Archives Photo of the Week: The Great Pi-ramid?

March 14, 2014

General view of the pyramids.
General view of the pyramids at Giza, ca. 1876-1885, by Felix Bonfils.
Penn Museum Image #165370.

A quick note: On most Fridays,  Archivist Eric Schnittke posts cool and interesting photos from the Penn Museum Archives here on our blog. I’m happy to say that Eric is at home with his wife Maureen and their brand new baby, Cormac Xavier, who was born just this past Monday. We at the Museum congratulate the new Mama and Papa, and in Eric’s absence, I’ve taken it upon myself to share an archival contribution of my own. Hope he doesn’t mind.

Today is March 14 (3/14), which means it’s Pi Day – an offbeat holiday in honor of the great, mysterious mathematical constant known as π (pi). And the photo you see above is a general view of the pyramids at Giza, taken in the 1870-80’s by French photographer Félix Bonfils.

Soooooooo… what do these two have to do with each other?

Sir William M. Flinders Petrie
Portrait of Sir William Matthew Flinders Petrie, 1903. Public domain image.

It depends on whom you ask. Take Sir William M. Flinders Petrie (shown at right), the British Egyptologist who excavated at many sites throughout Egypt, and who surveyed the Giza Necropolis. Petrie was one of numerous Egyptologists—neither the first, nor the last—who suggested the possibility of pi playing a role in the design of the Great Pyramid.

See, the Great Pyramid—one of the seven wonders of the ancient world, and the tallest man-made structure in the world for nearly four millennia—bears some interesting measurements. For ancient Egyptians, the basic unit of length was the mh, referred to in English as the cubit—roughly the length between an adult’s elbow and the tip of the middle finger. It was generally assumed that the base of the Great Pyramid was planned to be 440 cubits on each side (1760 in total) and 280 cubits in height.

Here’s where pi comes in. Petrie noted that the ratio of the base of the pyramid’s perimeter to its height, using these assumed ancient measurements, was 44:7. That’s exactly twice one common approximation for pi, 22/7, which led him to suggest the possibility of something referred to as “pi-theory”—the idea that the Great Pyramid was designed in such a way that, if if you drew a circle around the pyramid, its radius would match the pyramid’s height.

An extremely rudimentary mockup of what Petrie is talking about.
An extremely rudimentary mockup of what Petrie is talking about.

Petrie put it nicely in a letter to a friend when he wrote, “Thus we have a radius set upright [i.e. the altitude] on its parent centre, and its own exact circle’s length delineated systematically around it on the ground.” The implication was that the Egyptians had designed the pyramid with an approximation of pi in mind.

But unfortunately, there’s no written evidence to back up this very specific, but important, detail. While the Great Pyramid’s construction in the 26th century BCE, the earliest written approximations of pi don’t appear in history for another 600 years or more.

The pi-theory became well-known through its consideration or acceptance by numerous Egyptologists, before and since Petrie. But others argue that the perceived role of pi in the pyramid’s design was merely a coincidence. A book called The Shape of the Great Pyramid (2000) by Roger Herz-Fischler offers a fantastically thorough analysis of the history and propagation of pi-theory, as other theories surrounding the design of this fascinating structure.

In the end, we can entertain theories about the motives of those who came before us. But without concrete evidence to support a theory, it’s misleading to assume it as fact, no matter how unique a coincidence it appears to be—which is why we can’t say that the pyramids were designed using pi.

Photo (and baking) by my friend Sarah Lovelace.
Photo (and baking) by my friend Sarah Lovelace.

Eric will be back on the job in a few weeks – look forward to more weekly photos from the archives when he returns. As for me, all this thinking has given me an appetite.