Pyramids and Swastikas … how squares become circles.

Snaker wrote:
5 pages on topic labled for pyramids and not a single post that even touched on the questions i have bout pyramids.great work on boring down the topic and basically outwinding ur opponents here ralph, since obviously that was ur intention all along =p

Hello Snaker.

I recently responded to this objection to my comparative interpretations.
And then I realized I may have brought your query to a conclusion.

It is a lengthy post, but to have solved why pyramids are such an important symbol … and how they are ultimately connected to swastikas in a most sublime manner took TIME.

bogz wrote:
a 2-D representation of a 4-d vortex would be:a circle. if viewed from top or bottom.a triangle if viewed from the side.

bogz, have you ever heard of a fellow by the name of Clifford A. Pickover?

The following info was taken from his book The Wonders of Numbers.
Chapter 62 specifically.
Pickover assumes the identity of an alter ego in the book, a Dr. Googol, the chapters are filled with math puzzles and anecdotes.

Can we first discuss the “side view” you alluded too bogz?
Here we go…let’s do some math.
Not my strength…so I must do a lot of quoting.

Chapter 62…Triangular Numbers
Triangular numbers form a series.
In the development of early Greek math, the mathematicians noticed arrays or groups of dots, when used to represent numbers could also be used to form geometric figures such as these 5 triangles.

Do those images above resemble “a triangle if viewed from the side?”
I agree the first one does not…it looks more like a symmetrical sphere.

Here are the first 10 numbers in that series. (# of dots)
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, …

And if you look at T4, you realize, without a doubt it resembles the Pythagorean Tetracktys.

And Pythagoras also said we only needed the first 4 numbers (the base of the pyramid) to form the Universe.

And these 10 dots could easily be replaced with the 4 letters representing the name of the Jewish god.


As we see below in an inspired illustration by the Rosicrucian mystic Jakob Boehme.
A symbol that represents “religious devotion and transcendent wisdom”.

Inside the inverted heart we see a triangle that resembles the very same dot configuration of the Pythagorean Tetracktys, using 10 Hebrew letters. But we only use 4 specific letters, and these 4 letters have been associated with the 4 elements.
(please note: these associations were made long ago by the prophets, mystics and theologians, not by me)

Yod is Fire
Heh / Hay/ He is Water (various spellings)
Vav is Air (sometimes we see a W used)
Heh is also Earth

Please note that Heh representing Water or Earth represents both of the feminine aspects.
This is a significant ‘coincidence’ to be explained later.
Also to be noted, on the line below the triangle of Hebrew letters is added a 5th symbol, a 5th Hebrew letter is added to the foundation and is placed between the letter YH … Shin … VH.
More on the letter Shin later.

But god’s name (within the triangle) is really spelled using only a trinity of letters because the letter representing the 2 feminine aspects water and earth are represented by the same letter H = heh.
So essentially within the structure of the name of YHVH there exists a trinity.

Now what is interesting and I suggest NO coincidence is that the Norse also acknowledged a trinity of elements.
Air, Earth and (Fire and Ice were combined into one element)
Obviously, due to their northern latitudes, we can understand water being symbolized by ice.

And fire representing the beneficent sol, the sun is in ultimate control of our seasons as it moves through the universe on its own journey called the Precession of the Equinoxes, and the recording of Sol’s movements becomes even more critical, in a northern environment where the ‘growing season’ would be very brief indeed.

Oops, sorry bogz to get sidetracked on symbols again (which do in fact predate modern man’s ability to communicate using numbers), however you do suggest, “let’s do some math”…

So let’s do some math…

In the above sequence, if you want to figure out the 100th number in the series of infinite triangular numbers I offered above there is a formula.

n(n + 1 ) / 2

The variable n is called the index of the formula.
So if you want the 100th triangular number you substitute n = 100.

The answer is 5,050 and this number will be discussed later.

We do see in the sequence that the 8th triangular number is 36.
8 is a associated with infinity and the number 36 is used in establishing the odds of rolling certain numbers using 2 die, shaped like cubes of salt.

The 10th triangular number is 55 and its association to the number 5,050 will be discussed later.

The 12th triangular number is 78.
12 is associated with the 12 houses of the horoscope.
The overwhelming majority of Tarot decks have 78 cards.
78 is also the sum of 26 x 3
The Precession cycle is about 26,000 years.
I will discuss the implications of this relationship later.

The 36th triangular number is 666.
The sum of the all the numbers between 1-36 = 666.
(i.e. 1 + 2 + 3 + 4 …… + 36 = 666)
Who wants to discuss this relationship?
And the 666th triangular number is 222,111.
A strange configuration of 2s and 1s.

6 + 6 + 6 = 18 = 1 + 8 = 9 = 2 + 2 + 2 + 1 + 1 + 1

Now to quote from the book, taken from page 327.
please note I scanned the page to reproduce the formulas, my keyboard talents fall far short from reproducing these formula accurately.

Triangular numbers determined by n(n + 1 ) / 2 continue to fascinate mathematicians. Various beautiful, almost mystical, relations have been discovered. Here are just some of them:

Did you read that very last line?

Every number is expressible as the sum of 3 triangular numbers!

And exactly how would a Big Macro Brother keep track of Little Micro Brother in the Universe … what does GPS use?
Is GPS an acronym for God’s Pulling the Strings?

Seems I need to employ a little ‘triangulation strangulation’ to get my 3 points across …

Now bogz, may I present more math, you seem to love it!
Can we discuss the relationship between triangular numbers (SIDE VIEW … triangles) and square numbers (TOP VIEW … circles) ?

Upon closer investigation we find there exists a relationship between triangular numbers (side view) and square numbers (top view).

Each square number is the sum of 2 consecutive triangular numbers.


bogz, can you possibly visualize 2 triangles (side view) placed over each other to form the very esoteric hexagram?

The hexagram is a divine symbol that was shown reverence by the eastern religions for thousands of years before Judaism adopted this divine ‘geometric’ shape.
The Jews knew it as many things.
The Star of David, Seal of Solomon, Magen David and the Shield of David.

So there seems to be a process (related to in myth, folklore and scripture) where a shape represented by a 2D square or 3D cube eventually evolves into a circle…but there seems to be a process…swirling is involved…a distillation, a separation seems to be taking place…an process that could be defined as a universal alchemy.

Each square number is the sum of 2 consecutive triangular numbers!

Square numbers are 2 x 2 = 4, 3 x 3 = 9, 4 x 4 = 16, 5 x 5 = 25 ….

i.e. triangular numbers 1 + 3 = the square number 4
triangular numbers 3 + 6 = the square number 9
triangular numbers 6 + 10 = the square number of 16
… etc.

And each ODD square, i.e. 9, 25, 49, 81, … is 8 times a triangular number plus 1.
Going back to this diagram we see the relationship more clearly.

The Greek mathematician Diophantus found a connection between triangular numbers and square numbers expressed by this formula.

8T + 1 = K

T = triangular numbers
K = square numbers

The diagram below shows this relationship graphically.
please note: this diagram was also taken from the book…it is not graphically mapping out my illusions…though it does seem to support them!

Allow me to finish what the caption below the illustration reads …

62.1 A deep connection between square numbers K and triangular numbers T. A visual proof that 8T + 1 = K

And the illustration above resembles the illustration below, which can be used to prove Euclidean Proposition no. 47.
Please note that the graph is a 7 x 7 grid. Coincidence or design?

But wait … Euclidean Proposition no. 47 is better known as the Pythagorean Theorem.

i.e. a2 + b2 = c2

In fact it was this theorem that lead to the measurement of the right-angled triangle, which allowed men to become ‘builders’ and ‘creators’.

So the 2 main symbols of building are in fact the square and the compass.
These are the two main tools needed to navigate through the 4D linear, circular, cyclical, ‘elliptical’ world of SpaceTime.
The ancient Mason builders would rely on the square and the compass to help with creating empires more efficiently and effectively.

And then bogz where you see numbers and math, I see symbols, specifically swastikas.
Do you see any of these swastikas bogz, in those graphs above?

Look at the Balinese swastika in the above sketch, and the Aztec and the Greek and the Hopi versions.
It thus helps to explain why the 4 purple Ls (in my enhanced sketch below of the graph above), resemble the 3rd letter of the Greek alphabet, which is the gamma.
The closest key on my keyboard that I can find to represent the gamma, is the letter L, rotated 180 degrees either ‘clockwise’ or ‘counterclockwise’.
Is it a coincidence that the swastika is known to rotate either ‘clockwise’ or ‘counterclockwise’?

The swastika is constructed using 4 gammas.
It is known thus as the gammadion or the tetra gammadion.
4 Ls … 4 Legs in a dance …
… this motif is also related to the Triskelion, a symbol that had only a Trinity of legs or arms swirling about a central point.

Can we conclude the Greek Tetracktys, the Greek Tetra-gammadion, the Christian Tetra-morphs and the Judaic Tetragrammaton, ALL are in fact sharing a similar structure?

I think it is very obvious and should be filed under the heading … “It is self-evident”.
And ‘self evidence’, points toward a higher truth.

Are you still blinded by the light, a light projected, which has been proven time and again to have been dispensing self serving detail, selling admissions, requesting only about 10% of your annual wage…and it is suggested a further 20% of your annual wage is the recommended expenditure for a diamond engagement ring?
Throw the ring into the abyss Golem / bogz …
Descend with me, as I ‘Gand-Raphael the Grey’ voluntarily leap like a Fool into the abyss. It is here I will battle those inner demons and dragons that oppose me.
Fear not, later you shall see that I was resurrected as ‘Gand-Raphael the White’.

Sound familiar?
The script never changes.
Pick a role in the matrix.
Myth, folklore and ‘script‘ure provide plenty.

And I have also shown in the post prior to this one, that Persia’s 4 Royal Stars are linked to the same tetra archetypes as above.
And ALL of these archetypes are referencing a Time in our collective history when these 4 Royal Stars were in fact representing a ‘fixed cross’ in the heavens.
By no coincidence again …

The Royal Star Antares is in Scorpio representing the Eagle, Regulus is in Leo the Lion, Aldebaran is in the House of Taurus and Fomalhaut, which is associated with Aquarius, will soon be the Royal Star that is in the same ‘quadrant’ of space as our Sun.

This event, where these 4 stars formed a ’square fixed cross’ (not a crucifix), occurred approximately 70,000 years ago.
The picture below illustrates the ‘Fixed Cross’ position.

And here is more of what you will find when turning over rocks in the land of illusion.

Do you see the swirling gold and green swastika I overlay at the center?
A gold pinwheel with 4 bent right angles, 4 X 90 degrees?

What I find interesting is that the author of the book Wonders of Numbers used a 13 x 13 grid for his example.
Using the magical occult 13 yields interesting results.

And by no coincidence the Maya had a reverence for the numbers 13 and 5, both seen as ‘occult’ by the Christians. And both 13 and 5 were critical to the Maya in helping to establish a method for keeping TIME, to help in divination, in foretelling the future.
Maya priests were essentially Astrologers / Astronomers. Chemistry also ’split’ from Alchemy …

shhhh, here is a really BIG secret…tell everyone!!!!

13 is the center of the CIRCLE, or wheel or round table attended to by the 12 tribes or astrological houses or knights, or blah, blah,blah


5 is the center of a SQUARE and it also represents a star being born, the pentagram.

So in a 13 x 13 grid we have 169 squares.
Remove the center square and you are left with 168 squares.
168 squares divided by 8 distinct right angle triangles sharing a common center.

Note the numbers I placed on the grid 1-6, the sum of which totals 21 squares.
i.e. 1 + 2 + 3 + 4 + 5 + 6 = 21 squares.

Also please note how we can draw the number 7 in my photo.
Using the color blue I have shown 2 of the 8 sevens, that exist in the graph produced by the formula …

8T + 1 = K

So how does this graph / formula connect to the swastika and the magical number 7?

The Seal of Solomon with the 4 tetramorphs in the FIXED, a cross +, position.
They usually appear in an INTERCARDINAL or X position.
But there is a reason why they appear ‘Fixed’.
The above photo appeared in Paul Christian’s Histoire de la Magie, 1870

The Seal of Solomon as I have shown is really seven points.
Six are external and the magical 7th, the inner point, is invisible.

What is fascinating is the magic of the numbers contained within the hexagram.
The sum of the numbers 1-6 = 21 or the 7th point in the center.

Join the above points of the star to create X, Y and Z axis.
The 3 axis necessary to create 3D Space. i.e…

1 and 6 = 7
2 and 5 = 7
3 and 4 = 7

And by NO coincidence, by ‘Intelligent Design’, this is how the 6 numbers are structured on a die shaped like a cube.
In fact the 3 pairs of the opposite sides of a CUBE’s faces all add up to 7.
And the sum of all 3 axis … X + Y + Z = 21

Also I have shown by joining that dots that ALL symbols suggesting 6 points around a center, a 7th point, are suggesting the same basic architecture or geometric form shown below.

And both the esoteric Kabbalah and the Tarot are both structured on the Cube as this photo by Paul Foster Case demonstrates.

And what do all these swirling cubes also symbolize?
It is a sacred design.

(the above grid is 13 x 21)

We all know that swirling vortex movements, that began as little square headed Nazis, using triangular pyramid powers, eventually wants to become the ruler of the Circle and thus desires to take over the world … and in victory, the newly crowned Emperor wears the Crown of Thorns which represents the 6 pointed Star of David, the hexagram.

Have you read (the deceased) Itzhak Bentov’s book called A Brief Tour of Higher Consciousness?

He was considered a mystic.
He also built rockets for Israel after she took occupation of Palestine.
Read chapter 3 called … The Cosmos of his second book A Brief Tour of Higher Conciousness.
He and I are on the same pages in that chapter.
We could have written the chapter together.
Ben as he was called, died in ’79 when I was 22, and I was learning about life driving a cab in a large metropolitan Canadian city. And maybe it is just a coincidence I find myself now learning about the 22 letters of the Hebrew alphabet.
What I find interesting is that we, Ben and me, arrived at the same final cosmological conclusions … BUT based on entering through different doors / windows / chimneys of enlightenment.
I was totally unfamiliar with his work till a few months ago when someone suggested I read his books.
And when you compare what I have been writing about these past 2 + years, it converges with his work in a very profound way, that I can not overlook or dismiss as ‘coincidence’.
If anything … my purpose as I see it now is to continue building on the ‘self-evidence’ of this universal truth.

Mankind did not etch this symbol into stone for millennia as a way to pass time.
It actually marks TIME on the macro and micro scale.

I have even been tempted to contact his wife / widow, who actually finished chapters 2 and 4 in his second book, after his death.
However chapter 1, 3 (The Cosmos) and 5 … he completed before his death.

Need more proof?
It arrives all the time.

UPDATE November 7, 2014

The following needs to be incorporated into this blog.

triangular and square numbers



15 thoughts on “Pyramids and Swastikas … how squares become circles.

  1. Pingback: What A Site ! « Sovereignty Rules !
  2. The oldest sign = the cross = North, South, East and West.

    Swastikas is the movement of the cross off its axis as witnessed during the last ice age, fifteen thousand years past.

    Above the equator the shift was depicted as a left to right drawn Swastika and below the equator drawn right to left, as recorded by the ancient civilations living at these locations.

    Hitler, a freemason knew all about this, reasoning why he used this design. It is just too bad he gave the Swastika such a wicked reputation.

      • i have invented chautisa spautirem ——- 24 , and i have invented three chaitsa centuries one first century uploaded on youtube in the name of chautisa century with action you tube look into the matter and reply thanks

      • I have a problem with folks who think they INVENT or DISCOVER and sell their idea …
        (no offence – I am not claiming this is your motivation)

        IMHO we rEMEMber and RECOVER and then share our RECOVERY…

        so regarding ‘chautisa spautirem’ I AM leary of ‘new terminology’ that does not try to show links from whence it came.
        do you have an idEA from the past that seems similar to compare to chautisa spautirem?

        we reinvent the WHEEL of Fortunes all the time…I would need to see where your ‘chautisa spautirem’ evolved from.


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