Based on what I have read they mostly fell off in an earthquake and were then repurposed. In 1196 workers tried to dismantle one, they found it was more work then just quarrying new stones.
I mean certainly it is it worse shape now than it was in antiquity, but it is a far different thing to say “from the remaining ruins, we can make some inferences about where the coating used to be and where the capstone (which I’ve just learned is called a “pyramidion”) was and it was fairly close to where it ought to be” than it is “the tip of the pyramid is we measured it last week is fairly close to where it ought to be”.
The point is, if someone is saying “the tip is out of position by a few inches” I’d want to know the methodology they were using to find the “ideal” position of the tip. And given that the tip itself is missing, I’d also want to know what methodology they were using to determine the “actual” position of the tip. I’d expect there would be significant margin of error in both calculations.
The classic pyramid shape required several generations of experimentation. Archeologists have found designs that failed.
All that previous knowledge was used by the Giza pyramid builders.
It’s interesting to see the early tombs and step pyramids.
I don’t see the difficulty - it’s basic measuring. Eyeballs.
A trough or hose is a basic level - water surface at each end is the same height.
Build a level circular wall. Eyeball from center point where a star rises at dusk and sets at dawn, mark those points and the center of the line between them to the center of the circle is true north.
Use that level process to get a flat base. Giza was useful because it was a shelf of limestone overlooking the river, so a pretty good site. Had a nice lump sticking up, ready to be repurposed as a giant man-lion statue.
You’ve established the center point of the pyramid wall side. Mark that when you place the first stone for the next level at the center. By sight, you can ensure each level’s first edge stone, when placed, is exactly the right amount back to maintain the slope. the corners of that level edge are equidistant from this center point. Stones were cut on the ground before being hauled up so before stone A is hauled away, the side of stone B that faces it will be smoothed to fit exactly.
Rinse and repeat. Latest best guess is that they built a mud brick ramp circling the pyramid on the way up, on the ledges of the pyramid structure. This uses a LOT less material than a plain ramp would have. The classic “straight ramp” in illustrations would require more material than the pyramid itself.
Once they got to the top, they would have worked their way back down installing the perfectly smooth polished limestone sides as they removed the ramp. At this point, any additional minor corrections can be made. (Yes, only the middle Giza pyramid still has a noticeable collection of the original casing, and only near the top).
The first pyramid was the Step Pyramid at Saqarra - no fancy finish, made with much smaller bricks, and analysis shows it was built in stages - the base was originally a rectangular shape like traditional tombs, then expanded to square, then expanded again and successively smaller layers added. That look probably gave them the idea to make bigger and smoother ones - and using much bigger blocks made the process faster.
It was trial and error - for example, they started building the Bent Pyramid at too sharp and angle - too ambitious. As cracks appeared, they realized their mistake and half-way up changed the angle.
(Incidentally, if you are ever in Cairo, visit the “Cave Church” across the Nile from Giza where allegedly the blocks were quarried. It’s an amazing different sight, especially the drive through Garbage City to get there. Back in the day, the Nile flooded to the foot of the Sphinx and it was easy to barge the blocks across.)
As time went on and the First Kingdom fell apart, the building process got sloppier. They would build an outer wall and fill the interior with rubble, so many of the later pyramids simply did not last 3000-plus years. Earthquakes and weathering shook them down. You can visit Teti’s pyramid, it’s just a pile of rubble with access to the burial chamber. It was probably the best he could do, maybe 100 feet to 150 feet on a side and rubble-filled. They also eventually realized building a giant “come and get it” symbol over top of a bunch of valuable grave goods was not the best plan to provide for the dead for eternity - hence the tunnel graves of the later eras.
One way to do it is to have a range of blocks ready to go … say its 40 inches high at your start point.
well you have a whole bunch of 41, 40.5, 40,39.5,39 … lined up … ready to measure the required height.
You put the 40" one at your start point, then you set the measuring blocks at the 4 (or 3 other) corners.
Well you can then see you need a 38 at one corner, and there’s a peak along the way to it, so at the that way you collect a line of 36,36.5,37,37.5 ,38 on the peak , and 37.5,38, 38.5, 39.5’s in the closer regions. So you select the nice fitting blocks, clearly if there’s a 38 and a small space and 39, then maybe some 38.5’s go in the middle… the ones you don’t use will be used soon, they aren’t wasted.
When it comes to filling the last bit, you can have some narrow and short blocks ready too. These can go deep inside the layers where no one can see the rough fit from dropping a 36 in a 38 space… but height you want to keep accurate.
I’d assume they could run a string-line from opposite corners each course to re-establish the center and measure out from there to correct as needed.
Here’s the thing I find curious:
One description says 1° dip, so for half a 725 foot pyramid base, that would be 6 foot indent to the middle of the side at the base. Another description says "dip of 1° of 1/2° " which seems like several people copied someone’s typo. With the casing gone, the stones are pretty ragged, but a 6 foot indent should be noticeable.
Interesting article, but they left out a key item: The Red Pyramid of Sneferu. This was the first true pyramid of the Fourth Dynasty, predating the Great Pyramid by a generation or so.
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It may only be my imagination, but the reason this seems important to me is that this pyramid is less steep than the ones that followed. So after building the first uccessful true pyramid, they still needed to work out how to make them steeper, and accordingly much more impressive.
Why not make all your blocks of the same size and, if one doesn’t fit, you beat the bejesus out of it until it does? That is a standard way stonemasonry has been done.
These aren’t Lego bricks - moving them around by dragging is geometrically awkward, and this on a plane that is rapidly shrinking in size as it gets higher. There is no space to just park 2-10 ton blocks of stone in case one might come in handy.
One theory attributes the fine fit (and probably, the precision of block size) to “one simple trick”. Each block was cut to fit against the block that went up before it, on the ground before that previous block was taken up.
You can still visit the Red Pyramid, but the exterior is crumbling badly. Still, that’s pretty good shape for over 4,000 years. The Meidum pyramid, built just before that, seems to be originally the halfway point. You can still see the interior step structure. When they tried to cover the structure to make a rtue pyramid, it collapsed. Meidum - Wikipedia