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Hi Dr. Troglodyte,
Pardon the long answer and thanks for the food for thought question!
It would seem we are all still wanting the Ancient Egyptians to conform to our methods? Is there in the written records of the Ancient Egyptians mention of any irrational numbers? :-) Perhaps if we better understood the Ancient Egyptian mindset we would know for sure. We know the 5 1/2 seked is similar to the square root of phi, originally written: ((12 pi) / 61~~0, 1, 1/2, 2/3, 3/5, 5/8, 8/13, 13/21, 21/34, 34/55, 55/89 etc,.......a simple continued fraction convergent sequence known as the Fibonacci series) How would you calculate the square root of the above series in unit fractions? Fibonacci series in Egyptian Fractions 0, 1, 1/2, 2/3, (1/2 + 1/10), (1/2 + 1/8), (1/2 + 1/9 + 1/234), ( 1/2 + 1/9 + 1/126), (1/2 + 1/9 + 1/153), (1/2 + 1/10 + 1/55) there is a whole lot we don't understand and we are trying to comprehend their system with ours, instead of exploring their system.
There is always the possibility the ancient employed phi in the form of a rational number like 1 + 1/2 + 1/9 + 1/121 + 1/2178 = 196/121 = 14/11^2 but in irrational coronation, unless you know something I don't, not a chance. Now correct me if I am wrong but isn't phi as we use it actually an arbitrary and irrational number. Of course by our standards this means the Ancient Egyptians settled for a series of near misses. But then again we don't know their mindset, plus they were not aware of our mathematical standards, were they? There is always that possibility, but probably is based on all available evidence other than speculation?
Some additional information regarding my previous post referencing problem #50 Rhind Mathematical Papyrus demonstrates A = (d * 8/9)^2, in problem 50 with a diameter is 9 working through the problem is as follows problem #50: the area of a circle =
(9*(8/9))^2 = (9*8)^2 / 9^2 = 72^2 / 9^2 = 5184/81 = 64 this A = (d * 8/9) formula was and was used in all other geometric problems relating to circles. Even problem 10 of the Moscow Mathematical Papyrus used the same 8/9 formula for deriving the surface area of a hemisphere (basket). Even the lowly (8/9) divided by (2/3) = 4/3 equals the rise-run of G2's 5 1/4 seked
As it has always been, speculation is easy, confirming those speculations always proves a bit more difficult.
That is my perspective on your question.
Regards,
Jacob
Pardon the long answer and thanks for the food for thought question!
It would seem we are all still wanting the Ancient Egyptians to conform to our methods? Is there in the written records of the Ancient Egyptians mention of any irrational numbers? :-) Perhaps if we better understood the Ancient Egyptian mindset we would know for sure. We know the 5 1/2 seked is similar to the square root of phi, originally written: ((12 pi) / 61~~0, 1, 1/2, 2/3, 3/5, 5/8, 8/13, 13/21, 21/34, 34/55, 55/89 etc,.......a simple continued fraction convergent sequence known as the Fibonacci series) How would you calculate the square root of the above series in unit fractions? Fibonacci series in Egyptian Fractions 0, 1, 1/2, 2/3, (1/2 + 1/10), (1/2 + 1/8), (1/2 + 1/9 + 1/234), ( 1/2 + 1/9 + 1/126), (1/2 + 1/9 + 1/153), (1/2 + 1/10 + 1/55) there is a whole lot we don't understand and we are trying to comprehend their system with ours, instead of exploring their system.
There is always the possibility the ancient employed phi in the form of a rational number like 1 + 1/2 + 1/9 + 1/121 + 1/2178 = 196/121 = 14/11^2 but in irrational coronation, unless you know something I don't, not a chance. Now correct me if I am wrong but isn't phi as we use it actually an arbitrary and irrational number. Of course by our standards this means the Ancient Egyptians settled for a series of near misses. But then again we don't know their mindset, plus they were not aware of our mathematical standards, were they? There is always that possibility, but probably is based on all available evidence other than speculation?
Some additional information regarding my previous post referencing problem #50 Rhind Mathematical Papyrus demonstrates A = (d * 8/9)^2, in problem 50 with a diameter is 9 working through the problem is as follows problem #50: the area of a circle =
(9*(8/9))^2 = (9*8)^2 / 9^2 = 72^2 / 9^2 = 5184/81 = 64 this A = (d * 8/9) formula was and was used in all other geometric problems relating to circles. Even problem 10 of the Moscow Mathematical Papyrus used the same 8/9 formula for deriving the surface area of a hemisphere (basket). Even the lowly (8/9) divided by (2/3) = 4/3 equals the rise-run of G2's 5 1/4 seked
As it has always been, speculation is easy, confirming those speculations always proves a bit more difficult.
That is my perspective on your question.
Regards,
Jacob
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