Did the Egyptians know of Pi

 

“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
Albert Einstein, addressing the Prussian Academy of Science, Berlin, Jan 27, 1921

It is essential to underscore the enduring significance of cyclic digits and prime numbers, given their substantial impact within mathematics. The reasoning behind selecting specific operations, such as multiplication or division by values, will be outlined when relevant, as each choice is grounded in sound logic. Numerous interrelationships exist; the examples that follow represent only a small selection.  Similarly, it is inconsequential whether a “number” is divided, multiplied, subtracted from, added to, or subjected to other mathematical operations, as these processes are seamlessly interconnected in ways that we can currently only theorise about. Consequently, there are many potential options beyond those presented in the examples that follow

The question being did the ancient Egyptians identify actual Pi? on frequent occasions the retort being a resounding Nay. However, they constructed various astonishing buildings, clearly a “Pi” of one form or another ought to have been employed.

Cyclic digits and prime numbers hold sway.

Initially 19,440 divided by exactly 6,187.9441874128906546942 will obtain the Ancient Pi of  3.1415926535897932384626437487815.. accurate to 24 decimal places

The Earth Solar Year I calculated as : 365.2421989187444823444437169843…via employing a few Maya Calendar “numbers” along with Actual Pi and 6,080 Feet a British Admiralty Nautical Mile The, now abridged. 365.242198918744.. is also obtainable via 222,325,171,200 ÷ 299,008 ÷ 648 = 1,147.442208904109..that divided by Actual Pi obtains the 365.242198918744,….Had I employed the Ancient Pi the Earth Solar Year would be 1,147.442208904109…divided by Ancient Pi of 3.1415926535897932384626437487815 …= 365.242198918744482344….hence very slight variation of 1.0000000000000000000000001163429…

The Maya Earth initial Year I calculated to be 364.9122807017…that multiplied by the 1.0000000000000000000000001163429…then plus 0.33 obtains 365.2422807017543859649123… an Earth Solar Year that multiplied by 360,000 Degrees obtains 131,728,421.05263157…Feet which is 24,902.882775119…Miles of 5,280 Feet an Earth Equatorial Circumference. The Maya initial Year 364.9122807017..plus the 0.33 = 365.2422807017543859649122…

The 222,325,171,200 for example is 19,440 x 11,436,480 which is exactly 1,881 British Admiralty Nautical Miles of 6,080 Feet which is 320 x 19 a prime, the Metonic Cycle  The cyclic digit containing, now abridged 1,147.4422089041…multiplied by the prime 73 then by the Maya “Long Count” of 1,360,800 obtains exactly 113,985,073,125 which divided by the prior 11,436,480 obtains exactly 9,966.796875 that divided by the 6,080 Feet then multiplied by the 19 obtains exactly 31.146240234375 that multiplied by 65,536 = 2,041,200

John Michell indicated the distance from Stonehenge to Glastonbury Abbey to be 204,120 Feet, however from exactly which part to which part he did not specify The Platonic 25,920 x 10.5 = 272,160 which is 0.2 x 1,360,800 Maya Long Count The Maya 1,360,800 plus 272,160 = 1,632,960 that minus the 204,120 Feet obtains  1,428,840 which is 10 x 142,884 the Square Root of this is 378 Feet, half the GP base side-length of 756 Feet likewise the Synodic Days of Saturn being 378

The 204,120 minus a reduced Maya 136,080 = 68,040 which is 180 x 378 However, the 204,120 x 6.666…= 1,360,800 the 6.666..x 1.5 = 10 Therefore 8,712  ÷ 1,728 = 5.041666..this is 4.84 x 1.041666…which is the Conversion factor Greek to Roman Units of Measure, the 4.84 is a reduced 4,840  Feet, the Square Yards in One Acre. that multiplied by the prime 3 x 6.666… = 96,800 which is 18.333…x 5,280 the Mile, hence the prime 11 is 0.6 x 18.333..

The 204,120 x 6.666…= 1,360,800 the Maya “Long Count” the 6.666..x 1.5 =10  The 6.666….for example being 3.75 x 1.777..which is the Square Root of 3.160493827...the Rhind Papyrus fraction {256:81} that multiplied by 3.125 = 9.8765432098765432098765…so on and so forth

Indeed “Initially 19,440 divided by exactly 6,187.9441874128906546942 will obtain the Ancient Pi of  3.1415926535897932384626437487815.. accurate to 24 decimal places” However, I intended to highlight the digits involved in the cyclic digits,

{1} 19,440 divided by the prime 7 obtains 2,777.142857…

{2} 6,187.9441874128906546942 divided by 7 = 883.9920267732…

{3} 2,777.142857…÷ 883.9920267732..= 3.1415926535897932384626437… this being the Ancient Pi accurate to 24 decimal places, since the difference is indicated by the highlighted digits 7 and 3

Ancient Pi : 3.1415926535897932384626437… 

Actual Pi: 3.1415926535897932384626433…

Exactly 3,188,160 divided by 164 then by the {2} 6,187.9441874128906546942 will likewise obtain the Ancient Pi  of 3.1415926535897932384626437…The 3,188,160 for example, is 25,920 x 123 which is the primes 3 x 41 a prime the 164 is 4 x 41 a prime, the 3,188,160 is 86,400 x 0.9 x 41, the 3,188,160 is 2.3428571…x 1,360,800 the Maya “Long Count” The 2.3428571..multiplied by another cyclic digit containing number namely 1,185.3658536585…will regain the {1} 2,777.142857…in addition the 1,185.3658536585…multiplied by the prime 41 obtains exactly 48,600 which is 2.5 x 19,440 the 2.3428571..multiplied by the 2,777.142857…x 1,225 obtains exactly 7,970,400 which multiplied by another cyclic containing number soon to be seen below namely 2,351.8292682926829268292682926…obtains exactly 18,745,020,000 This 18,745,020,000 for example, divided by the {1} 19,440 = 964,250 which divided by the British Admiralty Nautical Miles of 6,080 Feet obtains 158.59375 that multiplied by 0.18285714…= 29 a prime the prime 7 x 0.18285714…=1.28 hence ample options re 0.18285714…

The 3,188,160 for example is 2.3428571…x 1,360,800 the Maya “Long Count” Or 2.3428571…x 64,638,000 = 151,437,600 which is exactly 24,907.5 British Admiralty Nautical Miles of 6,080 Feet  The 64,638,000 multiplied by the prime 29 = 1,874,502,000 because all the “numbers” are interconnected, this can continue forever and a proverbial day. Hence, to be brief as feasible, this 1,874,502,000 divided by the {2} 6,187.9441874128906546942 then by prime 41 then by the prior employed cyclic containing number 2,351.8292682926829268292682926…obtains 3.1415926535897932384626437…the Ancient Pi 

The now abridged  2,351.829268292..mutiplied by 56,088 = 131,909,400 which divided by the prime 29 = 4,548,600 which is 456 x 9,975 which is 525 x 19 a prime so on and so forth The 56,088 divided by the prior 2.3428571…obtains 23,940 which is exactly 3.9375 British Admiralty Nautical Miles of 6,080 Feet hence the prior 151,437,600 divided by this 23,940 = 6,325.714285..that divided by the {1} 2,777.142857 ..obtains 2.2777…The Greek Mile of 5068.8 x 10 = 50,688  to this add 5,400 to regain the 56,088 the abridged  2.2777…x 5,400 = 12,300

The 456 is 123 plus 333 which is the primes 3 x 3 x 37 and the 123 is the primes 3 x 41 The 2.2777..x 18 = 41 yet 2.2777…is exactly 1.28125 x 1.777..which is the Square Root of 3.160493827…the Rhind Papyrus fraction {256:81} The 1.28125 x 32 = 41

……………………………………………………………………………

Cyclic digits and prime numbers hold sway.

There is no written record of a “Pi” merely an Ancient Egyptian fraction {256:81} of 3.160493827 …titled the Rhind Papyrus fraction  given that this being written upon the Rhind Mathematical Papyrus Circa 1650 B.C.E by the  Egyptian scribe: Ahmes who likewise refers to the following:

Ahmes {A’h-mosè,} wrote: “Cut off 1/9th.of a diameter and construct a square upon the remainder, this has the same area as the circle” 

Therefore, this necessitated an investigation to observe the mathematical conclusion via following these instructions The magnificent Great Pyramid of Giza denoted as GP, the Ancient Gematria Values of particular “numbers,” phrases etc, denoted as Gem The GP base side-length of 756 Feet is 672 Feet multiplied by 1.125 this is 9 ÷ 8 of added importance is the ancient Comma of Pythagoras {531,441:524,288} of exactly 1.0136432647705078125 multiplied twice by the Musical Scale: Pythagorean Limma {256:243} of 1.0534979423868312...…also  obtains 1.125, the 1.0534979423868312… being one-third of 3.160493827…the Rhind Papyrus fraction {256:81} additional on this subsequently

There will be various occasions whereby cyclic digits will emerge within the numbers { I term all as “numbers”} such as within the Schooldays Pi 22:7 of 3.142857…the 142857 being cyclic, I normally indicate these cyclic digits as best as able hence I indicated the Rhind Papyrus fraction {256:81} as 3.160493827…the 160493827 being cyclic so on and so forth. Equally it may give the impression I am performing somewhat contrary to the norm calculations such as dividing Units of Measure by Musical Scales, otherwise Area by length, in fact I am simply employing the “numbers” the “labels” attached to them such as Feet, Cubits, Area, distance and so on will appear as we progress, the 672 being twice 336

The Ahmes Formula

Employing the GP 672 Feet as the Diameter of a Circle

The GP 672 ÷ 9 = 74.666..hence 672 minus 74.666…= 597.333…therefore the Ahmes Square Area will be 597.333…x 597.333..= 356,807.111., that is 1.006016430408029...x  354,673.24421967329…Feet  the Ahmes Circle Area Subsequently the 1.006016430408029...multiplied by Pi = 3.160493827… the Rhind Papyrus fraction {256:81} The 356,807.111..being one-ninth of exactly 3,211,264 which is 8,792.1494545..x 365.24219891869..a tolerable Earth Solar Year that multiplied by 360,000 Degrees then divided by the Mile of 5,280 Feet obtains. 24,902.87719900203..Miles, a tolerable Earth Equatorial Circumference

Whereas the Earth Solar Year that I calculated via employing Pi with the British Admiralty Nautical Mile of 6,080 Feet being 365.24219891874.. that multiplied by 360,000 Degrees then divided by the Mile of 5,280 Feet obtains 24,902.877199005..Miles, a tolerable Earth Equatorial Circumference, hence slight differences The 8,792.1494545…being 7,675.68603174…Egyptian Feet of 1.14545…and this 7,675.68603174…is exactly 7,555.7534375 x 1.015873...the Ancient Egyptian Eye of Horus fraction {64:63} that multiplied by 3.111…= 3.160493827...the Rhind Papyrus fraction {256:81}

The Circle Area

The GP 336 Feet x 336 Feet x Pi = 354,673.244219673…the GP Circle Area, identical as the Square outcome, which is 14.24222…x 24,902.94272099…Miles, a tolerable Earth Equatorial Circumference that multiplied by the Mile of 5,280 Feet then divided by 360.000 Degrees obtains 365.243159907…a tolerable Earth Year, the 14.24222…x 25,052.76954283…= 356,807.111...the Ahmes Square Area.

Consequently, this 25,052.76954283…divided by the ”Rhind” 3.160493827…then multiplied by Pi obtains 24,902.94272099…the Earth exactly as prior. The 14.24222…is exactly 8.01125 x 1.777…which is the Square Root of 3.160493827…,the Rhind Papyrus fraction the 8.01125 multiplied by the Acres in one Square Mile 640 x 10 = 6,400 = 51,272 which is the commencing GP 672 x 76.29761904…that is exactly 40.05625 x 1.904761…which multiplied by the GP base perimeter of 3,024 Feet obtains 5,760 the GP height in Inches {480 Feet}

Then again the 356,807.111..multiplied by the 14.24222..then divided by the 3.160493827...= 1,607,889.92 and this divided by the 354,673.244219673..Feet, then multiplied by Pi regains the 14.24222...all a tad obvious, I simply required to obtain the 1,607,889.92 which multiplied by 128.3247344970703125 = 206,332,047.084515625 this multiplied by the prior 1.006016430408029...x Pi = 652,111,161.156 wghich is  exactly 405.56953125 x 1,607,889.92 as prior 

Subsequently this 128.3247344970703125 x 256 x 256 = 8,409,889.8 this being the GP base perimeter of 3,024 Feet multiplied by 2,781.0482142857..that is, for example, 2,560.413707386363…Assyrian/Germanic Canonical Units of Measure of 1.0861714285…Otherwise 2,781.0482142857..is 4.0006464177911931818…Egyptian Stades {Geographic} of 695.149714285.. the 4.0006464177911931818…multiplied by the Modern-Day Mile of 5,280 Feet obtains exactly 21,123.4130859375 that is the 128.3247344970703125 x 164.609053497…that multiplied by 34.992 = 5,760 the GP height, this 34.992 being 20.412 Royal Egyptian Cubits of 1.714285...the Distance Stonehenge to Glastonbury being approximately 204,120 Feet far too many interconnections to display in one fell swoop, in a manner of speaking.

The 2,560.413707386363..being 5.109215561224489…Greek Stades {500 Ft.} of 501.13636..the 5.109215561224489…x 1,225 = 6,258.7890625 exactly, that is the prior 128.3247344970703125  x 48.7730528882…and this multiplied by the Arabian Hashimi Foot of  1.064448 then by the GP so-called “King’s Chamber” Wall height of 230.4 Inches {19.2 Feet} obtains 11,961.533629629…due to the cyclic digits 629 within there are options aplenty, in this case the 11,961.533629629…multiplied by the Platonic 25,920 obtains exactly  310,042,951.68

Dependent upon which publication is researched otherwise which internet source is analysed, the Diameters of Stonehenge, Silbury Hill, the Ring of Brodgar and additional vary, for want of a better term, wildly, I will employ the following statistics This 310,042,951.68  divided by the Ahmes Square Area of 356,807.111..= 868.93714285…which is 8.333…x 104.2724571428..Feet, the Stonehenge Sarsen Circle outer diameter that multiplied by 10.2752788299663...= 1,071.428571 …Feet the Orkney islands Ring of Brodgar base Circumference otherwise 104.2724571428 multiplied by 16.666…= 1,737.87428571…Feet, the Avebury Silbury Hill base Circumference

The Geographic Royal Cubit being 1.73787428571..which is 1.428571428571…Roman Remen of 1.216512. Obviously the 16.666…is twice the 8.3333..which is one-third of 25 hence ample scope. I shall leave the, now abridged 1.428571…for perusal The Standard Geographic Athenian Foot being 1.042724571428.. The odd-looking cyclic digits 299663 containing 10.2752788299663…multiplied by 76,032 = 781,250 that this 76,032 will obtain various Units of Measure Then again the 2,560.413707386363…is. 2,384.3005952380.. Assyrian/Germanic Reciprocal Units of 1.07386363…and this 2,384.3005952380…again merely as an example, is exactly 2,347.0458984375 x 1.015873...the Ancient Egyptian Eye of Horus fraction {64:63} that multiplied by 1.25 = 1.269841...the GP Tan {480:378} and much more.

The 2,347.0458984375 multiplied by the 9th PWS {Plato’s World-Soul} member 1,024 = 2,403,375 which is the, 1.428571...x 1,682,362.5 this divided by 11,652.727272727272…= 144.375 that multiplied by 5,411.255411…will regain the prior 781,250 this 5,411.255411…multiplied by 1,225 x 3960 = 26,250,000,000 This 26,250,000,000 is the Maya “Long Count” of 1,360,800 x 19,290.12345679012345679…this, likewise. I leave as is for perusal, much additional lies within the foregoing, nonetheless I consider it best to terminate here

Derek Skhane Copyright © 2024 All Rights Reserved