# SACRED GEOMETRY EXPLAINED

Sacred Geometry ascribes symbolic and sacred meanings to geometric shapes and geometric proportions. Sacred geometry may be understood as a worldview of pattern recognition, a complex system of symbols and structures involving space, time and form. According to this view the basic patterns of existence are perceived as sacred. By connecting with these, a believer contemplates the Great Mysteries, and the Great Design.

By studying sacred geometry patterns, forms and relationships and their connections, insight may be gained into the mysteries - the laws and lore of the Universe.

The word 'Geo-metry' comes from the Greek words Geos meaning 'Earth' and Metron meaning 'To measure', which together translate as the 'Measuring of the Earth' or 'Earthly Measurements'.

Geometric forms and/or ratios were given certain esoteric significance and meanings based on their attributes. These forms were thought to give insight into how the universe works, or at least symbolize some transcendental aspect of the universe. Specifically, the mathematical aspects of these forms means they will always be the way they are, by definition, no matter where or when one is.

Galileo once said, “Mathematics is the alphabet with which God has written the universe.”

Geometric patterns exist all around us – they are the perfect shapes and patterns that form the fundamental templates for life in the universe. From the Flower of Life, Fibonacci sequence to the Golden Ratio of Phi, design patterns can be broken down as a language of numbers (mathematics) that govern our entire visible and invisible world.

Artists, musicians, and philosophers have long evoked the power of sacred geometry in their work, from Leonardo da Vinci to Pythagoras. Leonardo da Vinci was known to have studied the Flower of Life pattern and derived the five platonic solids, as well as the Golden Ratio of Phi, from the symbol. Plato’s solids (platonic shapes) are said to form the basis for every design in the universe, even down to a molecular scale.

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The Asanoha pattern is based on regular hexagons, the pattern is a geometric motif which resembles a hemp leaf. The beautiful traditional design is used not only in architecture but also in fashion and graphic design. It's also one of the most popular traditional patterns often seen on Japanese kimono.

*Asanoha* means: *Asa* = hemp: *no *= of: *ha* = leaf. The regular geometric pattern, though abstract, represents overlapping hemp leaves.

Since ancient times the Asanoha motif has been used in holy rituals. The triangle denotes protection against evil, and Asanoha, an aggregate of triangles, conveys a meaning of strength and beauty.

In ancient Japan, the Asanoha pattern was used for making clothing, fibers, and paper, made from hemp, ramie, linden, elm, wisteria or mulberry. It was often used for baby clothing as it is believed to bestow health and long life.

The Asanoha pattern is currently one of the most popular traditional designs as it can be used for a variety of purposes.

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In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

The cube is the only regular hexahedron and is second of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.

The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations. The cube is dual to the octahedron. It has cubical or octahedral symmetry. The cube is the only convex polyhedron whose faces are all squares.

In Greek geometry the duplication of the cube was one of the most famous of the unsolved problems. It required the construction of a cube that should have twice the volume of a given cube. This proved to be impossible by the aid of the straight edge and compasses alone, but the Greeks were able to effect the construction by the use of higher curves, notably by the cissoid of Diocese.

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A fractal is a non-regular geometric shape that has the same degree of non-regularity on all scales. Fractals can be thought of as never-ending patterns. The term "fractal" was coined by Benoit Mandelbrot in 1975. It comes from the Latin fractus, meaning an irregular surface like that of a broken stone. Fractals are the kind of shapes we see in nature.

We can describe a right triangle by the Pythagorean theorem, but finding a right triangle in nature is a different matter altogether. We find trees, mountains, rocks and cloud formations in nature, but what is the geometrical formula for a cloud? Fractal geometry, chaos theory and complex mathematics attempt to answer questions like these. Science continues to discover an amazingly consistent order behind the universe's most seemingly chaotic phenomena.

The word "fractal" often has different connotations for the lay public as opposed to mathematicians, where the public are more likely to be familiar with fractal art than the mathematical concept. The mathematical concept is difficult to define formally, even for mathematicians, but key features can be understood with little mathematical background.

Mathematicians have attempted to describe fractal shapes for over one hundred years, but with the processing power and imaging abilities of modern computers, fractals have enjoyed a new popularity because they can be digitally rendered and explored in all of their fascinating beauty. Fractals are being used in schools as a visual aid to teaching math, and also in our popular culture as computer-generated surfaces for landscapes and planetary surfaces in the movie industry. The use of algorithms to generate fractals can produce complex visual patterns for computer generated imagery (CGI) applications.

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The Flower of Life is a name for a geometrical symbol composed of multiple overlapping circles that are spaced evenly apart from one another. The pattern formed by the circles creates images of perfectly symmetrical flowers. Some Flower of Life symbols are arranged so that they form a flower-like pattern with a sixfold symmetry like a hexagon.

The Flower of Life is a fascinating and ancient symbol. It has been found to hold significance in multiple cultures all around the world. The Flower of Life symbol has been found in ancient manuscripts temples, synagogues, and artwork. However, it was only dubbed as the 'Flower of Life' quite recently in the 1990s.

The oldest known depictions of the Flower of Life were found in the Temple of Osiris in Egypt and date back to at least 6,000 years ago, and recent research has concluded that they could not have been made earlier than 535 BC. These depictions of the symbol are fascinating because they were not carved into the rock, but rather burned or drawn onto the granite with red ochre with great precision. Some believe that the symbol could have been used to represent the Eye of Ra.

Leonardo da Vinci was known to have studied the Flower of Life pattern and derived the five platonic solids, as well as the Golden Ratio of Phi, from the symbol. Leonardo was particularly interested in the form and mathematical proportions of the Flower of Life and its connection to physical space and human consciousness.

Nowadays, the Flower of Life symbol is commonly found on jewelry pieces, tattoos, decor items, and other decorative products.

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In geometry, a honeycomb is a *space filling* or close packing of polyhedral or higher-dimensional *cells*, so that there are no gaps. It is an example of the more general mathematical *tiling* or tessellation in any number of dimensions.

Each cell in a section of honeycomb has a hexagonal (‘hexagon-like’) opening and is in the shape of a type of irregular polyhedron called a decahedra. This means that the honeycomb cell has 10 flat sides – the prefix ‘deca-’ means ‘10’ and the suffix ‘-hedra’ means ‘geometric figure’. Also, all the flat sides of honeycomb cell except for the hexagonal opening are quadrilaterals.

There are infinitely many honeycombs, which have only been partially classified. The more regular ones have attracted the most interest, while a rich and varied assortment of others continue to be discovered.

Honeycombs are usually constructed in ordinary Euclidean ("flat") space. They may also be constructed in non-Euclidean spaces, such as hyperbolic honeycombs. Any finite uniform polytopecan be projected to its circumsphere to form a uniform honeycomb in spherical space.

The simplest honeycombs to build are formed from stacked layers or *slabs* of prisms based on some tessellations of the plane. In particular, for every parallelepiped, copies can fill space, with the cubic honeycomb being special because it is the only *regular* honeycomb in ordinary (Euclidean) space.

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Metatron’s Cube starts with the Fruit of Life shape, and connects all 13 circles with straight lines. Metatron’s Cube includes all 5 Platonic Solids hidden inside, symbolizing the underlying geometric patterns found throughout our universe.

While most people are familiar with the archangel Michael or Gabriel, perhaps one of the most potent of these angels is Metatron. While his name might sound like something from a comic book, Metatron is a figure in the Old Testament. Metatron is an angel who guards the tree of life. Additionally, Metatron is thought to have walked the earth as the prophet Enoch before he was raised to the status of a divine being after he arose to heaven. It is because of this status that Metatron is often thought of as being at the top of the Tree of Life diagram in the Kabbalah.

Perhaps the most famous symbol associated with him, is the one that bears his name; Metatron's Cube. And, for those interested in Sacred Geometry, it is a symbol that acts as a metaphor for the known universe, and how everything no matter how seemingly small or insignificant is actually connected.

Metatron’s Cube is a symbol that's meant to represent the journey of energy throughout the universe, and of balance within the universe. It represents the feminine and masculine as intimately tied together, showing that everything in the universe is attached to everything else. The Cube is also a representation of how energy flows throughout the universe.

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The golden ratio of phi has been claimed to have held a special fascination for at least 2,400 years. Ancient Greek mathematicians first studied what we now call the golden ratio of phi because of its frequent appearance in geometry; the division of a line into "extreme and mean ratio" (the golden section) is important in the geometry of regular pentagrams and pentagons.

In mathematics, two quantities are in the golden ratio of phi, if their ratio is the same as the ratio of their sum to the larger of the two quantities. The golden ratio of phi is also called the golden mean or golden section (Latin: *sectio aurea*).^{ }Other names include phi ratio, divine proportion, divine section (Latin: *sectio divina*), golden proportion, and golden number.

The golden ratio of phi has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets, in some cases based on dubious fits to data.^{ }The golden ratio of phi appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts.

Some twentieth-century artist have proportioned their works to approximate the golden ratio of phi—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aseptically pleasing.

Leonardo da Vinci's illustrations of polyhedron *Divina proportione*^{ }have led some to speculate that he incorporated the golden ratio of phi in his paintings. But the suggestion that his Mona Lisa, for example, employs golden ratio of phi proportions, is not supported by Leonardo's own writings.^{ }Similarly, although the Vitruvian Man is often shown in connection with the golden ratio of phi, the proportions of the figure do not actually match it, and the text only mentions whole number ratios.

Salvador Dali, influenced by the works of Matila Ghyka, explicitly used the golden ratio of phi in his masterpiece, The Sacrament of the Last Supper. The dimensions of the canvas are a golden rectangle. A huge dodecahedron, in perspective so that edges appear in golden ratio of phi to one another, is suspended above and behind Jesus and dominates the composition.

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In the Western world the swastika is synonymous with fascism, and induces feelings of disgust and remorse. With good reason, the swastika is a symbol that was used in the 20th century by of one of the most hated men ever to have lived, a symbol that now represents the slaughter of millions of people and one of the most destructive wars on Earth.

But Adolf Hitler was not the first to use this symbol. In fact, it was used as a positive and powerful symbol,** **thousands of years before him, across many cultures and continents.

The earliest known swastika is from 10,000 BCE found in Mezine, Ukarine. The symbol is found in the archeological remains of the Sintasha culture and Indus Valley Civilization.

The swastika (as a character, 卐 or 卍) is a geometrical figure and an ancient religious icon, and has been used as a symbol of good fortune, divinity and spirituality in almost every culture in the world.

The symbol has been used by Hindus, Buddhists, Jains and many religions for millennial. In the ancient Hindu language of Sanskrit, swastika means "well-being". In Hinduism, the symbol with arms pointing clockwise (卐) is called *swastika*, symbolizing suyra ('sun'), prosperity and good luck, while the counterclockwise symbol (卍) is called sauvastika, symbolizing night or tantric aspects of Kali.

In Jainism, a swastika is the symbol for Suparshvanatha– the seventh of 24 Tirthankaras (spiritual teachers and savirous), while in Buddhism it symbolizes the auspicious footprints of the Buddha. It is often placed at the beginning and end of inscriptions, and modern Tibetan Buddhists use it as a clothing decoration. With the spread of Buddhism, the swastika passed into the iconography of China and Japan, where it has been used to denote abundance, prosperity, and long life.

In several Indo-European religions, the swastika symbolizes lightning bolts, representing the thunder god, and the king of the gods such as Indra in Vedic Hinduism, Zeus in the Ancient Greek religion, Jupiter in the ancient Roman religion, and Thor in the ancient Germanic religion.

In Nordic Myths, Odin is represented passing through space as a whirling disk or swastika looking down through all worlds. In North America, the swastika was used by the Navajos. In Ancient Greece, Pythagoras used the Swastika under the name ‘Tetraktys’ and it was a symbol linking heaven and earth, with the right arm pointing to heaven and its left arm pointing to Earth.

The swastika is a powerful geometric figure and an ancient religious icon, and has been used as a symbol of good fortune, divinity and spirituality, for** **thousands of years, across many cultures and continents.

It is ironic, that many Westerners see no possibility for the symbol to move beyond its negative connotations. Some believe that the swastika is unredeemable because not only is it linked indelibly to the Nazi crimes, it is still worshiped by the neo-Nazi ‘haters.

It is unfortunate, that a symbol of good fortune, divinity and spirituality, that was considered sacred for thousands of years has become a symbol of hatred.