January 13, 2012 12:49AM
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Registered: 16 years ago
Posts: 756
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RLH wrote:
Aha! This is where I see an uncertainty on my part. It is a given that seked 5 ½ has a natural pi byproduct. So they could have used seked 5 ½ and be completely unaware of any circular byproduct. But as you say “Since it is a given that the perimeter of the square is equal to the circumference of the circle, they already knew the circumference of the circle” then how would they know this? In order for them to know this wouldn’t they need to do something like side 440*4 = 1760 then 1760/ 3 1/7 = 560 diameter and 560/2 = 280 radius.
Just to be clear I understand they could have used seked 5 ½ and were unaware of the circular byproduct. But if they knew the perimeter of the square was equal to the circumference of the circle wouldn’t that imply they understood 3 1/7?
Hate to sound repetitive but how would they know the squares perimeter equaled circle circumference without some form of pi like 3 1/7 ?
Logic would dictate that no matter how it is calculated it the result would be equal pi, for the ratio of diameter to circumference is inherent in all circles like the square root 2 in the square. You bring up a good point, but when did I ever say they were not cognizant of pi, because that was never my assertion. My problem lies in the fact, if they did employ 22/7 or 3 1/7 why is there not even a footnote in any of the papyri? They also used seked which is the equivalent of our modern cotangent to establish gradient, why did they use the cotangent? Why did they work in unit fractions?
Now, it doesn't matter what I put in this post I will be accused of just playing with the numbers by certain parties. I am not saying this is how they found the circumference of the circle since there are no records, but verifying the circumference can be done in this manner: side / (11/7) * 2^3 / (14/11) = circumference and gives a square perimeter equal to the circumference of the circle. I used the radius because that is the chord length of a hexagon and the basis of the sexagesimal system.
440 / (11/7) * 2^3 / (14/11) = 1760
Regards
Jacob
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