Hi All,
So I thought, everyone else is speculating, why not!
Wiki definition: “The mathematical concept of a function expresses the intuitive idea that one quantity (the argument of the function, also known as the input) completely determines another quantity (the value, or the output). A function assigns a unique value to each input of a specified type.”
Concepts such as the pi, phi, and square root 2 etc.... in the simplest form would relate to the many diverse mathematical theories and hypotheses regarding the Pyramids.
G1 lends itself to many of these theories and in order to accommodate these theories it would have to be constructed using at least the basic form of geometrical and mathematical concepts. However due to a lack of evidence very few, if any, of these theories can be proved. Most of what is known today is based on consensus, which unfortunately is not science.
The Ancient Egyptians did not build the pyramids with the intent to encode pi, phi, square roots or any other mathematical concepts, they, like us, used their concepts to explain universal phenomena as it related to Ancient Egypt! As demonstrated in earlier post the length of the cubit can be categorized as 1/20th the surface area of a 36 inch sphere. This can be derived and demonstrated by the Kepler Conjecture of 1611, relating to Cubic and Hexagonal Sphere Packing have maximum densities of π / (3 √2) = 0.740480489%)
[www.wolframalpha.com] "The Kepler conjecture, now proved, posited that cubic and hexagonal close packing are the densest possible sphere packings." The formula is: (π / (3 √2)). It is therefore possible to calculate a cubit length from the Kepler Conjecture! Calculated in irrational numbers as follows:
π / (3 √2) = 0.740480489....and 0.740480489 / √Φ = 0.582127566 (note: in irrational numbers G1's rise-run of 14/11 is often confused with our value √Φ).
The inverse of 0.582127566 is 1.718785694 which in feet is very close to the value of a cubit.
1.718785694×12 = 20.61396081 inches which is an acceptable value for the cubit according to Petrie, but is just not possible with Ancient Egyptians rational system of mathematics. But we all know, based on all available evidence the Ancient Egyptians did not use decimals or irrational numbers, don't we?
What happens when Kepler's formula using "rational numbers", fractional values? This introduces the possibility the Ancient Egyptians might have been cognizant of this formula. So using proper and improper fractions as the Ancient Egyptians would have calculated: in rational form: (4/(14/11)) / (3 * 99/70) = (20/27)…0.740740740…(20/27) / (14/11) = 110/189 = the inverse of the Royal Egyptian Cubit which is 189/110… and 189/110 * 12 = 20 34/55 inches, that is (20.6181818…inches). For those who are unaware of this little fact: 20 34/55×10,000 is equal to the radius of the 1296000 unit arc second circle, which is 440000/7 cubits, 440000 palms, 1760000 digits.
(20/27) x 28 = 20 20/27 = 20.740740740… a viable candidate for the cubit. Interesting that G2 Sarcophagus Cubit of (2592/125)x(1/28)= 648/875 = .74057142857... has a 4375/4374 relationship to one another (20 20/27) / (2592/125) = 4375/4374.
The Kepler Conjecture has the same mathematical relation to the inverse of the Royal Egyptian cubit as the area of a square circumscribing a circle's area, as demonstrated by G1's 5 1/2 seked, rise-run of 14/11.
Is the Kepler formula for cubic and hexagonal sphere packing just another in the long line of possible mathematical artifacts of the Ancient Egyptian system of mathematics?
Among the many things missing from everyone's evidence locker is proof the 'inch' and 'foot' were known units of measure to the Ancient Egyptians.
Regards,
Jacob
So I thought, everyone else is speculating, why not!
Wiki definition: “The mathematical concept of a function expresses the intuitive idea that one quantity (the argument of the function, also known as the input) completely determines another quantity (the value, or the output). A function assigns a unique value to each input of a specified type.”
Concepts such as the pi, phi, and square root 2 etc.... in the simplest form would relate to the many diverse mathematical theories and hypotheses regarding the Pyramids.
G1 lends itself to many of these theories and in order to accommodate these theories it would have to be constructed using at least the basic form of geometrical and mathematical concepts. However due to a lack of evidence very few, if any, of these theories can be proved. Most of what is known today is based on consensus, which unfortunately is not science.
The Ancient Egyptians did not build the pyramids with the intent to encode pi, phi, square roots or any other mathematical concepts, they, like us, used their concepts to explain universal phenomena as it related to Ancient Egypt! As demonstrated in earlier post the length of the cubit can be categorized as 1/20th the surface area of a 36 inch sphere. This can be derived and demonstrated by the Kepler Conjecture of 1611, relating to Cubic and Hexagonal Sphere Packing have maximum densities of π / (3 √2) = 0.740480489%)
[www.wolframalpha.com] "The Kepler conjecture, now proved, posited that cubic and hexagonal close packing are the densest possible sphere packings." The formula is: (π / (3 √2)). It is therefore possible to calculate a cubit length from the Kepler Conjecture! Calculated in irrational numbers as follows:
π / (3 √2) = 0.740480489....and 0.740480489 / √Φ = 0.582127566 (note: in irrational numbers G1's rise-run of 14/11 is often confused with our value √Φ).
The inverse of 0.582127566 is 1.718785694 which in feet is very close to the value of a cubit.
1.718785694×12 = 20.61396081 inches which is an acceptable value for the cubit according to Petrie, but is just not possible with Ancient Egyptians rational system of mathematics. But we all know, based on all available evidence the Ancient Egyptians did not use decimals or irrational numbers, don't we?
What happens when Kepler's formula using "rational numbers", fractional values? This introduces the possibility the Ancient Egyptians might have been cognizant of this formula. So using proper and improper fractions as the Ancient Egyptians would have calculated: in rational form: (4/(14/11)) / (3 * 99/70) = (20/27)…0.740740740…(20/27) / (14/11) = 110/189 = the inverse of the Royal Egyptian Cubit which is 189/110… and 189/110 * 12 = 20 34/55 inches, that is (20.6181818…inches). For those who are unaware of this little fact: 20 34/55×10,000 is equal to the radius of the 1296000 unit arc second circle, which is 440000/7 cubits, 440000 palms, 1760000 digits.
(20/27) x 28 = 20 20/27 = 20.740740740… a viable candidate for the cubit. Interesting that G2 Sarcophagus Cubit of (2592/125)x(1/28)= 648/875 = .74057142857... has a 4375/4374 relationship to one another (20 20/27) / (2592/125) = 4375/4374.
The Kepler Conjecture has the same mathematical relation to the inverse of the Royal Egyptian cubit as the area of a square circumscribing a circle's area, as demonstrated by G1's 5 1/2 seked, rise-run of 14/11.
Is the Kepler formula for cubic and hexagonal sphere packing just another in the long line of possible mathematical artifacts of the Ancient Egyptian system of mathematics?
Among the many things missing from everyone's evidence locker is proof the 'inch' and 'foot' were known units of measure to the Ancient Egyptians.
Regards,
Jacob