Magli said.
The northwest corners of three chronologically successive pyramids in Abu Sir -- those identified with the tombs of Sahure, Neferirkare and Neferefre -- align on a diagonal similar to that of Giza, said Magli.
Again, the line points to Heliopolis, though the view is blocked by the rock outcrop which today is occupied by the Cairo citadel.
"Although of topographical-dynastical origin, these diagonals probably also included a deep astronomical meaning," Magli added.
He found that the Abu Rawash, Giza, and Abu Sir diagonals point to three stars -- Sirius, Crux-Centaurus, and Canopus, respectively. These stars sat in alignment over the pyramids when viewed from Heliopolis.
"This is an interesting and thought-provoking study," said David Jeffreys, senior lecturer in Egyptian archaeology at the University College London and an expert on the topography of Heliopolis.