Sacred Geometry Explains Atomic Structure

In this video, we will begin with the most basic geometrical building blocks of two dimensional and three-dimensional manifolds and work our way towards understanding the multi-dimensional space-time of our universe. What many of you call sacred geometry can actually be derived from logic and symmetry. Modern theoretical physics is based almost entirely around the idea of supersymmetry, since all the laws of physics are perfectly symmetric and relative. For every action there is an equal and opposite reaction, which together sum to zero. This means that nothing ever really happens unless it is relative to something else. Let's start with the basics. We'll start in two dimensions with the problem of circle packing. The circle is just a two-dimensional shadow of a sphere. Sphere's work identical to circles as long as we stack them all in the same plane. We'll be using Bucky Balls for our demonstration. First we stretch all of our magnets out into a chain. One end is north and the other end is south. So there are only two possible linear alignments, tip-to-tip and tip-to-tail. We see that they connect in a circle with the tip-to-tail alignment. If we fold that circle in half, we get a square in line alignment. This is the same alignment that you need in order to build cubes. If we take the circle apart on both ends, we see that the opposite ends repel each other. Now if we purposely place two strings side by side with the pulse facing in the same direction, we get a tighter arrangement of magnets. I call this arrangement staggered since you can also build it by alternating magnets into two rows from a single string. Here are in line and staggered rows next to one another so you can compare the spacing. If we stack lines of these in a row in this manner, we create a two-dimensional tiling. We notice that six circles will fit perfectly around a single circle in the middle, leaving no spaces. The mathematician Gauss was the first to prove that this is the tightest possible packing arrangement of circles in two dimensions. So next we need to figure out the tightest possible way to pack spheres in three dimensions. Once again, with the magnetic spheres, it turns out that the even alignments create a tighter packing arrangement. The loosest possible packing arrangement while still having all the spheres touching each other is the cube, or cubic symmetry. The tightest possible packing arrangement is the tetrahedron or tetrahedral symmetry. The tetrahedron is the most simplistic shape, four sides or faces, and four points or vertices, which is plural for vertex. A vertex is a connecting point on the surface of a solid where the edges connect together. Edge is usually connected together at a single point and these points or vertices usually stick out on the surface of the solid. However, if the solid has some points that stick inward is called a concave solid. Here you will see the simplest tetrahedron made from two black and two silver buckyballs to show the contrast and symmetry. This shape is naturally unstable with the buckyballs and can be difficult to get them to stick in this orientation. The trick is to rotate the ball's 90 degrees out of alignment so it stabilizes the bond. You can also make larger tetrahedrons by extending the symmetry to another tier. With the larger tetrahedron we can examine the stacking arrangement much more closely. The tetrahedron is one of the five platonic solids, which are the only five convex regular polyhedra, regular meaning that all the faces are congruent regular polygons, which are assembled in the same way around each vertex. Basically every face has exactly the same shape and number of sides, and every point has the same number of edges connecting to it. The hea-dra and tie-leans are both intimately related and can be categorized into a table based on the number of sides of each polygon and how many polygons touch at each vertex. For instance, if we take a square, which is a four-sided polygon and have four squares touch each other at each vertex, we get a chessboard style tie-lean of the two-dimensional plane. However, if we instead say that only three squares touch each other at each vertex, we get a three-dimensional cube. If six triangles touch at each vertex, we get a triangular tie-lean of the two-d plane, but if five touch at each vertex, we get the icosahedron. In the same way that only certain shapes will tile the two-dimensional plane, only certain shapes will tile the three-dimensional plane. These shapes are known as the platonic solids. The five platonic solids are the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron. One of the first things I noticed when I began to study the platonic solids was the concept of doali. Dual polyhedron are polyhedron, which the faces of one correspond to the vertices or points of another. For instance, the tetrahedron is a self-dool, since if you turn the points into faces, you simply get another tetrahedron. In fact, all pyramids are self-dools, since they are symmetric around a single-based polygon, since all regular polygons are self-dools, all pyramids are also self-dools due to their symmetry. The octahedron is the dole of the cube, while the icosahedron is the dole of the dodecahedron. Here is the smallest possible icosahedron that can be built, or is it a dodecahedron? Depending on whether you view each buckyball as a face or a vertex, the interpretation changes. Here we make a larger dodecahedron by first pulling off 12 sets of five, each set represents a face, and then assembling them into a sphere. If we then add another buckyball to each face of the dodecahedron, we can watch it transform into an icosahedron. This is duality. Another important concept is called a truncation. Truncation is cutting the points off of each vertex. If we truncate this icosahedron by taking the points off, we get back to the dodecahedron. Truncation can happen in different steps. The middle step between two doodles is called rectification, while bi rectification produces a dual. These balls are an excellent educational tool, which make learning about geometry and symmetry both fun and easy, although there is a challenge to it, because buckyballs are dipole or magnets and only stick together in certain ways. Also they are powerful magnets, so certain shapes are unstable because the force of the magnets simply collapse them. For instance, you should be able to make a smaller dodecahedron like this out of 20 buckies, but it will collapse in on itself instead of staying in such a position. We could use mathematics to calculate the gap inside of this 20 vertex shape. Then we could order a custom ball bearing of that diameter to fit the gap, but why stop there? We could calculate the gaps of all the platonic solids and find the proper diameter fillings sphere to fill the gap, given our 5mm buckyball diameter. The octahedron is perhaps the easiest, each sphere represents a vertex, and we can simply calculate from the center of each sphere to the next, knowing the angle. Use some trigonometry, which is a complicated word for triangle math, since all geometric shapes can be reduced to triangles, the trick to measuring things is to break them down into triangles and measure those triangles. The sides, lengths, and angles of triangles are all related to one another through simple mathematical formulas. The main one is known as the Pythagorean Theorem, which the Egyptians also knew about. But it doesn't matter who invented it when or what it's called. The meaning of it is what is essential. A squared plus B squared equals C squared. One way to look at it is to take all the sides of the triangle and make them actual squares. The two smaller areas will always be equal to the larger area formed by the hypotenuse. The ancients who discovered this used pieces of string are rope for the sides of the triangle, and also notice that if you took the length of string and made a circle with it, the area of the two smaller circles would always equal the area of the larger circle. The area of a circle is PyR squared, so circles and squares are both related by the number Pi, which is also the ratio of a circle's circumference to its diameter. I've compiled a list of different sphere sizes with all my calculations based on the 5mm Bucke balls, and will post it on my website as well as send it to the Bucke Ball CEO in case they decide to make different sized Bucke's in the future, so they will know what sizes will work and why. Maybe they will come up with a platonic solid's expansion pack or something. Bucke balls get their name from Buckeminster Fuller. Buckeminster Fuller is famous for his lifelong study into structural geometry and solids. MC Escher was a famous artist who made wonderful illustrations of elaborate two-dimensional tylines and other geometrically inspired artwork. Both Escher and Fuller were inspired by an even lesser-known individual, whose work is perhaps more important. Old Scott McDonnelld, or HSM Coxitor. Coxitor was the first to compile the complete list of uniform polyhedra and also to prove that it was the complete list. Dink and diagrams are sometimes called Coxitor Dink and diagrams because they were first used in a paper by HSM Coxitor in 1934 before using Dink and use them in two papers in 1946 and 47. Simplifying the classification of semi-simple the algebra. The theory was developed by Sophously and Le Algebra's are the same mathematics which Garrett Lecy researched for his exceptionally simple theory of everything. This type of mathematics is everything in physics. Forces are produced by spontaneous symmetry breaking. The minimal supersemitric standard model is one of the best studied candidates for physics beyond the standard model. Therese of gravity that are also invariant under supersymmetry are known as supergravity theories. A bit of a huge jump from the things I covered in this video, but it's nonetheless important because you'll see where the foundations of simple geometry will lead you in the future of as you go further and further into these types of mathematics. For those of you interested in learning more, please check through the links in the description and I recommend taking some math classes as the stuff can be hard to teach yourself. I've also included a link in the description to where you can buy buckyballs. As an added bonus, I also get $5 for every set sold through that link, so be sure to use my link if you intend on buying buckyballs so I can get paid for all the hard work it takes to research, write, and put together more videos in the future. And believe me, I would do so much more if I had the time and money to do so. I also have a donate button on my website, alienccientist.com if anyone is feeling generous. I'm going to be doing a couple more videos related to this, including one on zero theory, or the theory of nothing, which will show how the universe could be created from nothing using holographic supersymmetry. Although currently in complete, you can check out some of the foundational work on my website. Thanks for watching and stay tuned.