Wheels are always a fraction of pi. Whether you like it or not. Lengths of string can be arbitrary, but a circle’s dimensions are always tightly related to and proportional to pi in some way. I also recall that wheel measurements are more precise for large scale building because, unlike rope, leather and cloth, a wooden wheel doesnt stretch. Two wheels made similar will stay more between a much tighter error factor than two pieces of rope. The rope might start at the same length but will deform differently as they are used.
I didn’t make clear, that I mean using something for measuring really large distances, like the length and width of a large building’s base. A typical measure stick would have less stretching than rope, sure, but would also be tedious to measure with. Counting the spins of a wheel as you roll it is trivially easy and quick in comparison. Wood warps, but not really that much.
I think they are saying that the circumference of a wheel can be any arbitrary measurement, you just change the size of the wheel. So how can that be notably different from having a straight ruler the same length as whatever that circumference is?
The spoke of the wheel is the same length used to measure the blocks. Other comments here have gone into detail. If the height of the blocks is the same as the diameter or radius of the wheel used to measure the base, then the relations will always be some function of pi. You don’t have to know any definition of pi for this to always be geometrically true.
Wheels are always a fraction of pi. Whether you like it or not. Lengths of string can be arbitrary, but a circle’s dimensions are always tightly related to and proportional to pi in some way. I also recall that wheel measurements are more precise for large scale building because, unlike rope, leather and cloth, a wooden wheel doesnt stretch. Two wheels made similar will stay more between a much tighter error factor than two pieces of rope. The rope might start at the same length but will deform differently as they are used.
I don’t know if I’d say wooden wheels “stretch” per se, but wood absolutely warps due to all sorts of factors
I didn’t make clear, that I mean using something for measuring really large distances, like the length and width of a large building’s base. A typical measure stick would have less stretching than rope, sure, but would also be tedious to measure with. Counting the spins of a wheel as you roll it is trivially easy and quick in comparison. Wood warps, but not really that much.
I think they are saying that the circumference of a wheel can be any arbitrary measurement, you just change the size of the wheel. So how can that be notably different from having a straight ruler the same length as whatever that circumference is?
The spoke of the wheel is the same length used to measure the blocks. Other comments here have gone into detail. If the height of the blocks is the same as the diameter or radius of the wheel used to measure the base, then the relations will always be some function of pi. You don’t have to know any definition of pi for this to always be geometrically true.