Like, if you have a wheel who’s diameter is 3.18m (10/3.14), it will have a circumference of 10m. So 14 wheel rotations will be 140m, and 5 wheel rotations will be 50m.
Comparing 14 rotations to 5 rotations (140m to 50m) doesn’t seem to yield pi in any meaningful way?
Though, it seems like if you were measuring using wheels, to use the diameter to measure something would be a little odd? It’s way easier to roll a wheel a certain number of times vs trying to use it as a circular yardstick.
And if rotations isn’t giving you the granularity you want, just use a smaller wheel?
You have a standard measuring stick of length 1u. The guy at the quarry cutting blocks cuts them to 1u (or 2u or some other small integer multiple of u) because that can be conveniently measured by stick. The guy making measuring wheels makes them 1u radius (or diameter or whatever) because, again, that’s convenient to measure by stick. But the guy responsible for surveying the whole pyramid base uses the wheel because it’s easier to go “100 wheel rotations that way” than mess about putting sticks end on end hundreds of times.
Several millennia pass and some conspiracy nut looks at the number of blocks per side and it comes out to a round number of multiples of pi. OMG, what were they trying to tell the aliens etc.
Yeah measuring in diameters is pretty strange but it was the first thing that poped into my head that would yield factors of pi.
Could also be that they a standard unit (1u) and would use both 1u radius wheels and 1u circumference wheels.
Or its all derived measures like “the length of a wheel spoke” and “the length of a string around the same wheel” so never the actually physical wheel is used for the measuring.
So your example starts with a wheel who’s diameter is a divisor of pi, which I think it a flawed example (since pi gets divided out in C = [pi] * d)
I wouldn’t expect a craftsman to deliver a wheel who’s dimensions are specified by its circumference, I’d expect them to make a wheel based on diameter (or maybe radius). We can see that even in today’s measurements (e.g. a 8mm bolt has a diameter of 8mm).
So with that, a 1m wheel would have a circumference of 3.14 ish meters (which would then emerge when doing math on the side length of a structure).
My thoughts then go to the units (at top level commenter noted. If they used an arcane ancient unit of measure like the Roman pes (using cause I’m most familiar with that one) to measure their wheel and say the wheel is 5 pes in diameter, their wall will be 5 * [pi] * [rotation count] pes long.
But a pes is .296 meters. So assuming the wall is 10 rotation counts long; we come along and measure the wall as ~4.67 meters long…I don’t see pi in that number.
…so how did the “ancient astronaut theorists” conclude pi was involved in this at all? I suppose that means they knew the units the Egyptians used to build the pyramids? But that doesn’t seem very likely.
I wouldn’t expect a craftsman to deliver a wheel who’s dimensions are specified by its circumference, I’d expect them to make a wheel based on diameter
it would be hard to make such wheel in practice, but it doesn’t change their point.
If you find both circumference and diameter based measurements then searching for a ratio can uncover the unit size of the wheel. Which is probably something you do when you already expect pi to appear.
Yeah, I missed that he said 5 diameters, not rotations.
Though, it strikes me as odd that people would be making diameter based measurements with a wheel tool for the same reason it would be weird for people to be making measurements with the short side of a yard stick. Seems like a needlessly difficult way to get a measurement when your existing tool already has an easy and codified way of getting measurements.
I’m no historian or whatever, so maybe that’s something they did do in antiquity. But it seems unlikely to me, and if we have evidence that they did, I’d be interested to see it.
The unit is arbitrary. Let’s say 1 unit of measurement equals the radius of the wheel. As long as they used the same wheel for all sides of the pyramid, each side will follow the formula: n * 2 * pi where ‘n’ is an integer (whole number). The formula could easily be written in any other unit of distance by multiplying by the conversion ratio.
Are we implicitly using their units? Metric factors of pi would be quite surprising.
If you compare distances like 14 wheel rotations to 5 wheel diameters, then the size of the wheel does not matter. Your ratios will be related to PI.
I don’t think that’s true though?
Like, if you have a wheel who’s diameter is 3.18m (10/3.14), it will have a circumference of 10m. So 14 wheel rotations will be 140m, and 5 wheel rotations will be 50m.
Comparing 14 rotations to 5 rotations (140m to 50m) doesn’t seem to yield pi in any meaningful way?
How are you suggesting that pi would emerge?
The second distance is 5 diameters not 5 rotations.
Ah, reading is hard. My bad.
Though, it seems like if you were measuring using wheels, to use the diameter to measure something would be a little odd? It’s way easier to roll a wheel a certain number of times vs trying to use it as a circular yardstick.
And if rotations isn’t giving you the granularity you want, just use a smaller wheel?
Hypothetical example:
You have a standard measuring stick of length 1u. The guy at the quarry cutting blocks cuts them to 1u (or 2u or some other small integer multiple of u) because that can be conveniently measured by stick. The guy making measuring wheels makes them 1u radius (or diameter or whatever) because, again, that’s convenient to measure by stick. But the guy responsible for surveying the whole pyramid base uses the wheel because it’s easier to go “100 wheel rotations that way” than mess about putting sticks end on end hundreds of times.
Several millennia pass and some conspiracy nut looks at the number of blocks per side and it comes out to a round number of multiples of pi. OMG, what were they trying to tell the aliens etc.
That’s fair. A standardized stick measurement for shorter lengths, and a standardized wheel of diameter 1-stick for longer lengths. That tracks.
Yeah measuring in diameters is pretty strange but it was the first thing that poped into my head that would yield factors of pi.
Could also be that they a standard unit (1u) and would use both 1u radius wheels and 1u circumference wheels.
Or its all derived measures like “the length of a wheel spoke” and “the length of a string around the same wheel” so never the actually physical wheel is used for the measuring.
Maybe we should ask the tired archeologists?
So your example starts with a wheel who’s diameter is a divisor of pi, which I think it a flawed example (since pi gets divided out in C = [pi] * d)
I wouldn’t expect a craftsman to deliver a wheel who’s dimensions are specified by its circumference, I’d expect them to make a wheel based on diameter (or maybe radius). We can see that even in today’s measurements (e.g. a 8mm bolt has a diameter of 8mm).
So with that, a 1m wheel would have a circumference of 3.14 ish meters (which would then emerge when doing math on the side length of a structure).
My thoughts then go to the units (at top level commenter noted. If they used an arcane ancient unit of measure like the Roman pes (using cause I’m most familiar with that one) to measure their wheel and say the wheel is 5 pes in diameter, their wall will be 5 * [pi] * [rotation count] pes long.
But a pes is .296 meters. So assuming the wall is 10 rotation counts long; we come along and measure the wall as ~4.67 meters long…I don’t see pi in that number.
…so how did the “ancient astronaut theorists” conclude pi was involved in this at all? I suppose that means they knew the units the Egyptians used to build the pyramids? But that doesn’t seem very likely.
it would be hard to make such wheel in practice, but it doesn’t change their point.
If you find both circumference and diameter based measurements then searching for a ratio can uncover the unit size of the wheel. Which is probably something you do when you already expect pi to appear.
Yeah, I missed that he said 5 diameters, not rotations.
Though, it strikes me as odd that people would be making diameter based measurements with a wheel tool for the same reason it would be weird for people to be making measurements with the short side of a yard stick. Seems like a needlessly difficult way to get a measurement when your existing tool already has an easy and codified way of getting measurements.
I’m no historian or whatever, so maybe that’s something they did do in antiquity. But it seems unlikely to me, and if we have evidence that they did, I’d be interested to see it.
The unit is arbitrary. Let’s say 1 unit of measurement equals the radius of the wheel. As long as they used the same wheel for all sides of the pyramid, each side will follow the formula: n * 2 * pi where ‘n’ is an integer (whole number). The formula could easily be written in any other unit of distance by multiplying by the conversion ratio.