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Sacred geometry can be found everywhere in the world around us. Since the time of the Ancient Egyptian Pyramids, men have been creating architecture based in forms found in sacred geometry. There are patterns in nature as well. The world and the universe around us are filled with sacred geometry. From seashells to the human body, from the cosmos to the atom, all forms are permeated with the shapes found in sacred geometry. While sacred geometry theories can be verified mathematically, it is also a field which holds much interest to many different religious communities who can find that it holds deep spiritual meaning for them. Sacred geometry is found within the Jewish Kabalistic system. Hindus, Christians and Jews have all built holy buildings with architecture based in sacred geometry. Scientists, archaeologists, mathematicians, and many spiritual seekers study sacred geometry as well.
The Sphere
While the sphere may be one of the simplest forms in sacred geometry, it is also the container that can hold all of the other forms. All measurements are equal in a sphere. It is a figure that is complete in its entirety. The earth, a seed, and an atom are all spheres.
The Circle
A circle is another simple form found in sacred geometry. The circle is two dimensional and is a symbol of oneness. The ratio of the circumference of a circle to its diameter is called Pi. Pi is an irrational number and never ends nor does it ever repeat. It is infinite.
The Point
The point is found at the center of the sphere or the circle. All measurements must either begin with the point or pass through the point. It is the beginning and it is the end. In sacred geometry the center point is thought to be the place creation began.
The Square Root of 2
The square root of 2 is an irrational number. When a square with sides that measure one unit is divided diagonally, the square root of 2 is the length of the diagonal. Like Pi, square root of 2 never ends. The total of the square root of 2 equals more than half of itself.
The Golden Ratio
The golden ratio, or phi, is the unique ratio in which the ratio of the larger portion is equal to the ratio of the smaller portion. The golden ratio is another irrational number. It is usually rounded to 1.618. It is also known as the golden mean, divine proportion, or golden section. The golden ratio has been used since ancient time in architecture of buildings.
The Square Root of 3 and the Vesica Piscis
The square root of 3 is a positive real number. When it is multiplied by itself it equals 3. The vesica picis is the name for the almond shaped area that is created when two circles of the same radius which intersect so that each circle lies within the circumference of the other. The geometric ratio of the almond space area is the square root of 3. It is considered to be the symbol for Jesus, part of the Ark of the Covenant along with other sacred meanings.
Spirals
There are a number of different types of spirals. There are flat spirals, 3D spirals, righthanded spirals, lefthanded spirals, equiangular spirals, geometric spirals, logarithmic spirals and rectangular spirals. The most well known spiral is that of the nautilus shell. All spirals have two things in common: expansion and growth. They are symbols of infinity.
Toroids
A toroid is a circular shaped object, such as an oring. It is formed through repeated circular rotations. Each circle meets in the center of the toroid. A popular childhood toy, a spirograph, can be used to create one.
Dimensionality
We see things in either 2 or 3 dimensions. But what about a 4th dimension? Physics debates whether we exist within 3 or 4 dimension. Sacred geometry takes all 4 dimensions into consideration.
Fractals and Recursive Geometries
Fractals are a relatively new form of mathematics, beginning only in the 17th century. A good example of a fractal form is a fern. Each leaf on a fern is made up of smaller leaves that have the same shape of the larger whole. In recursive geometry the formula making up a form can be used repeatedly.
Perfect Right Triangles
Right triangles with sides that are whole numbers are called perfect right triangles. 3/4/5, 5/12/13 and 7/24/25 triangles are examples of perfect right triangles. A 3/4/5 perfect right triangle can be found in the "King's Chamber" of the Great Pyramid in Egypt. The Pythagorean Theorem is used to measure the sides of right triangles.
Platonic Solids
A Platonic solid is a convex polyhedron. Platonic solids are made up of equal faces and are made up of congruent regular polygons. There are 5 Platonic solids. They are named for the number of faces: tetrahedron  4 faces, hexahedron  6 faces, octahedron  8 faces, dodecahedron  12 faces, and icosahedron  20 faces. The ancient Greeks believed that these 5 Platonic solids symbolized the elements, with the dodecahedron symbolizing the heavens.
Archimedean Solids
Archimedean solids are made up of two or more different regular polygons. There are 13 different solids. 7 of the 13 solids can be made by truncating a platonic solid.
Stellations of The Platonic & Archimedean Solids
When a Platonic or Archimedean solid is stellated they create new forms. The process of stellation creates a 3D form with tetrahedrons, or pyramids. For example, if you stellate a cube, a cube based pyramid will be created. Stellation can create a large number of new forms.
Metatron’s Cube
Metatron is the name of the angel that guards God's throne in Judaism. The figure of Metatron's Cube has been in sacred art for thousands of years. The 5 Platonic solids can be found within the cube. Because it contains the 5 Platonic solids, it is thought that it contains the building blocks of creation.
The Flower of Life
Images of the Flower of Life have been found all around the world and in most ancient civilizations. The Platonic solids, Metatron's Cube, the Vesica Piscis can be found within the Flower of Life. Other sacred geometric forms such as the Seed of Life, the Tripod of Life, the Egg of Life, the Fruit of Life and the Tree of Life are also found inside the Flower if Life. This sacred shape is said to contain patterns of creation.