> 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.
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…
“Quis custodiet ipsos custodes?“ - Decimus Junius Juvenalis
Η άγνοια είναι η μητέρα του μύθου και του μυστηρίου.
“Numero, Pondere et Mensura“