No, the pyramids bases and its height have an relation which is exact Pi, but only because the Egyptians used a Wheel to measure with x turns tha base and the hight with x diameters of this Wheel, so the relation of 2 sides/height is Pi, without knowing the value of this number. They did it because the Wheel was a sacred symbol of the Egipcians.
I don’t think that’s the case. Weirdly enough, I think it’s a coincidence.
Who would use circumferences of a wheel in one axis, but diameters of a wheel for another?
See…have you ever laid out a roof? Here in inch land, the slope of a roof isn’t given in degrees, it’s given in rise over run, and run is typically 1 foot or 12 inches. So a slope of 45 degrees works out to 12 in 12, it rises 12 inches for every 12 inches. You’ll find a lot of American roofs have a 33.69 degree angle. Why that weird number? It’s a slope of 8 in 12.
Pause for the Europeans to cope with being carried through the industrial revolution by the English and Americans by pontificating about metric. Are we done? Good. Moving on.
The ancient Egyptians didn’t have feet and inches, they had cubits, palms and fingers. Four fingers to a palm, seven palms to a cubit. The Egyptian unit of slope is the Seked, palms of run per cubit of rise. Notice that: We’re now in run over rise, not rise over run.
The first (attempt at a) smooth sided pyramid is the Bent Pyramid built for Sneferu. It starts off at a Seked of 5, which works out to a smidge over 54 degrees. The popular lore is the building started showing cracks, so to save weight they reduced the slope to a Seked of 7.5, which works out to 43 degrees. The nearby Red pyramid, also attributed to Sneferu and apparently built immediately after, is built entirely at that 43 degree angle.
The pyramid at Meidum, Sneferu’s other pyramid, was first built as a stepped pyramid like Djoser’s, and then modified into a smooth sided pyramid, with a Seked of 5 palms, 2 fingers, or about 51 degrees. This worked, at least in antiquity (the Meidum pyramid is heavily ruined in the modern day).
So when his son Khufu decided to build the biggest pyramid of all time (and nobody has proven the magnificent bastard wrong yet), that’s the slope he used. 5 palms, 2 fingers. 51 degrees.
So the ratio of the Great Pyramid’s height to the distance from the center to the middle of a base edge is 7 to 5.5. That means the ratio of the height to the length of a base edge is 7 to 11. Which means if we take the length and width of the pyramid’s base, and divide it by the height, we just so happen to get 22 / 7, which about a millennia later the Greeks would discover is a pretty good approximation for Pi, but the 4th dynasty Egyptians didn’t know about that.
That’s not what Khufu’s son Khafre did. Khufu was a magnificent bastard but Khafre was clever sumbitch. Khufu built the world’s biggest pyramid. Khafre built his slightly smaller pyramid uphill from his dad’s so his would look bigger. And, he built it very slightly steeper, with a Seked of 5.25 (about 53 degrees). That works out to the same slope as a 3-4-5 triangle. 3/4 is 0.75, and because Seked is given as palms per cubit we multiply by 7, 0.75 * 7 is 5.25. And they DID know about that in the 4th dynasty. Clever sumbitch.
To get a pi ratio, you need one measurement to be made with the diameter of the wheel, and another made with the circumference of the same wheel. You can certainly use ropes, but one of those ropes needs to be a multiple of the diameter, and the other a multiple of the circumference.
You might be measuring short lengths with a particular unit, say, a “stick”. To get consistent longer measurements, you might measure 100 turns of rope around a spool one “stick” in diameter. The length of that rope might be called a “string”.
The architects of a building might pound two rods into the ground, one “string” apart, and tell the masons to construct a wall between those rods. The architect wants a wall; the architect doesn’t particularly care how long the bricks are. The masons don’t particularly care how long the wall is going to be, just where they need to start and stop. The brickyard workers don’t care how long a string is, they just need a consistent measurement for their molds.
Nobody involved particularly cares about pi, and yet the resulting building will have pi ratios all over the place.
You still need to have one specific circle that you want to make the unit of measure because if you have 2 different circles, they will have different measurements.
Every number is divisible by pi.
No, the pyramids bases and its height have an relation which is exact Pi, but only because the Egyptians used a Wheel to measure with x turns tha base and the hight with x diameters of this Wheel, so the relation of 2 sides/height is Pi, without knowing the value of this number. They did it because the Wheel was a sacred symbol of the Egipcians.
I don’t think that’s the case. Weirdly enough, I think it’s a coincidence.
Who would use circumferences of a wheel in one axis, but diameters of a wheel for another?
See…have you ever laid out a roof? Here in inch land, the slope of a roof isn’t given in degrees, it’s given in rise over run, and run is typically 1 foot or 12 inches. So a slope of 45 degrees works out to 12 in 12, it rises 12 inches for every 12 inches. You’ll find a lot of American roofs have a 33.69 degree angle. Why that weird number? It’s a slope of 8 in 12.
Pause for the Europeans to cope with being carried through the industrial revolution by the English and Americans by pontificating about metric. Are we done? Good. Moving on.
The ancient Egyptians didn’t have feet and inches, they had cubits, palms and fingers. Four fingers to a palm, seven palms to a cubit. The Egyptian unit of slope is the Seked, palms of run per cubit of rise. Notice that: We’re now in run over rise, not rise over run.
The first (attempt at a) smooth sided pyramid is the Bent Pyramid built for Sneferu. It starts off at a Seked of 5, which works out to a smidge over 54 degrees. The popular lore is the building started showing cracks, so to save weight they reduced the slope to a Seked of 7.5, which works out to 43 degrees. The nearby Red pyramid, also attributed to Sneferu and apparently built immediately after, is built entirely at that 43 degree angle.
The pyramid at Meidum, Sneferu’s other pyramid, was first built as a stepped pyramid like Djoser’s, and then modified into a smooth sided pyramid, with a Seked of 5 palms, 2 fingers, or about 51 degrees. This worked, at least in antiquity (the Meidum pyramid is heavily ruined in the modern day).
So when his son Khufu decided to build the biggest pyramid of all time (and nobody has proven the magnificent bastard wrong yet), that’s the slope he used. 5 palms, 2 fingers. 51 degrees.
So the ratio of the Great Pyramid’s height to the distance from the center to the middle of a base edge is 7 to 5.5. That means the ratio of the height to the length of a base edge is 7 to 11. Which means if we take the length and width of the pyramid’s base, and divide it by the height, we just so happen to get 22 / 7, which about a millennia later the Greeks would discover is a pretty good approximation for Pi, but the 4th dynasty Egyptians didn’t know about that.
That’s not what Khufu’s son Khafre did. Khufu was a magnificent bastard but Khafre was clever sumbitch. Khufu built the world’s biggest pyramid. Khafre built his slightly smaller pyramid uphill from his dad’s so his would look bigger. And, he built it very slightly steeper, with a Seked of 5.25 (about 53 degrees). That works out to the same slope as a 3-4-5 triangle. 3/4 is 0.75, and because Seked is given as palms per cubit we multiply by 7, 0.75 * 7 is 5.25. And they DID know about that in the 4th dynasty. Clever sumbitch.
I like your funny words magic man
Couldn’t you use a straight line equal in length to the circumference of said circle? Or a rope of such length, or a multiple of such length?
To get a pi ratio, you need one measurement to be made with the diameter of the wheel, and another made with the circumference of the same wheel. You can certainly use ropes, but one of those ropes needs to be a multiple of the diameter, and the other a multiple of the circumference.
You might be measuring short lengths with a particular unit, say, a “stick”. To get consistent longer measurements, you might measure 100 turns of rope around a spool one “stick” in diameter. The length of that rope might be called a “string”.
The architects of a building might pound two rods into the ground, one “string” apart, and tell the masons to construct a wall between those rods. The architect wants a wall; the architect doesn’t particularly care how long the bricks are. The masons don’t particularly care how long the wall is going to be, just where they need to start and stop. The brickyard workers don’t care how long a string is, they just need a consistent measurement for their molds.
Nobody involved particularly cares about pi, and yet the resulting building will have pi ratios all over the place.
You still need to have one specific circle that you want to make the unit of measure because if you have 2 different circles, they will have different measurements.
Sure but wouldn’t a wheel be easier?
Maybe. But my point is what does it have to do with pi?