Sacred geometry - AbsoluteAstronomy.com

Sacred geometry is the geometry used in the planning and construction of religious structures such as churches, temple

Temple

A temple is a structure reserved for religious or spiritual activities, such as prayer and sacrifice, or analogous rites. A templum constituted a sacred precinct as defined by a priest, or augur. It has the same root as the word "template," a plan in preparation of the building that was marked out...

s, mosque

Mosque

A mosque is a place of worship for followers of Islam. The word is likely to have entered the English language through French , from Portuguese , from Spanish , and from Berber , ultimately originating in — . The Arabic word masjid literally means a place of prostration...

s, religious monuments, altar

Altar

An altar is any structure upon which offerings such as sacrifices are made for religious purposes. Altars are usually found at shrines, and they can be located in temples, churches and other places of worship...

s, tabernacles

Church tabernacle

A tabernacle is the fixed, locked box in which, in some Christian churches, the Eucharist is "reserved" . A less obvious container, set into the wall, is called an aumbry....

; as well as for sacred spaces such as temenoi

Temenos

Temenos is a piece of land cut off and assigned as an official domain, especially to kings and chiefs, or a piece of land marked off from common uses and dedicated to a god, a sanctuary, holy grove or holy precinct: The Pythian race-course is called a temenos, the sacred valley of the Nile is the ...

, sacred grove

Sacred grove

A sacred grove is a grove of trees of special religious importance to a particular culture. Sacred groves were most prominent in the Ancient Near East and prehistoric Europe, but feature in various cultures throughout the world...

s, village green

Village green

A village green is a common open area which is a part of a settlement. Traditionally, such an area was often common grass land at the centre of a small agricultural settlement, used for grazing and sometimes for community events...

s and holy well

Holy well

A holy well, or sacred spring, is a small body of water emerging from underground and revered either in a Pagan or Christian context, often both. Holy wells were frequently pagan sacred sites that later became Christianized. The term 'holy well' is commonly employed to refer to any water source of...

s, and the creation of religious art

Sacred art

Sacred art is imagery intended to uplift the mind to the spiritual. Sacred art involves the ritual and cultic practices and practical and operative aspects of the path of the spiritual realization within the bosom of the tradition in question....

. In sacred geometry, symbolic and sacred meanings

Sacred

Holiness, or sanctity, is in general the state of being holy or sacred...

are ascribed to certain geometric shapes and certain geometric proportions

Proportion (architecture)

Proportion is the relation between elements and a whole.-Architectural proportions:In architecture the whole is not just a building but the set and setting of the site. The things that make a building and its site "well shaped" include the orientation of the site and the buildings on it to the...

, according to Paul Calter:

As worldview and cosmology

The belief that God created the universe according to a geometric plan has ancient origins. Plutarch

Plutarch

Plutarch then named, on his becoming a Roman citizen, Lucius Mestrius Plutarchus , c. 46 – 120 AD, was a Greek historian, biographer, essayist, and Middle Platonist known primarily for his Parallel Lives and Moralia...

attributed the belief to Plato

Plato

Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...

, writing "Plato said God geometrizes continually" (Convivialium disputationum, liber 8,2). In modern times the mathematician Carl Friedrich Gauss

Carl Friedrich Gauss

Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...

adapted this quote, saying "God arithmetizes."

At least as late as Johannes Kepler

Johannes Kepler

Johannes Kepler was a German mathematician, astronomer and astrologer. A key figure in the 17th century scientific revolution, he is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican...

(1571–1630), a belief in the geometric underpinnings of the cosmos persisted among scientists. See also Kepler conjecture
Kepler conjecture
The Kepler conjecture, named after the 17th-century German astronomer Johannes Kepler, is a mathematical conjecture about sphere packing in three-dimensional Euclidean space. It says that no arrangement of equally sized spheres filling space has a greater average density than that of the cubic...

, Mysterium Cosmographicum
Mysterium Cosmographicum
Mysterium Cosmographicum, is an astronomy book by the German astronomer Johannes Kepler, published at Tübingen in 1596 and in a second edition in 1621...

, Pythagoreanism
Pythagoreanism
Pythagoreanism was the system of esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics. Pythagoreanism originated in the 5th century BCE and greatly influenced Platonism...

Natural forms

The study of sacred geometry has its roots in the study of nature, and the mathematical principles

Fibonacci number

In mathematics, the Fibonacci numbers are the numbers in the following integer sequence:0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\; ....

at work therein. Many forms observed in nature can be related to geometry, for example, the chambered nautilus

Chambered Nautilus

The Chambered Nautilus, Nautilus pompilius, is the best-known species of nautilus. The shell, when cut away reveals a lining of lustrous nacre and displays a nearly perfect equiangular spiral, although it is not a golden spiral. The shell exhibits countershading, being light on the bottom and dark...

grows at a constant rate and so its shell forms a logarithmic spiral

Logarithmic spiral

A logarithmic spiral, equiangular spiral or growth spiral is a special kind of spiral curve which often appears in nature. The logarithmic spiral was first described by Descartes and later extensively investigated by Jacob Bernoulli, who called it Spira mirabilis, "the marvelous...

to accommodate that growth without changing shape. Also, honeybees construct hexagonal cells to hold their honey. These and other correspondences are seen by believers in sacred geometry to be further proof of the cosmic significance of geometric forms. These phenomena can, however, be explained through natural principles.

Art and architecture

The golden ratio

Golden ratio

In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989...

, geometric ratios, and geometric figures were often employed in the design of Egyptian

Ancient Egyptian architecture

The Nile valley has been the site of one of the most influential civilizations which developed a vast array of diverse structures encompassing ancient Egyptian architecture...

, ancient Indian, Greek

Architecture of Ancient Greece

The architecture of Ancient Greece is the architecture produced by the Greek-speaking people whose culture flourished on the Greek mainland and Peloponnesus, the Aegean Islands, and in colonies in Asia Minor and Italy for a period from about 900 BC until the 1st century AD, with the earliest...

and Roman

Roman architecture

Ancient Roman architecture adopted certain aspects of Ancient Greek architecture, creating a new architectural style. The Romans were indebted to their Etruscan neighbors and forefathers who supplied them with a wealth of knowledge essential for future architectural solutions, such as hydraulics...

architecture

Architecture

Architecture is both the process and product of planning, designing and construction. Architectural works, in the material form of buildings, are often perceived as cultural and political symbols and as works of art...

. Medieval European cathedrals also incorporated symbolic geometry. Indian and Himalayan spiritual communities often constructed temples and fortification

Fortification

Fortifications are military constructions and buildings designed for defence in warfare and military bases. Humans have constructed defensive works for many thousands of years, in a variety of increasingly complex designs...

s on design plans of mandala

Mandala

Maṇḍala is a Sanskrit word that means "circle". In the Buddhist and Hindu religious traditions their sacred art often takes a mandala form. The basic form of most Hindu and Buddhist mandalas is a square with four gates containing a circle with a center point...

and yantra

Yantra

Yantra is the Sanskrit word for "instrument" or "machine". Much like the word "instrument" itself, it can stand for symbols, processes, automata, machinery or anything that has structure and organization, depending on context....

.

Many of the sacred geometry principles of the human body and of ancient architecture have been compiled into the Vitruvian Man

Vitruvian Man

The Vitruvian Man is a world-renowned drawing created by Leonardo da Vinci circa 1487. It is accompanied by notes based on the work of the famed architect, Vitruvius. The drawing, which is in pen and ink on paper, depicts a male figure in two superimposed positions with his arms and legs apart and...

drawing by Leonardo Da Vinci

Leonardo da Vinci

Leonardo di ser Piero da Vinci was an Italian Renaissance polymath: painter, sculptor, architect, musician, scientist, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist and writer whose genius, perhaps more than that of any other figure, epitomized the Renaissance...

, itself based on the much older writings of the roman architect Vitruvius

Vitruvius

Marcus Vitruvius Pollio was a Roman writer, architect and engineer, active in the 1st century BC. He is best known as the author of the multi-volume work De Architectura ....

Contemporary usage

A contemporary usage of the term sacred geometry describes assertions of a mathematical order to the intrinsic nature of the universe

Universe

The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...

. Scientists see the same geometric and mathematical patterns as arising directly from natural principles.

Among the most prevalent traditional geometric forms ascribed to sacred geometry are the sine wave

Sine wave

The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields...

, the sphere

Sphere

A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...

, the vesica piscis

Vesica piscis

The vesica piscis is a shape that is the intersection of two circles with the same radius, intersecting in such a way that the center of each circle lies on the circumference of the other. The name literally means the "bladder of a fish" in Latin...

, the torus

Torus

In geometry, a torus is a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle...

(donut), the 5 platonic solids, the golden spiral

Golden spiral

In geometry, a golden spiral is a logarithmic spiral whose growth factor is , the golden ratio. That is, a golden spiral gets wider by a factor of for every quarter turn it makes.-Formula:...

, the tesseract

Tesseract

In geometry, the tesseract, also called an 8-cell or regular octachoron or cubic prism, is the four-dimensional analog of the cube. The tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of 6 square faces, the hypersurface of the tesseract consists of 8...

(4-dimensional cube), Fractals and the star tetrahedron (2 oppositely oriented and interpenetrating tetrahedrons) which leads to the merkaba.

Fringe theory

As is pointed out by Stephen Skinner in his book Sacred geometry: deciphering the code, it is possible to place a geometric diagram over virtually any image of a natural object or human created structure, and find some lines intersecting the image. If the geometric diagram does not intersect major physical points in the image, the result is what Skinner calls "unanchored geometry." Unanchored geometry, and speculation about the meaning of the geometry itself unsupported by any reliable sources, frequently leads the subject of sacred geometry into the area of New Age fringe theory

Fringe theory

A fringe theory is an idea or a collection of ideas that departs significantly from the prevailing or mainstream view in its particular field of study. Examples include ideas that purport to be scientific theories but have little or no scientific support, conspiracy theories, unproven esoteric...

Music

Pythagoras

Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him...

found that an oscillating string stopped halfway along its length produces an octave

Octave

In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...

relative to the string's fundamental, while a ratio of 2:3 produces a perfect fifth

Perfect fifth

In classical music from Western culture, a fifth is a musical interval encompassing five staff positions , and the perfect fifth is a fifth spanning seven semitones, or in meantone, four diatonic semitones and three chromatic semitones...

and 3:4 produces a perfect fourth

Perfect fourth

In classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...

. Pythagoreans believed that these harmonic ratios

Harmonic series (music)

Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...

gave music powers of healing which could "harmonize" an out-of-balance body. This belief has been revived in modern times.

As worldview and cosmology

Natural forms

Art and architecture

Contemporary usage

Fringe theory

Music

See also

Further reading