05-06-2017, 11:05 PM
(This post was last modified: 05-07-2017, 05:47 AM by Ancient Vizier.)

Memoirs of a Pi Jedi

Chapter Five

Giza and Stonehenge: Circular Logic?

The earliest recognition by modern man that Giza's pyramids represent mathematical constructs is the recognition of elements of circular mathematics. When I say that simple circular mathematics serves as an "entry-level" for ancient mathematics at Giza, I'm referring to something that is a matter of historical record.

A Pi Jedi recognizes at Giza not one but two colossal monuments to the ratio of double Pi, the ratio between radius and circumference of a circle

Radius x 2 Pi = Circumference

Using the radian value as the "generic" radius for circles of unknown or unspecified proportion,

57.29577951 x 2 Pi = 360*

The formula for the area of a circle (Area = pi x r^2) is rendered in the same way as

57.29577951^2 x Pi = 10313.24031 Area of a Circle (AC)

Note that this is a "decimal harmonic" (decimal point moved) of 1/2 of the geometrically-derived value of the Royal Cubit in inches

10313.24031 x 2 = 20626.48062

Royal Cubit in feet 1.718873385 x 12 = 20.62648062

Had Berriman only noticed (see biographical data previously posted) that he'd inadvertantly squared the circumference (perimeter) value of the generic circle (360^2 = 129600)...

"His interest in the matter may have stopped there but for the chance reading that a royal Egyptian cubit may be expressed as 20.6265 inches. He recognised this number as the radius of a circle of which the perimeter would be 129.6 inches"

The formula for the surface area of a sphere (4 Pi x R^2) gives us

4 x Pi x (57.29577951^2) = 41252.96124 Surface Area of a Sphere (SAS)

i.e, four times the area of the corresponding circle, or a decimal harmonic of 24 Royal Cubits in feet

1.718873385 x 24 = 41.25296124

The formula for the volume of a sphere (V = 4/3 Pi x R^3) yeilds the generic construct

1.3333333333 x Pi x (57.29577951^3) = 787873.5239 Volume of a Sphere (VS)

Those exploring ancient mathematics may wish to be aware of these values in case they encounter them. As previously mentioned, the square root of the Volume of a Sphere may often serve as a useful mathematical probe or reference value.

sqrt 787873.5239 = 887.6223994 Square Root of the Volume of a Sphere (SRVS)

Having recently revised the Pi oriented Great Pyramid model in these very pages to a "Thoth model" which may represent the proportions of the Great Pyramid sans pavement, this affords us (as previously mentioned) an apothem value which is a close and recognizable approximation of 611.5970155 feet, and I have posted data suggesting the length of the descending passage roof to the point where it meets the ascending passage, is a convincing likeness for 97.3386882 ft.

611.5970155 / 97.3386882 = 2 Pi

To review our data for Stonehenge (based on measures by Petrie and Thom), the inner sarcen circle has a radius of 48.6693441

feet.

Radius 48.6693441 x 2 = Diameter 97.3386882; Radius x 2 Pi = Circumference 305.7985078 ft

Given these figures, we can say that the length of the passage roof in the Great Pyramid's descending passage is equal to the inner sarcen circle diameter of Stonehenge, and that the apothem length of the Great Pyramid (unpaved) is precisely twice the inner diameter of the Stonehenge sarcen circle

GP Apothem 611.5970155 / 2 = 305.7985078 Stonehenge SC (sarcen circle) inner circumference

Those searching for the tracks of tetrahedra may wish to observe that

611.5970155 / Pi = 194.6773764

and

97.3386882 x 2 = 194.6773764

Because the Pi Jedi considers that the Stonehenge sarcen circle is a 360* degree circle, we apply that value to these figures

360 / SC Circumference 305.7985078 = 1.177245771 Yoda's "Alternate Pi"

(Or we can apply the Radian value to the SC Radius

57.29577951 / 48.6693441 = 1.177245771 Yoda's "Alternate Pi"

360 / SC Radius 48.6693441 = 7.396853331 The Squared Yoda Megalithic Yard (SYMY) = (2.719715671^2)

1440 / 7.396853331 = 19.4673764

This will be the third time I have related the story of how I found the apparently Top Secret, allegedly "Hall of Records locating" number 1.067438159 at Stonehenge, as the outer/inner sarcen circle ratio, using my "Alternate e' Meg Yard" (AEMY) value of 2.720174976

Outer: 120 Meg Yards = 120 x 2.720174976 = 326.4209964 Outer Sarcen Circle Circumference

Outer / Inner = 326.4209964 / 305.7985078 = 1.067438160

However, if we were to work purely with the inner sarcen circle data, it is still available to us

Inner SC Circumference 305.7985078 / Radian 57.29577951 = 5.337190809 = 10.67438159 / 2

When you have important data, you tend to want to make backups.

Last night I reviewed the geometry of the Thom Type A flatted circle. Treating that too as a circle of unknown measures and therefore providing it with a generic radius of 57.29577951 = Radian, I managed to derive from it most of the data shown thus far for Stonehenge, and more.

Professor Thom's flattened circles: Left to right are Type A, Type B and Type D.

Also an interesting thing happened - finding an unsolved version of it, I presumed it had never been solved, so I set out to finish it. Awhile later, I found a version that did have some of the solutions worked out after all, and was quite taken with the fact that the solutions I plotted last night are the same as when I worked on it ten years ago. I don't know that the trigonometric functions have been solved, but I noticed I seemed to have gotten further toward finding meaningful solutions (if there are some) in that respect ten years ago than I did last evening.

What I have on my paper from either attempt shows at least several values derived from the flattening that are strong responders to "Alternate Pi" 1.177245771, answering back to 1.177245771 as a mathematical probe with significant figures to as high as 1.177245771 to the fifth power.

I have no idea yet if there were ever any real-life examples of Professor Thom's Type A circle that were solved by any Pi Jedi (or anyone), but for tetrahedra trackers there is in the generic design a value that can probably be taken with considerable confidence to mean either 2 x (19.46773764^2) or 2 x (19.47122063^2) depending on one's preference - and because that's encoded into their basic design, it appears in all ancient circles with the Type A motif regardless of their actual measurements.

(Some Type A flattened circles, according to Professor Thom: Duloo, Moscar Moor, Botallack, Black Marsh, Mitchell's Fold, Castle Rigg, and Dinnevar Hill in England, and Loupin Stanes, Aviemore, Callanish I, Seven Brethren, and Farr West in Scotland. No doubt there are more examples at large. If I recall correctly, Thom probably only made these types of pronouncements for stone circle cites he was able to carefully survey personally).

I know I've already been on my soapbox in this thread about the perils of allowing one's self to become distracted while attempting the mathematical decoding of Giza (i.e., my very large and very dusty map collection), but having recently announced that the Great Pyramid seems to represent a "fusion" of multiple designs, I've become freshly intrigued with Thom's flattened circle motifs as representing "fusions" of multiple circular-oriented designs. It's definitely the flattening that makes them considerably more interesting than ordinary circles, even when their regular circular component simply has them spouting simple radian fractions.

SUMMARY OF A GENERIC TYPE A FLATTENED RING:

AO = OM = ON = 57.29577951 (Radian / 1)

OE = EC = ED = OK = KH = KC = 28.64788976 (Radian / 2)

AE = EK = 75.79519188

EF = FK = 24.80980029

OF = 14.32394488 (Radian / 4)

AF = 71.61972439 (Radian / 8)

Angle (theta) = 19.10660535*

Angle (beta) = 40.89339465*

Perimeter of arc from O = 240.0000000

Perimeter of arc from A = 69.65793147

Perimeter of arc from E = 20.44669733

Total perimeter = 350.5513216

Total area = 9329.067655

I've also been reminded that the ancient British, Scottish, and Irish circles still have a few things left to teach me, that for all I know may still complement my understanding of Giza's mathematical messages.

"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911