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Sirfiroth Wrote:

-------------------------------------------------------

> 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:

> 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

Hello Sirfiroth:

Any reliance on numerical expressions/representations, in any ‘written’ form, would have appeared long after studies of graphical solutions were serviceably spent. The ‘insoluble’ geometric construction problems often attributed to the Greeks had,

A mathematical circle is infinite; a geometrical circle is finite…

Dr. Troglodyte

-------------------------------------------------------

> 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

> = 64this A = (d * 8/9) formula was and was> a circle =

> (9*(8/9))^2 = (9*8)^2 / 9^2 = 72^2 / 9^2 = 5184/81

> = 64

> 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

Hello Sirfiroth:

Any reliance on numerical expressions/representations, in any ‘written’ form, would have appeared long after studies of graphical solutions were serviceably spent. The ‘insoluble’ geometric construction problems often attributed to the Greeks had,

*at a minimum*, their origins in Ancient Egypt. The priestly class of designers would have conceived, geometrically/finitely, solutions prior to execution via constructed configuration.A mathematical circle is infinite; a geometrical circle is finite…

Dr. Troglodyte

*“Quis custodiet ipsos custodes?“*- Decimus Junius Juvenalis

*Η άγνοια είναι η μητέρα του μύθου και του μυστηρίου.*

*“Numero, Pondere et Mensura“*

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