Tetrahedral Tombstone

We all know about the Egyptian pyramids—those tetrahedral tombstones built to house the great pharaohs' bodies, preserved as mummies in perpetuity. For well over four thousand years the Great Pyramids of Giza have fascinated people. They are magnificent engineering feats that were included in every list of the ancient world's wonders. All the other wonders have vanished, while the pyramids endure.

I recently took an online course from Harvard University, on the Pyramids of Giza. The experience inspired me to construct my own pyramid—a 250^th scale model of the Pyramid of Khufu, which is also known as the Great Pyramid at Giza. Here are a few impressive geometric facts about this largest Egyptian tetrahedral tombstone: It is 481 feet (147 m) tall. That's equivalent to nearly the height of a 50-story building! The length of a side is 755 feet (230 m). That's equivalent to two and a half American football fields long! It is a perfect tetrahedron—that is, its faces are four equilateral triangles, and was built up using over 2.5 million stone blocks. That's pretty impressive!

The course noted that the origin of the idea for Egyptians to build pyramids came from the small, pyramid-shaped mounds of mud left behind, when the Nile River flooded each year. The flooded Nile was literally worshiped as a life-giving phenomenon, so its leftover mud deposits took on a mystical quality. Eventually, some ancient pharaohs began building geometric structures inspired by the mud mounds. The first few did not do well. Some were later torn down (or collapsed), and some had their design modified during construction, in attempts to make them stable. Finally the architect Hemiunu designed and oversaw the building of the largest pyramid for Pharaoh Khufu—built nearly 4600 years ago. The accuracy with which these tombs were built is astounding. Their longevity is astonishing.

I became inspired by the Giza Pyramids, and decided to build my own great pyramid, out of mortar (mixing cement, sand, and lime). It would be a 1:250 scale model—that is, 250 times smaller than the original. So the 481 foot tall Khufu's pyramid scaled down to a height of 23 inches (60 cm), with a side about 36 inches (90 cm) long. I would not try to build my pyramid from a couple million stone blocks as the original, but by constructing a wooden mold, and then filling it with mortar. I'd cast it while it lay on its side, and then tip it up into place.

The Great Pyramid at Giza is much more than a solid pile of stone—its interior is riddled with tomb chambers, passageways, and shafts of air that point toward the sky. Some of these chambers were hidden, but robbers excavated and stole many burial artifacts from several of the pyramids.

My 1:250 copy of Khufu's tetrahedron also has its secret chambers—in the form of bottles and cans that I immersed in the mortar, in order to decrease its potential weight from over 800 pounds (370 kg) to something about half that. Otherwise, tipping it upright would have been more of a job than I wanted.

I found that my engineering and construction skills paled in comparison to Egyptian architect Hemiunu. Maybe I can take solace in the fact that the design and construction of my pyramid required but a couple of weeks, rather than the more than 20 years for Khufu's. I discovered a few complicating factors that I'd not expected, although probably far fewer than those ancient Egyptians encountered.

So now I have my own cementaceous tetrahedron—even if it's just a tomb for trash. Will it acquire some of the mystical powers reputed to be possessed at Giza? I may have to wait a millennium or two, to find out. I possibly have a mysterious energy field already, however. The next couple of blog postings describe what has happened.