Thijs on The Universal Pyramidal Structure |
Thijs on Bifurcation, Moons of Jupiter, Feigenbaum and mathematical constant "e" |
Thijs on Influence of Saturn, Precession & Planck's constant |

Other TOPICS on this page:
1- Sun & Metonic Cycles.
2- Repetition Relations & 6.
3- Pythagoras Triangle in the Solar System.
4- Biblical "666", Sun Cycle "555" & Light Speed.
5- Venus & "5555".

The Solar System and the Sun Cycle
It is typical that an 8-times repetition of 10 / Ksaturn gives a very special circle, that may be considered as a composition of all previous circles.
for, (10 / Ksaturn)8 = 4 x pi7.

A circle circumference 4 x pi7 is the result of a sequence of other circles, starting with a diameter of pi and their equivalent pyramid models.

Here "4" may be considered as the 4 phases of a process (similar to 4 seasons in a year, 4 weeks in a month) wherein the 4 phases are a further reflection again of the permanent repetition of "6", because number "4" (and also "40") may be written in the form 4 = 6 x 0.666666.

The repetition mechanism of (10 / Ksaturn)8 is used in the Bible New Testament in the Multiplication of the Breads. It allows investigation of special characteristics of cosmic order.

The values 2 phi and 10 / Ksaturn are shown to give a consistent image of the evolution scheme of the Sun Cycle:

The Sun Cycle, represented by a circle of pi x 7 x 107 years, may be drawn as a pentagram (development model) inside a circle equal to the arithmetical average of the specific proportions 2 phi16 and (10 / Ksaturn)16.

The circumference of this circle equates to the little base of the trapezium, in which its big diagonal represents the Solar Cycle.

Cosmic situations may consequently be considered as "repetitions" of models based on 2phi or 10/Ksaturn

Sun & Metonic Cycles.
The diagram shows the plane wherein the moon moves around the Earth.

This plane makes an angle of 5.145° with the ecliptic ( plane where in the Moon moves around the Sun)

The Moon is once above, then once below the ecliptic. Points of the Moon situated within the ecliptic are called nodes (on the same way other planets paths have each 2 nodes). Where the Moon goes under the ecliptic is called a descending node, the opposite a ascending node.

The nodes are not fixed in space but make a circular movement opposite to the Moon direction. So Sun or Moon obscuration may arise. A full Moon or Sun obscuration arises when the Moon is in one node and the linking line of the 2 nodes is directed to the Sun. If the plane of the Sun and the Moon were the same, then each month a full Sun and Moon obscuration would arise.

The time needed for the nodes for 1 full revolution is between 6798 and 6799 days (+/- 18.61 years), known as the Metonic cycle.

We can see that the movement of the Moon nodes is an "Eastern" reflection of the Sun Cycle (220 million years), because 22000 / (2Phi) = 6789.37.

Repeating relations in the evolution schema of sun and planets.
An idea about the evolution of the sun and the planets is obtained by linking the planetary sum, (Kplanets), with the unity pentagram, a pentagram in a circle with radius 1, where the length of each of the 5 sides evaluates to 1.902113.

Taking Kplanets, as 25.235 (0.03% more accurate than the calculated value 25.227337) gives a 240 (6 x 40) pentagram, and a repetition of the proportion 6.666666 gives 1600:
40 = 6 x 6.666666,
then 6.666666 x 25.235 x total pentagram (5 x 1.902113) = 1600

The magnitude 1600 equals the proportion between the surfaces of the base sides of a golden-section pyramid (total height = h, top height = h/40) and its top: (1 + phi)2 divided by ((1 + phi) / 40))2 =1600.

For Cheops, which is a golden section pyramid, (760 x 760) / (19 x 19) =1600.

Consequent division by 6 generates repetitive number - as shown:
[6.666666 x 25.235 x total pentagram (5 x 1.902113)] /6 = 266.666666
[6.666666 x 25.235 x total pentagram (5 x 1.902113)] / (6 x 6) = 44.444444
[6.666666 x 25.235 x total pentagram (5 x 1.902113)] / (6 x 6 x 6) = 7.407407407
[6.666666 x 25.235 x total pentagram (5 x 1.902113)] / (6 x 6 x 6 x 6) = 1.23456789

6 x 6 x 6 x 6 is symbolic of the Number of Priest Worship at Tabernacle
1.23456789 contains the first 9 Numbers (cf. Sun & 9 Planets).

The Repetition 6 x 6 x 6 x 6 = 6.23 + 7.53 + 8.63 = TOTAL NUMBER OF PRIESTS OF ARK OF COVENANT :
Bible texts:
Eastern: Numbers 3;38 : Moses,
Northern: Numbers 3;35-37 : the Suns of Merari Priests, third range priests : 6200 (6.2 above), where 6.23 = (Phi -1)2 x 252
Western: Numbers 3;21-37 : caste of the Gersonites, moon priests : 7500 (7.5 above), where 7.53 = T(moon) x (Phi - 1) x 25
Southern: Numbers 3;37-31 : high-priests Suns of Kehath, sun-priests: 8600 (8.6 above), where 8.63 = (25.227337)2 or Kplanets.

Triangle of Pythagoras in our Sun System.
Instead of dividing the planetary space into two "dynamic" areas we can also fit it in the more "static" 3, 4, 5 Pythagorean triangle:

"Planet Characteristic" is defined as "the cube root of the orbital period of a planet about the Sun" and denoted by Kplanet (or just K), where K = cube root( planet's sidereal cycle time, in years, about the Sun).
Kplanet : Mercury = 0.6221725, Venus = 0.8504891, Earth = 1, Mars = 1.2343776, Jupiter = 2.2809721, Saturn = 3.0884886, Uranus = 4.380798, Neptune = 5.4827976, Pluto = 6.2872412.
The sum of Planet Characteristics (Kplanets) = 25.227337

For a regular pentagon, side length Z5 inscribed in a circle of unit radius:
2p= Kpluto
p2= Kuranus + Kneptune
1/Z5=Kvenus

The same factor, which reduces the sum of the planet characteristics, 25.2273370 to the whole number 25, is then used to multiply the sum of the first 6 and the sum of the last 3 planets, giving 16 & 9.

A Pythagorean triangle can be used as the "static" representation of our planetary system, in which the hypotenuse represents the whole Solar System, the long perpendicular represent the sum of the last 3 planets, and the small perpendicular the sum of the first 6.

The numbers 25, 16, 9 depicting the whole planetary system are in agreement with Pythagoras theorem since 522 + 32:

Pythagoras' theorem also includes phi, the "golden section", shown:

AB, drawn to bisect the angle at A, meets the perpendicular at B.
This line cuts the perpendicular at 1.5 height, BC, which is one half of AC.

By drawing 2 circles, one radius 1.5 and the other AX, we get the golden section of 3:
3(phi -1) = 1.854.
3 - 1.854 = 1.146.
1.854 / 1.146 = phi

The same method may be used to build directly the side of regular 10-angle from the radius of a circle. Further we shall discuss the association of this construction with the biblical "10 commandments".

The 2 divisions of our planetary system:
In the "dynamic" shaping of our planetary space, Jupiter is the last planet of the first area and Saturn the first of the higher area.

In the "static" representation Saturn is the last planet of the lower space.

Consequently "Saturn" has a planetary status on the frontier of two planetary systems.
The planet is closing the lower from the higher space.

Or it belongs to the lower area, or it may be defined as the first planetary status of the higher "dynamic" echelon.

The association of Saturn as a "buffer" or transition planet can be described mathematically by an expression showing that the characteristics of Saturn are similar with "transition phenomena" in actual sciences.

Transition phenomena are related to the exponential functions involving the constant "e" = 2.7182818.

Saturn shows the characteristic of a translation of the number "e", and at the same time a reflection of the circle wherein we can describe in the shape of a pentagram the sum of the planets (as a system in movement). With accuracy of 0.002% we find:
Ksaturn x Ksat x Ksat x Ksat = e x e x e x e x 1.666666, where e = 2.7182818.

Saturn, the last of the first six planets, fulfils in a very practical way the function of transition element in the planetary space.

Saturn, the 6th planet counting from the sun may be associated with "manifestation or creation" of the Unity, rhythm "6", and visual natural reality.
Saturn delimits visual and non-visual cosmos.

Powers of 10 and Quadrates of Circles based on Solar System's Development
The Solar System in development creates squares of "circles" and powers of 10.
It seems that a combination of 2 circles (one with Kplanets as radius and one with Kplanets as diameter) results in the quadrates of the previous situation as powers of ten.
Kplanet = cube root (planet's sidereal cycle time, in years, about the Sun). The sum, Kplanets = 25.2273377

The diagram shows the development of a circle circumference of (pi x Kplanets)2 has a radius of 103.

This circle can be split into 2400 + 3883.3 which is in the same proportion as 1 + phi.
2400 represents the total length of the 5 sides of a pentagram, enclosed by a circle, circumference 2pi x 10 x the circumference of the original circle, of radius Kplanets.

A representation of the relation between the Sun Cycle, Kplanets and the Earth and Moon rhythms as a function of Pi x 7 ( or 42 el, where el = 0.5236 ) is shown below :

Our Solar System (Kplanets value) shows a direct reflection of 7.

The higher domain of our Solar System, connected with the Sun Cycle (or Pi x 7), is a function of Phi and a repetition of 7: (sum planets) x Pi x 7 = Phi x 7 x 7 x 7.
(This expression is extremely accurate if the calculated planetarian sum is increased by 0.03 %).

The Biblical Number 666 and the Sun Cycle(555).
The number 666 is an immediate projection of the relation 7 and the Sun Cycle.
It is equal to the golden-section of (Pi x 7) x 7 x 7, and so 666 = (Phi -1) x (Pi x 7) x 7 x 7.

If we draw 666 as the small arc of the golden-section of a circle, then the bigger arc is equal to (Pi x 7) x 7 x 7 and the diameter of this circle is 555. Via 666 we get 555 or Phi x 7 x 7 x 7 :

We can see that 555 is a direct result of a nucleus of "7" of our universe and 111, a consistent reflection of the unit "7", linked to the repeating frequency 5, since 555 = 5 x 111.
Magnitude 555 is, within 0.03% accuracy, related to Kplanets and Pi x 7 (reflection of the sun cycle):
555 = (Solar System or Kplanets) x (Pi x 7) = Phi x 7 x 7 x 7

The diameter of the circle, giving rise to 666, is a translation of the higher number 7 and a reflection of the rhythm 5, being a model for pentagons and pentagrams.

In biology "five-rings" represent chemical elements in relation to "life-functions".

We can find those in the composition of DNA of cells. The DNA molecule is a spiral double chain, with a positive loaded chain and a negative one. The totality may be compared with the plus - minus opposition necessary for live and growth.

All genetic information is stored by positioning of only 4 substances called nucleotides. Only the positioning sequence and adhesion of this 4 ring-shape structure determines the heredity characteristics.

The 4 nucleotides are two six-rings and two composed six-and five rings. A nucleotide with only one five-ring is always linked with a nucleotide having a six-ring.

So the DNA molecule is a reflection of the creation characteristic 6, the dynamic aspect 5, the 4 phases in the development of an event, and the polarity and spiral schema of creation.

A circle of circumference 555 will enclose an 840el pentagram (or 3 x 280el).
This is a reflection of 3 times the height of the Great pyramid of Cheops (280el).

We may consider 3 x 280 as the small part of a golden section of a circle.

The pentagram enclosed in a circle of circumference (1 + phi) x 840 evaluates to 3330. The radius of this circle is equal to the Western number of Soldiers around the Ark of the Covenant, multiplied with the Eastern rhythm 2Phi.

For the circle with circumference 840 (3 x 280), the enclosed pentagram is 666 with 1% accuracy.
The radius of this circle is 70 and the side of the enclosed pentagon, 43.63379, is equal to the relation between the Earth-and Moon Cycle, 21.639 multiplied by 2Phi.

Since the pentagram 666 is enclosed in a circle of circumference equal to 3 times the height of the Great pyramid, then the height of Cheops is a direct reflection of the diameter of the Sun Cycle.

The content of the pyramid with height 3 times Cheops (in metre) is equal to 70 million.

The height of the great pyramid is a reflection of the Sun Cycle and of the repetition of 6, because: 146.608 (Cheops) = Pi x 7 x 6.666666

Light: Structure element of the Cosmic Pyramid.
We experience as relative forms of "unity", projections of higher echelons that we may represent as circles , or that we may consider as relative non-split situations.

The photon (the equivalent "light-part" measured by us), as well as light-speed are reflections of a higher hierarchical system, materialized for instance by the Sun as a higher nucleus of our Solar System. A higher system is not imaginable for our thinking. For this reason we perceive the light-speed as a constant.

Light as a structure element of the cosmic pyramid may also be deduced:

The distance travelled by light in one year is 63,242.1791 AU ( astronomical units ).

If we draw this distance as height of the pyramid, then the content (volume) of the top is exactly 555,000 times the content of a pyramid with the sum of the characteristic last four planets as its height, that may be identified as a higher level of the planets. The sum of the last four planet characteristics (cube root of their orbital periods about the Sun) is 19.239326.

The magnitude 555,000 is equal to 1000 times the diameter of a circle, the circumference of which can be divided into two showing golden section proportion.
The length of the smaller arc is 666.

The whole circle is an average measure for the average time of the Sun Cycle.

Venus and Five.
Venus orbits the Sun in 224.7 days, its sidereal period.
Venus takes 243.233 days to make one revolution about its axis..
This means that Venus has not even made a complete revolution about its axis, one Venus day, when it has made one orbit around the Sun.

The synodic period of Venus is 583.92 days, the time to return to exactly the same position against the Sun, as seen from the Earth.

The movement of Venus corresponds to a pentagram.

When we designate the stations of Venus in the Zodiac we get a slowly rotating pentagram.

Between these Venus stations we have periods of 584 days.

 

Drawing a pentagram where total length of its 5 sides equal 5555 (improving the association with number "5"), the movement of Venus is symbolized by the pentagram.


Additionally the radius of the circle around the pentagram is 584, the synodic rotation of Venus (0.029% precision).

After 100 synodic-Venus-periods there have passed 240 days on Venus (0.027% precision).

For us on Earth (0.0091% precision) 77.666666 x square root of Phi3 have passed.

Furthermore, 700 synodic Venus cycles, 1119 years (0.0054 % accuracy) = 6.66 x 6.66 x Kplanets (0.0024% accuracy), are a perfect reflection of the Solar System, showing 6 in the form "666", with the planet characteristics sum, Kplanets = 25.227337.

Thijs on The Universal Pyramidal Structure |
Thijs on Bifurcation, Moons of Jupiter, Feigenbaum and mathematical constant "e" |
Thijs on Influence of Saturn, Precession & Planck's constant |

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created April 2004