Geoffroy Coutellier - Chanvrier. Joel Nadeak. Joseph Stanovsky. Admec Multimedia. Jean Ovo Yolo. Patrick Mulcahy. Heath Watson. Homers Simpson. Alfred IDunno. Kalyan Chakravarthy. Thomas Encyclopaedia. Popular in Graphics Software. Amudha Arul. Anar Mammadov. Muhammad Chavez. Eyris Suario. Miguel Nieva. Roger Supriyanto. When the tetrahedron is overlaid on the flower of life this represents a powerful concept; the spheres represent space and the lines lines represent where space and time come together.
One of the most fascinating aspects of the 64 tetrahedron is the number 64 itself and how it appears throughout the natural world. This metaphysical symbol can produce many trees of life which radiate inward, this is why the 64 tetrahedron is symbolic of linking up ones individual paths in harmony with our soul family. A true symbol of the mastermind principle of harmony with among a group of individuals.
The shape known as a ' Torus ' is a type of vortex. So what is a torus? In sacred geometry it is the first shape to emerge from the Genesis Pattern. The torus is found in everything from atoms, to life forms and even in all cosmic bodies such as stars and galaxies. It is a primary shape in existence. Energy flows through the center of the body and loops around to connect the feet and head. The flow from the feet to the head is bi-directional. The energy is flowing through the surface of the torus and inside an in a spiraling pattern, this is why the sacred geometry shape is shown with curves lines throughout the middle, while also adding the illusion of a 3d perspective to the 2d depiction.
The Torus is a 2d depiction of a 3 dimensional shape, like many other sacred geometry forms. The 3d shape is known as a horn torus. This can be mathematically described here.
The Merkaba symbol also spelled Merkabah translates to light, spirit, body. The symbol consists of 2 intersecting tetrahedrons that rotate in opposite directions, this creates an energy field that is commonly referred to as a light body.
The teachings were based on visions found in the Book of Ezekiel and hekhalot literature. These stories speak of ascents into the heavens and to the Throne of God. Everyone has access to their own personal Merkaba or vehicle of light with practice in meditation. It is said that once one has access to their Merkaba it can provide a powerful protection and transport your consciousness to higher dimensions. The Merkavah symbol can remind us of the potential power we hold when we unite our bodies energy to Source.
This symbol combines opposing energies in perfect harmony and has allegedly been used by ascended masters to connect to higher realms. In modern esoteric teachings, the Merkaba is considered an interdimensional vehicle. It is also known as a star tetrahedron and can be imagined as a 3-dimensional Star of David.
All of the basic Sacred Geometry shapes can be easily derived from this cubic grid developed by Pardesco. Let me show you how nature created its very first pattern. However it should be known that this knowledge is most likely taken from the ancient Egyptian mystery schools and it is not original to the bible. In the beginning, there was an infinite void or complete emptiness. A space with zero dimensions and no time.
The first creation started when nature, god, spirit or whichever term you prefer projected itself in all six directions, starting from a single point. In this depiction nothing material has been created, only imaginary lines that represent pure consciousness expanding out front, back, left, right, up and down.
To define boundaries in space all that needs to be done is connect the end of each point to every other point. The beauty of this is that you cannot make a mistake, it is simply impossible.
Once all the ends are connected we have what is called an octahedron, which if viewed from the correct perspective reveals a hexagram, also known as the Star of David. Now that boundaries have been created, relative movement within the void are possible; where as previously consciousness had nothing to move relative to. The octahedron is made up of perfectly straight lines. In sacred geometry straight lines are considered to be male and curved lines female. At this stage we have a purely male shape, this is why the freemasons consider the male to be the generating principle.
These are the odd squares centered octagonals plus triangular numbers x12 and can be seen here in my addition to the OEIS: A Perhaps the biggest trick of all for the generalized polygonal numbers is how they regulate the Multifactorials :.
What we are seeing is how perfectly stellated two-dimensional bodies are perfectly enabled to do the same in higher dimensions. We can also see a profound connection then between the non-centered Star Numbers octagonal numbers and the Star-of-David-Star-Numbers centered dodecagonal or C. Adding cross-numbers to the mix creates a 2-dimensional and 3-dimensional life-cycle.
This 3D patterns can also be seen in the 2D version of the octagonal star. The opposite cross numbers four times the first pentagonals can be found likewise in all the even octagonal stars.
Both the 8-gonals and the gonals are stellated polygonals, i. The 8-gonal 'stellate' off of the square and the gonals stellate off of the hexagon. Both of these can be seen as twin triangles in the stages of merger see animation below.
Where the odd octagonal numbers see above highlight the star and the cross, the even octagonal numbers highlight in the same way the first pentagonal numbers. Indeed, the even octagonals are the pentagonals numbers x8. The two merging triangular configurations tessellates with centered hexagonal numbers,. Octagonal numbers come in a variety of forms. The classic for which they are named are a series of concentric octagons.
The next for which they used to be named is a four pointed star configuration. Two other important configurations are either new or relatively unknown. The cubic configuration, is well explored on 37x The latest configuration the third represent two triangles beginning to merge, which makes these 'old' stars of the same category of the 'new' stars which are two triangles at equilibrium.
To see how this 'merger of triangles' connects to the decimals of pi and the most quoted passage in all the Bible check out pi. Figurative geometry, i. It was of course the Greeks Pythagoras, Plato and the rest of the gang who established the science and importance of figurative geometry as an aid to understanding the mathematics that governed the universe.
However, since then, figurative geometry has fallen on hard times and is now something of a mathematical backwater. Nevertheless, it is science, real science, it is true and it may be terribly important. Not long ago I began to realize that figurative geometry, after all this time, was still relatively unexplored.
A savvy student can, if they so desire, find dozens of new connections between figurative bodies on a daily basis, for who knows how long. All that being said, it is still something of a shock to find unknown connections related to the Platonic Solids, the five most majestic geometric bodies, that are the crown jewels of geometry itself and among the first such bodies to ever be discovered.
If figurative geometry is a backwater of mathematics, then figurative frame geometry is the absolute hinterlands in the middle of nowhere. It should noted however, that is in such places that science often hides its most important secrets. This being said, there really should be no connection between star numbers and the Platonic Solids.
Yet, looking closely we find a strong connection to every one of all five of the shapes. Here however, we must remind ourselves of a very important fact: yes, figurative geometry is not cool and yes figurative frame geometry is almost unheard of, BUT they are both just as true and just as scientific a concept as all other geometry, or the power of pi or even the Riemann Zeta Hypothesis. Scientific Truth is scientific truth. And figurative frame geometry is just as important as line geometry only it is more rigorous and more exacting.
By examining the frame geometry of the hexagram Star of David we find it is highly integrated with all five of the Platonic frameworks. New and true science:. The first two platonic frames doubly connect to the hexagram. The same n-valued tetrahedron and cube frames produce a hexagram while a triangle of tetrahedrons does the same. To a scoffer, this may look like a lark, but the following cannot be so considered, for it is fundamental to the very construction of the hexagram:.
So far that makes a tetrahedron, a cube and an octahedron, 3 out of 5. The next platonic frame is then the dodecahedron, or 12 faced solid body. Here the hexagram frames helps out the cube frame in order to build the dodecahedron frame, which is the master frame of all five of the platonic bodies. Finally we move onto the icosahedon sided body which has at least two strong connections to the stars.
The hexagram Star of David is one of the very few 2D geometries that has both a perimeter and a distinct proper frame. In most cases the two are one and the same. It is this difference and distinction that produces yet another profound connection to the Platonic Forms. The second connection is a triple concoction of starry wonder.
By taking the star numbers proper and subtracting a n - 1 frame and then subtracting an n - 4 star one finds the framework of the last and perhaps most beautiful of the platonic solids. To the mind of a historian, one of the most interesting things about biblical mathematics may be how it is largely informed by figurative geometry.
This, it will be remembered, was a creation of the first Greek mathematicians, whose pebbles in Greek calculi, which is where we get the word calculus were the first prototypes of a calculating machine.
In the absence of computers, handheld calculators or the ever handy abacus, these little patterns of stones helped the Greeks show the relationships between number, something we now call mathematics. These 'rock-calculators' were the very beginnings of the disciplines of science and mathematics, which now hold court over all the world. So it is a great irony that the wise men of ancient Greece barely tapped the surface of the calculating potential of these rock calculators.
Only 2, years later are we beginning to understand the infinite depth of possibility that these humble patterns made of pebbles can produce. The amount of information packed into these simple geometric formations is something akin to an ancient alien technology, whereby arranging rocks in a certain way one can demonstrate the entire array of polygonal numbers.
Somebody tell the producers of Ancient Aliens stat! Imagine, if you will, the great Greek minds of history, Plato, Pythagoras and the like, playing with pebbles in the dirt not knowing the incredible calculating potential that they had in their very hands. A simple example of this function can be found in the frames of triangles, which when combined, create centered hexagons whose frames then create centered gonal numbers star numbers whose frames then combine on and on forever.
The opposite alternation the even iterations of any polygonal series will always produce an appropriate multiple of the squares: triangles x3, hexagons x6 and hexagrams, which are actually dodecagrams geonumbers , and render x12 the square numbers. But this is just the beginning of the rock-calculators hidden functions.
Here we will use square numbers as an example. Square numbers and centered square numbers both share the same perimeter as seen below:. By comparing the square perimeters to their index numbers we find a coordination that runs the gamut of all centered polygonal numbers. But this is by no means a feature unique to squares. All figurative bodies are encoded in this perimeter to index relationship. But the best way to understand this is backwards! Looking at the centered square numbers, listed below, you can see that by subtracting from each number you get a square perimeter number.
By cross-referencing that number with its index number the top row that index number reveals the monogon or central polygonal numbers. The next is digon 2-gonal followed by the centered triangle and so on. In other words the index numbers are the 'Equals' window.
Take the centered square numbers 1,5,13, By comparing these numbers against their original square perimeter index value, you will find that those index values will produce the entire array of all centered polygonal numbers.
That's a 'Caveman Calculator'. What's really interesting, however, is when we try this trick with the 'super-number series' the Star Numbers. As can be seen on this page and almost everywhere else on this website, Star Numbers do things that no other number series can. They connect to other number series like no other number series can. So it is no surprise then that Star Numbers, once again, have a special function that stands out from the rest of the polygonal numbers. What's really surprising is that Star Numbers do this with three of the three-dimensional frames of three of the five platonic solids.
A simple example of this can be found in the matrix between Stars times n - m, which index with tetrahedron frames which connect to multiples of the triangular numbers. All of which are tetrahedron frame numbers. Take the index value of those tetrahedron frames and you will find two-times a triangle.
Do it again but now star numbers times two minus ten and you get four times the triangles. And on and on it goes forever. By playing around with the multiplier and the subtracted value, you will find these tetrahedron frames hold the pattern to all even central polygonal numbers.
If you muck around with the numbers again you will find another entire array of number series:. And of course the Star Numbers do this with tetrahedrons, hexahedrons cubes and octahedron frames. How many different way it does this, is unknown. But it does do this infinitely in probably an infinite number of different ways.
So what value do these caveman calculators have? We have yet to find out! What I mean by that, is that this is an entirely new form of scientific calculation. The basic polygonal perimeter calculator produces as seen above with the square perimeters Calculi Codex I , which is the infinite array of all central polygonal numbers. Calculi Codex II is almost entirely unexplored, virgin mathematical territory.
I played around with it and found the coefficients will still connect to known numbers series listed on the OEIS well up into the hundreds. After that the numbers become to large for most of the entries at the OEIS database. So here is the thing though: Calculi Codex II or the Star-Rock Calculator will produce positive connections to series after series of well known and established mathematical formulas.
It just means that these are unknown and yet to be discovered. This powerful form is called the Merkaba as well. It contains the octahedron and the tetrahedron within the geometry of the cube.
Read more: Star Tetrahedron: What is it? Everyone knows auras. You can have the colors of your aura photographed or seen by a medium. It has the shape of a star tetrahedron — actually three of them. Stand straight and keep your arms out. Your static field is the width of a hand beyond the edge of your finger and the top point of this field is the width of a hand above your head and the bottom of this field is the width of a hand under your feet.
The orientation of the star tetrahedron in our aura depends largely on our gender. They represent your physical body and are neutral. There are two other stellar tetrahedra in our aura.
The other stellar tetrahedron is female and magnetic and rotates clockwise and relates to our emotional thinking. The tetrahedron represents the fire element and is connected to the solar plexus which is the center of personal strength, acceptance, and the natural balance between body and mind. Each side is flat regardless of rotation, making it the ideal symbol of stability and balance. This platonic solid can be used indefinitely for manifestation, healing, grid, or energy work.
The most common use is to focus the energy at each of the three corners, which combine to form a strong, focused current that flows to the top point.
You can protect your energy no matter where you go with our line of personal protection pendants. The Orgone Shell Necklace provides a complete defense against electro magnetic pollution, electromagnetic radiation, and all varieties of dangerous and destructive energy.
This amazing Orgone Seashell Necklace is made from natural Kabibie shell and delivers you with ten metres for thirty two feet of personal space and protection from electromagnetic fields EMF , radiation and all forms of detrimental Positive Ions. According to many teachings, sacred geometry is described as the origin of all forms and the blueprint of creation. Considered an ancient science, Sacred Geometry explains and explores the energy patterns that create and unites all things, and reveals the exact way in which the energy of creation is organized.
Any natural pattern of growth or movement is said to be reduced to one or more geometric shapes. Artists, ancient philosophers, and musicians around the world are known to integrate aspects of sacred geometry into their work.
Sacred geometry symbols are considered to be the basis of all life forms in different cultures and religions. Also, they represent the immaterial and mystical elements of the universe.
0コメント