RLH Wrote:
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> Do any of the MP’s have a problem to find the
> circumference of a circle when the diameter is
> known?
Don't think so.
> Would you agree that if the AE did not know the
> formula (A = pi r squared) then there would not
> be any reason for them to use pi(22/7)?
First there would need to be proof the AE knew that value first. They didn't need to square the radius as the conversion(D - 1/9th or 8/9ths of diameter) to a square's side length allowed for the area of the circle.
> Could they know that C = D * pi (22/7) and yet
> not know that radius needed to be squared for
> areas and volumes?
Again, this is based on an unproven assumption of them knowing Pi as 22/7 or at all.
Could they have known it? Possibly, smart enough and obviously had time to play "What IF..." math problems but there is no real proof to "insert" Pi into the FACT column for the AE culture. That means it stays in the "POSSIBLE" column.
> I’m just asking is it fair to judge what the AE
> knew about 3 1/7 from the problems in the MP’s.
>
Not really.
I have posted before a "possible" using the same style of progression as they used to find area but to find the circumference. Is it proof? Nope just more possible but at least it uses what we do know is fact for the AE culture.
A= (D-1/9th)^2
C= (D+1/9th)*2 *sqrt2. View it as instead of using the diameter of the circle to find the side length, you turn the diameter to lay upon the diagonal of the square to find the diagonal length(D+1/9). Now find the perimeter of that circle.
Many have proposed they had ratios for the sqrt 2(diagonal of a square) such as 10/7 or 99/70. IFFFFF this was true then:
C= 2(D+1/9) * 10/7(or 99/70)
The example used was D=9
D - 1/9th = 8
Side length + 8
A=S^2 = 64
Area of circle was approx. equal to 64.
Actual A= 63.617... About 0.6% error
My point was if they played around enough to figure the square to circle would work by subtracting 1/9th, what would it do with adding 1/9th?
Well it works if you turn the diameter from side to diagonal of a square.
D=9
Di= D+1/9th
Di=10
C= 2(10) * 10/7 = 28.571... or 28 + 4/7(1/2 + 1/14) about 1.05% error
C= 2(10) * 99/70= 28.285... or 28 + 2/7(1/4 + 1/28) about 0.04% error
Actual C= 28.274...
As visuals go, the AE took the Diameter shortened it by 1/9th and placed it as the side of a square. They then figured the perimeter.
For mine, I just took the diameter and added 1/9th and placed it as the diagonal of a square and found the perimeter.
Treat the earth well, It was not given to you by your parents, It was loaned to you by your children.
Native American Proverb