*The SOHO spacecraft was used to measure the diameter of the Sun by timing transits of Mercury across the surface during 2003 and 2006. The result was a measured radius of 696,342 ± 65 kilometres (432,687 ± 40 miles). Staying within the margin of error,  measured radius of the Sun is 432,647 miles (or diameter 865,294 miles).

7 x 8 x 9 x 11 x 12 x 13 = 864,864 which is only 0.05%  (430 miles)  smaller than the measured value.
Also, 930 x 930 = 864,900 (only 394 miles less than measured value).

Equatorial Circumference of the Earth: 1,000 x 360 x 365.24 feet
= 131,486,400 feet = 40,077km

Official value for equatorial circumference of the Earth: 40,075 kilometers
That is truly a “cosmic” coincidence !!!

There is more… and the Great Pyramid has these values encoded in its proportions!

The radius of the Moon compared to the Earth is three to eleven, ie. 3:11.

 Radius of Moon = 1,080 miles = 3 x 360 = 1 x 2 x 3 x 4 x 5 x 6 x (3/2 )
 (  1080.030 miles = 1738.1 km )

  Radius of Earth = 3,960 miles = 11 x 360 =  1 x 2 x 3 x 4 x 5  x 6 x  (11/2)
 (3963.167 mi 6378.1 km )
 
 Radius of Earth plus Radius of Moon = 5,040 miles =  14 x 360 =
=1 x 2 x 3 x 4 x 5 x 6 x (14/2) = 7 x 8 x 9 x 10
 (Actual 5043.197 miles )

1 x 2 x 3 x 4 x 5 x 6=720
1+2+3+4+5+6 = 21
21 x 240 = 5040

(720 x 21) / 3 = 5040
(720 x 21) / 14 = 1080

The ratio 3:11 is 27.3 percent, and the orbit of the Moon takes 27.3 days.
 (Sidereal rotation period 27.321582 d (synchronous).
 27.3 days is also the average rotation period of a sunspot.

Here is another unbelievable “coincidence”:

“Pi” approximated to the 9^th decimal place is exactly

Pi = 3.141 592 654

3 x 1 x 4 x 1 x 5 x 9 x 2 x 6 x 5 x 4 = 129,600 

129,600 x 2 = 25,920  x 10
which is 10x Earth’s precession cycles ( 10 x period of precession of the equinoxes)

The Earth is spinning on its axis in a counter-clockwise direction, and rotating around the sun also in a counter-clockwise direction, while the earth’s spinning axis wobbles like a gyroscope in a clockwise direction. As the result,  as the twelve constellations appear to move clockwise along/around the horizon during the course of its annual rotation around the sun during a year, the constellations, from spring or fall equinox to equinox, appear to move counterclockwise at the rate of 72 years/per degree, or one full wobble in 25,920 years (also known as Great Year).of the earth’s axis.
The galactic year is the duration of time required for the Solar System to orbit once around the center of our galaxy (the Milky Way). Estimated length of the galactic year is close to 1000 precession cycles of the Earth.

Fibonacci Sequence, Phi and Pi

The golden ratio is an irrational mathematical constant, approximately 1.6180339887.

phi = 1.61803 39887 49894 84820 45868 34365 63811 77203 09179 80576

phi, 1.618 …  is the Golden Ratio in life and the universe.

phi + 1 = phi ²

Phi = 1/phi = 0.618034…
Phi = phi – 1

( 1 + sqrt(5) )/2 = 1.61803 3988…
which is an excellent approximation of Phi

The following formula connects “Pi” (3.14159…)  and “phi ” (1.6180…):

  (6/5 ) x  phi ² = Pi
or
(12/5) x phi ² = 2 x Pi

sqrt(phi) nearly equals 4/pi
( 1.272 vs 1.273 )

This Formula is expressed by the numbers describing Pyramids of Giza !!!
Here is how:

Proportions (base to height ratio) of the 1st Pyramid: 11/7
Proportions (base to height ratio) of the 2nd Pyramid: 3/2
Proportions (base to height ratio) of the 3rd Pyramid: 8:/5

(24/10) x phi² = 2 x Pi

the same formula written with ratios of 3 pyramids:
2 x [ 2 x (11/7)] = (3/2) x (8/5) x phi² 

Note: the Great Pyramid is a Golden Pyramid: length of the slope side (356) divided by half of the side (440/2 = 220) height is equal to 1.6181818… which is the Golden Ratio Phi

The dimensions of the Earth and Moon are in Phi relationship, forming a Golden Triangle:

The Summation Series (Fibonacci)

The natural progression follows a “summation series” that is known today as the “Fibonacci Series“ [ of course this Series was in existence before Fibonacci (born in 1179 CE) – he simply “re-discovered” it.] The Summation Series is a progressive series, where you start with the first two numbers, then you add their total to generate the next number, and so on. By definition, the first two Fibonacci numbers are 0 and 1, and each subsequent number is the sum of the previous two. The first summation progression:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, …

It is worth to note that the first summation (Fibonacci) progression generates  approximation of the golden ratio (PHI):

3/2 =1.5000
5/3 =1.666…
8/5 =1.6000
13/8 =1.6250
21/13=1.6154…
34/21=1.6190…
55/34=1.6176…
89/55=1.61818…
144/89=1.618….

The second of Fibonacci progression (provides approximate geometry of the pentagram and also leads to the golden ratio ‘phi’ )

1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, …
just like in the above example: 
199/123 = 1.61788…
322/199=1.618…
…

The Summation Series is reflected throughout nature. The number of seeds in a sunflower, the petals of any flower, the arrangement of pine cones, the growth of a nautilus shell, etc…all follow the same pattern of these series.

The overwhelming evidence indicates that the Summation Series was known to the Ancient Egyptians. Throughout the history of Ancient Egypt, temples and tombs (including pyramids) show in their design  expression of the Summation Series: 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, . . .

Pi = 3.141 592 653 5…

3 x 1 = 3
3 x 1 x 4 = 12 (12/3=4)
3 x 1 x 4 x 1 x 5 = 60 (60/12=5)
3 x 1 x 4 x 1 x 5 x 9 = 540 (540/60=9)  :::  540/360=1.5
3 x 1 x 4 x 1 x 5 x 9 x 2 = 1080 (1080/540=2)  :::  1080/360=3 (3/1.5 =2)
3 x 1 x 4 x 1 x 5 x 9 x 2 x 6 = 6480 (6480/1080=6)  :::  6480/360=18 (18/3=6)
3 x 1 x 4 x 1 x 5 x 9 x 2 x 6 x 5 = 32400 (32400/6480=5)  :::  32400/360=90 (90/18=5)
3 x 1 x 4 x 1 x 5 x 9 x 2 x 6 x 5 x 3 = 97200  :::  97200/360=270 (270/90=3)
3  x 1 x 4 x 1 x 5 x 9 x 2 x 6 x 5 x 3 x 5 = 486 000 ::: 486000/360=1350 (1350/270=5)

Another important observation:

No matter what units of measure we use, the sides of the Giza Pyramids Rectangle (layout for all 3 pyramids)
generate the base of the 1st pyramid:

If we use Royal Egyptian Cubits:

1732/1417  =  440/360

This rectangle shows also relationship of
the Royal Egyptian Cubit 20.62 inch
to the Sacred Cubit 25.2 inch:

1732/1417 = 25.2/20.62

Another interesting coincidence encoded in the Royal Cubit:

• Royal Egyptian Cubit = 0.524 m
• pi = 3.1416
• 3.1416 feet = 0.957 m = 1.8263 RC
• 2x (0.957 / 0.524 ) = 2x  1.8263 = 3.6526 = 365.26 x 10^-2

Number of days in a year: 365.25

Another interpretation of the above:
circumference of a a circle with diameter equal 100 feet is
2 x pi x 100 feet = 2 x pi x 1200? =7539.8? = 365.74 RC
(or 356.25 RC measured in King’s Chamber)

Laws Written in Stone

The Pyramid of Kukulkan in Chichen Itza

Chichen Itza Pyramid Calendar

The Pyramid of Kukulkan at Chichén Itzá, constructed circa 1050 was built during the late Mayan period, when Toltecs from Tula became politically powerful. The pyramid was used as a calendar: four stairways, each with 91 steps and a platform at the top, making a total of 365, equivalent to the number of days in a calendar year.

The ancient Mayan Pyramid at Chichen Itza, Yucatan, Mexico.
Copyright A. Sokolowski

Latitude of the pyramid of Quetzalcoatl: 20° 40? 58.44? N

20 x 40 x 58.44 = 46752

This pyramid is a precise calendar (it has 91 steps on each of 4 sides plus platform on top: 4×91 +1 = 365).
The calendar connection is also confirmed by pyramid’s orientation marking equinoxes and solstices.

The pyramid has 4 sides with 4 staircases dividing each side into 2 sections (in total 8 sections).
Using these numbers and accurate value for 1 year equal 365.25, the pyramid “number” will perfectly relate its latitude:

365.25 x 4 x4 x 8 = 46752

Note:  46752 = 365.25 x 128  (perhaps there is a better fit for the 128?)

For Munck’s  number crunching related to the Pyramid of Quetzacoatl in Chichen Itza go to:  http://www.world-mysteries.com/chichen_kukulcan.htm

Gate of the Sun at Tiwanacu

The Gate of the Sun is a very sophisticated calendar called “The Muisca Calendar”.

The Gateway of the Sun from the Tiwanku civilization in Bolivia

The Muisca calendar is another important piece in the jigsaw of the lost knowledge of the Andes. If the origins of the Muisca calendar were to be found at Tiwanaku, then perhaps they were also built into the Gate of the this calendar at Tiwanku is not based upon a divison of the solar year into twelve, but into twenty, and this is represented by the eleven smaller icons forming the freize at the bottom which represents the eleven pillars on the west side of the Kalasasayo which is the actual calendar. So if you count from the central icon or pillar out to the right hand end, then back past the central icon to the left hand end, then back to the centre, you will have effectively counted in twenty divisons and followed the path of the sun over a year.

This wonderful graphic by Ken Bakeman
shows colored version of the Sun-god
from the Gate of the Sun relief.
Image source: http://www.kenbakeman.com/art.html

So if the chasquis do not relate to the days in whichever number of days we choose for the months of the year, could it be that the chasquis represent the years themselves?

If each chasqui were to represent a solar year, then each column of three chasquis would represent three revolutions of the sun around the eleven pillar calendar wall and three solar years are equivalent to 1 x Muisca Acrotom year of 37 synodic months of 29.53 days and also equivalent to 2 x Muisca Zocam years of 20 sidereal months of 27.32 days.

There are fifteen chasquis on each side of the central figure and each block of 15 chasquis would represent fifteen solar years which would be
   5 Muisca Acrotom years of 37 synodic months of 29.53 days or
10 Muisca Zocam years of 20 sidereal months of 27.32 days

The total number of chasquis is thirty chasquis representing thirty solar years which would be
  10 Muisca Acrotom years of 37 synodic months of 29.53 days or
20 Muisca Zocam years of 20 sidereal months of 27.32 days

The choice of thirty chasquis as thirty solar years is no random figure, because after thirty solar years have gone by, it becomes necessary to add one sidereal lunar month to the Muisca Zocam calendar making it 20 x 20 + 1 = 401 sidereal lunar months to bring it back into line with the solar year.

At the same time of adding one sidereal month to the Zocam sidereal calendar, it also becomes necessary to add one synodic lunar month to the Muisca Acrotom calendar making it 10 x 37 + 1 synodic lunar months to also bring it into line with both the sidereal lunar calendar and the actual solar year.

Each of the sections with fifteen chasquis corresponds to the period of fifteen solar years which Duquesne tells us was one quarter of the great “century” of the Muiscas so to sum up, each block of fifteen chasquis represents fifteen solar years which is 10 Muisca Zocam years or 5 Muisca Acrotom years, the two blocks together make 30 chasquis representing 30 solar years which is 20 Muisca Zocam years or 10 Muisca Acrotom years and 2 x the 30 chasquis gives 60 chasquis representing 60 solar years completing the great “century” of the Muiscas which was therefore, 40 Muisca Zocam years or 20 Muisca Acrotom years.

Above, detail of the “Gate of the Sun” at Tiwanaku, Bolivia, the 30 Chasquis represent 30 Solar years, equal to 20 Zocam years of 20 sidereal lunar months or 10 Acrotom years of 37 synodic lunar months. At the end of this period, 1 x lunar month had to be added to the lunar calendars to bring them back into phase with the solar year..

Above, the “Gate of the Sun” at Tiwanaku, Bolivia, the 30 Chasquis represent 30 Solar years, equal to 20 Zocam years of 20 sidereal lunar months or 10 Acrotom years of 37 synodic lunar months. At the end of this period, 1 x lunar month had to be added to the lunar calendars to bring them back into phase with the solar year. Beneath the chasquis can be seen the freize with 11 smaller chasqui heads representing the 11 pillars on the calendar wall which in turn divide the solar year into 20 months of 18 days, and the 40 condor heads represent the 40 sidereal months which mesh with the solar calendar every three years.

Above, when the sun reached the end of the pillars, it appeared to “stand still” before beginning its journey back in the opposite direction.

The Great Pyramid of Giza

John Taylor, in his 1859 book “The Great Pyramid: Why Was It Built? & Who Built It?”, claimed that the Great Pyramid was planned and the building supervised by the biblical Noah, and that it was “built to make a record of the measure of the Earth.”

Now let’s look at the coordinates of the Great Pyramid:

29°58? 45.03? N
31°08?03.69?E

Let’s multiply latitude numbers 29x58x45.03 = 75740.46

Now, this pyramid has 4 sides, its perfect slope angle is 51.8428° and there are 365.2425 days in a year:
4 x 51.8428 x 365.2425 =  75740.775

Note: Another very strange  “coincidence” was discovered by John Charles Webb Jr. : Precise latitude of the centre of the Grand Gallery (inside GP) is 29°58? 45.28? N = 29.9792458° N
The speed of light in vacuum, usually denoted by c, is a universal physical constant important in many areas of physics. Its value is 299,792,458 metres /s

This single, fundamental design principle: 11 : 7 Base to Height Ratio  generates ALL amazing mathematical properties of the Great Pyramid:

• the Golden Ratio Phi=1.618 (the Great Pyramid is a Golden Pyramid: length of the slope side (356) divided by half of the side (440/2 = 220) height is equal to 1.6181818… which is the Golden Ratio Phi
• squaring the circle ratio 1.571 (base/height = 44/28 = 1.571)
• pi=3.14159… (2 x base/height = 2 x 44/28 = 3.14286 which is very close approximation of “pi” = 3.14159…)
• Perimeter of the square base, 4×440=1760, is the same as circumference of the circle with radius = height: 2x ”pi” x height (2x 22/7 x 280=1760)
• The ratio of the perimeter to height of 1760/280 cubits equates to 2x pi
  to an accuracy of better than 0.05%
• Side of the base (440) plus double height (2x 280=560) = 1,000
• Perimeter of the square base is equal 4×440=1760 RC = 0.5 nautical mile = 1/7,200th of the radius length of the earth
• the slop angle 51°.843
• The Pyramid exhibits in the design both pi and by Phi,  given the similarity
  of 2/ sqrt(phi) (2 divided by the square root of Phi) with pi/2 :

• 11/ 7 equal 1.5714
• 2/ sqrt(89/55) equal 1.5722
• 2/ sqrt(Phi) equal 1.5723
• pi/ 2 equal 1.5708

• Royal Cubit = 0.5236 m,  pi – Phi² = 0.5231

1¹ + 2¹ + 3¹ + 4¹ = 10

  1!+2!+3!+4! =33

1 + 2 + 3 + 4 + … + 36 = 666

For penulum with length L= 1 MY = 0.83 m,
the pendulum period T= 1.827 seconds
666/1.827 = 364.5

PS 1 Titus-Bode Law and Pascal’s Triangle

In 1768, Bode published his popular book, “Anleitung zur Kenntnis des gestirnten Himmels” [Instruction for the Knowledge of the Starry Heavens]. In this book, he described an empirical law on planetary distances, originally found by J.D. Titius (1729-96), now called “Bode’s Law” or “Titius-Bode Law”.

The original formula was:

  a = ( n + 4 ) / 10 
where n=0,  3,  6,  12,  24,  48,  96,  192, 384, …

To find the mean distances of the planets, begin with the following simple sequence of numbers:
0     3     6     12     24     48     96     192     384   …
These numbers (after 0) derive from the Pascal’s triangle as the sum of a row added to the sum of the previous row:

Row 1:  2+1=3
Row 2:  4+2=6
Row 3:  8+4=12
Row 4:  16+8=24
Row 5:  32+16=48
Row 6:  64+32=96
Row 7:  128+64=192
Row 8:  256+128=384

Next, add 4 to each number and you will get:
4     7     10     16     28     52     100     196     388
Then divide it by 10:
0.4     0.7     1.0     1.6     2.8     5.2     10.0     19.6     38.8

The resulting sequence is very close to the distribution of mean distances of the planets from the Sun
expressed in Astronomical Units (AU): 

1 AU is approximately the mean Earth–Sun distance equal AU = 149.597 *10⁶ km

All planets (and asteroid belt) fit Titus-Bode Law except for Neptune!

Here is another way to connect Bode’s Law with Pascal’s Triangle
(Source: http://milan.milanovic.org/math/english/titius/titius.html)

The modern formulation of the Titus-Bode law is that the mean distance a of the planet from the Sun in astronomical units ( AU = 149.597 *10⁶ km ) is:

   a = 0.4 + 0.3 x k  

where ”k’=0,1,2,4,8,16,32,64,128 (sequence of powers of two – from Pascal’s Triangle)

PS2 Spiral Solaris

.. For these reasons and from such constituents, four in number, the body of the universe was brought into being, coming into concord by means of proportion, and from these it acquired Amity, so that coming into unity with itself it became indissoluble by any other save him who bound it together. (Timaeus, 31b-32c, Plato’s Cosmology: The Timaeus of Plato, Trans. Francis MacDonald Cornford, Bobbs-Merrill, Indianapolis, 1975:44, emphases supplied)

“The three-fold number is present in all things whatsoever; nor did we ourselves discover this number, but rather nature teaches it to us”  – quotation from Ovid provided by Nicole Oresme in his major work, Le livre du ciel et du monde.

Commentaries of Proclus on the Timeus of Plato:

    The figure of the spiral likewise, is no vain, fortuitous things, but gives completion to the media between bodies that move in right lines, and those that are moved in a circle. For the circle alone, as we have said, is in the inerratic sphere, but the right line in generation. And the spiral is in the planetary region, as having a co-mixture of the periphery and the right line. The motions also according to breadth and according to depth, viz. of the upward and downward, and the oblique motions. Perhaps likewise, the theurgist [Julian] in celebrating time as a spiral form, as both young and old, directed his attention to this, conceiving that the temporal periods, were especially to be known through the motions of the planets. [Trans. Thomas Taylor, Vol. II, Book IV, p.239]

    With these things however, not only Plato as we have observed, but theurgists likewise accord. For they celebrate time as a mundane God, eternal, boundless, young and old, and of a spiral form. And besides this also, as having its essence in eternity, as abiding always the same, and as possessing infinite power. For how could it otherwise comprehend the infinity of apparent time, and circularly lead all things to their former condition, and renovate them, and also recall things which become old through it, to their proper measure, as being at once comprehensive both of things that are moved in a circle, and according to a right line. For a spiral is a thing of this kind; and hence, as I have before observed, time is celebrated by theurgists, as having a spiral form. [trans. Thomas Taylor, Vol. II, Book IV, pp.207-8, emphasis supplied]

Without going into the finer details we may nevertheless take an initial cue from the information provided by Archimedes that :

“the area bounded by the spiral in the first revolution is a sixth part of that added in the second revolution”.

Simply stated, if the first area is 1 (i.e.,unity) then the second area will be 6, the third 12, the fourth 18, and so on, for according to Archimedes:

“generally the areas added in the later revolutions will be multiples of that added in the second revolution according to the successive numbers”,

thus the areas expand by successive multiples of 6.

But what does this have to do with the equiangular period spiral as derived in the previous section which concerns time and successive heliocentric revolutions?

Since the revolutions in the latter also proceed according to a fixed increment, i.e., by the fundamental period constant associated with the equiangular square and the construction of the spiral itself – Phi ²- we can also obtain successive “areas” from the corresponding periods (as “radii”) from the Phi-series planetary framework. And as it so happens, the “areas” pertaining to the planetary positions also expand in a uniform manner – not by 6 as given by Archimedes – but by a constant factor of 6.854101966 (Phi ⁴) instead, and thus 6 may (or may not) be considered a simplified approximation for the latter.

But however one looks at it, the number “6″ is undoubtedly of importance in Pythagorean contexts while a similar weight appears to have been placed – either directly or indirectly – on the numbers 6, 12 and 18 by Plato in the Epinomis, in the Timaeus, and elsewhere. And here we might also recall that with respect to the equiangular period spiral (with notable exceptions) that the heliocentric distances occur at the 60 and 300-degree points, thus a six-fold division is also a feature of the basic configuration.

So what indeed is Archimedes referring to here? One can hardly be certain at this stage, but from what we have seen so far, one might begin to suspect that these seemingly simple operations are neither numerology nor primitive mathematics, but something quite different. It may well be that it is not common practice to treat time in radial form per se, but then again, we are not used to working with such an all-encompassing, complex entity as this particular equiangular spiral either. But if we are not dealing with numerology and elementary mathematics in this context, then what are dealing with? It may be too early to be definitive, but it is beginning to look more and more like highly condensed, competent methodology clothed in disarmingly simple terms.

Source: http://www.spirasolaris.ca/sbb4d2.html

THE THREE BASIC FIGURES THAT FILL A SPACE

Returning to Oresme’s diagram, by coincidence or chance, perhaps – but assuredly not by manipulation – even the direction of the circumscribed spiral matches our own: 

Moreover, if we recall that our final product – the equiangular period spiral, is

• (a) just that, i.e., equiangular,
• (b) that this spiral includes all three mean parameters – Periods, Distances and Velocities – and significantly
• (c), that the latter trio are delimited by three basic equiangular figures – the triangle, the square (more correctly the rectangle) and the hexagon

- we are then able to examine Oresme’s closing religious summations in Du Ciel from a more tightly focussed viewpoint:

Notwithstanding that He is everywhere, still is He absolutely indivisible and the same time infinite with respect to the three qualities that are divisible in living creatures, which we call duration, position, and power or perfection; for temporal duration of creatures is divisible in succession; their position, especially of material bodies, is divisible in extension; and their power is divisible in any degree or intensity. [Du Ciel, Book IV, Chapter 10, fols. 200a-200c, p.721]

… Besides the varieties of trinity noted there, there is another which is pertinent to our present discussion, because, in accord with what we said in chapter Twelve of Book II [see fol. 176b], there are three regular plane figures - the triangle, the square, and the hexagon – each of which we can imagine to be capable of filling so completely a flat area or surface that it is absolutely impossible that there could be more space to be filled; likewise there are three divine persons, each of whom fills all space. Isaiah the Prophet spoke of them thus: Holy, Holy, Holy, Lord God, etc. all the earth is full of thy glory. And there is one God, who spoke through His Prophet Jeremiah: I will fill the heaven and earth; and of who Virgil said: All things are replete with Jove.[Du Ciel, Book IV, Chapter 10, fols. 200d-201b, p.723]

The Double-formed Spiral k = Phi ⁴ and the Whirlpool Galaxy M51 [Color (200kb)]
Edge-on Whirlpool Galaxy M51 image by the Hubble Heritage Team (NASA/STScI/AURA) using data collected by
Principal Astronomer N. Scoville (Caltech) and collaborators.

TO GOVERN ALL THINGS

THE THREE-FOLD NUMBER

it is conceivable that the parameters and structure of Spiral Solaris might provide not only the necessary element of “luck”, but also some degree of understanding concerning the “binding.” Certainly there are enough parameters and associated concepts available (both past and present) as already touched upon in the last two sections. However, it would still be optimistic to expect that either the application or the precise details would be immediately apparent. In fact–after the manner of Orpheus, Pythagoras and Plato — it might well be that certain related matters were indeed: “promulgated mystically and symbolically (by the first); by the second, enigmatically and through images; and scientifically by the third.” Or, as Thomas Taylor put it: “conformably to the custom of the most ancient philosophers, (information) was delivered synoptically, and in such a way as to be inaccessible to the vulgar.” 

 Said Aristotle, prince of philosophers and never-failing friend of truth:
All things are three; The three-fold number is present in all things whatsoever…
Nor did we ourselves discover this number, but rather natures teaches it to us.

The Monad is enlarged, which generates Two.
For the Dyad sits by him, and glitters with Intellectual Sections.
And to govern all things, and to order all things not ordered.
For in the whole World shineth the Triad, over which the Monad Rules.
This Order is the beginning of all Section.
for the Mind of the Father said, that all things can be cut into three,
Governing all things by mind.
……..
The Center from which all (lines) which way soever are equal.
for the paternal Mind sowed Symbols through the World.
………..
Fountain of Fountains, and of all Fountains.
The Matrix containing all things . . .

The content of the above passage from the Chaldean Oracles may surprise some readers, but nevertheless the historical side of the matter is not that difficult, although it is clearly out of kilter. The Fibonacci series (and thereafter the Golden Ratio) have long been associated with natural growth from Fibonacci onwards for the moderns, through Kepler, and later via the efforts of a veritable host of investigators, as R.C. Archibald’s lengthy Bibliography ⁵ in Jay Hambidge’s Dynamic Symmetry (1920:146-156) ⁶ clearly attests. Though “to err is human,” noticeably absent from the latter list are the contributions of Samuel Coleman (Nature’s Harmonic Unity,1911)⁷ and those of Louis Agassiz ⁸ Essay on Classification, 1857)–but more on these omissions later. In passing, though, it is relevant to point out that the claim that the Fibonacci series was only discovered in the early part of the second millennium is surely invalid–a doubly ignorant assertion (in Thomas Taylor’s understanding of the term) that in any case was largely demolished by D’arcy Wentworth Thompson years ago as follows:

The latter also pointed out, however, that:

This is true enough, but it also adds weight to his previous observation.

For example, consider the following Pythagorean reference (or mnemonic device, if one prefers) concerning the number 36 as explained by W. Wyn Westcott:

Subject Related Links

• Ancient Timekeepers, Part 1: Movements of the Earth
• Ancient Timekeepers, Part 2: Observing the Sky
• Ancient Time Keepers, Part 3: Archaeoastronomy
• Ancient Timekeepers, Part 4: Calendars
• Ancient Timekeepers, Part 5: Units of Measurement
• Numbers Magick
• http://www.spirasolaris.ca/
• the three-fold number – to govern all things

More to come…
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