The Mysterious Geometry That ‘Connects’ Ancient Greek Temples

Credit: GreekReporter Archive

Sacred geometry is simply a conception developed successful past times grounded connected the thought that the satellite is created based connected a accordant geometrical pattern. This “mysterious” geometry tin beryllium recovered successful ancient Greek temples each implicit Greece. The conception ascribes symbolic and ineffable meanings to definite geometric shapes and geometric proportions associated with the content of an orderly universe.

Geometry triangles ‘connecting’ past Greek temples

During past Greece, this conception was manifested successful 2 triangles formed by 3 ineffable places each. One is formed by the ancient Greek Temple of Poseidon astatine Cape Sounio, the Temple of Aphaia Athena connected Aegina, and the Temple of Hephaestus successful Thissio of Athens. The 2nd triangle is comprised of the Temple of Apollo astatine Delphi, the Parthenon successful Athens, and the Temple of Aphaia connected Aegina.

Sacred geometry recovered successful past Greek temples is grounded connected the thought that the satellite is created based connected a accordant geometrical pattern. Credit: Google Maps / GreekReporter Illustration

In 1938, world-renowned designer Doxiades discovered that the monuments and altars were not randomly placed oregon constructed, but determination was a pattern. In 1967, French researcher Jean Richer, wrote the publication Sacred Geography of the Ancient Greeks, successful which helium analyzes those connections.

In his book, Richer claims that if lines were drawn from altar to altar, they would reflector constellations on with zodiac cycles. Richer argues that galore of the patron animals of these past Greek cities were correlated to the locations of constellations that often included mythological attributions.

Furthermore, successful the 1950s, an chartless idiosyncratic stated that the distances betwixt the 3 temples of Sounion, Aphaia, and the Parthenon created a cleanable isosceles triangle.

If a ellipse was constructed with the Parthenon arsenic the halfway and a radius enactment to Thision, it would beryllium recovered that the circumference of this ellipse passes by 3 main points. The orator’s measurement of Pnyx, the monument of Filopappou, and the temple of Olympian Zeus. Even much interestingly, the radius of this ellipse is adjacent to 2,058 feet, oregon 3 100 times the aureate ratio. Another absorbing information is that the halfway of the temple of Olympian Zeus lies equidistant with Hephaestion and the measurement of the rhetors astatine Pnyx. 

Researches tin besides find the five-edged prima of the Pythagoreans. The prima falls with these 5 locations, Thebes, Cromion, Aphaia, Stiris, and Amfiaron. Thus, this points to the geometric harmony of these locations arsenic good arsenic their purposeful arrangement.

Sacred triangle of Greek temples.
Parthenon (Athens), Temple of Poseidon (Sounion), Temple of Aphaia (Aegina) signifier a cleanable isosceles triangle, each facing east.
Geometric distances factored successful gathering temples#Greece #Greek #archaeology #ancientgreece #geometry #Athens #Museum pic.twitter.com/ja6GBvAc5Q

— SpartiatisΣπαρτιατης (@KSpartiatis) April 7, 2019

According to Greek historiographer Herodotus (c. 484-425 BC), geometry was established arsenic a subject by the past Egyptians. There is written grounds of this successful Egypt. The past Mesopotamians are besides known to person practiced geometry, arsenic did aboriginal Chinese and Indians. The Greek sanction for this subdivision of mathematics is derived from the words ‘geo’ (Earth) and ‘metron’ (measure), virtually meaning “measuring the world.”

The past Greek mathematician Euclid is considered the begetter of geometry. His treatise connected geometry, The Elements, is 1 of the astir influential works successful the past of mathematics. Euclid’s work is simply a premier illustration of the rational and world attack to the survey of geometry. Other geometers and thinkers, however, saw symbolic and ineffable meanings successful geometry, and, therefore, their tract of survey whitethorn beryllium referred to arsenic ineffable geometry.

A radical of these thinkers was the Pythagoreans, whose schoolhouse of doctrine was founded by Pythagoras of Samos.

Pythagoreans and the tetractys

The archetypal awesome successful ineffable geometry originates from the Pythagoreans and is called the tetractys, oregon the tetractys of the decad (tetractys meaning “four” and decad meaning “ten”). This awesome consists of 10 dots arranged successful 4 rows, frankincense forming an equilateral triangle. The tetractys is afloat of symbolic meaning. For example, each enactment of dots is said to incorporate a hidden meaning.

The archetypal row, which has a azygous dot, represents the progressive principle, oregon divine powerfulness down each creation. The 2nd represents the passive principle, oregon matter, portion the 3rd refers to the satellite proceeding from the national of the progressive and passive principles. The 4th is associated to the 4 wide arts and sciences of which the satellite is composed.

The ineffable geometry tetractys triangle created by the Pythagorean schoolhouse by Jossifresco. Public Domain.

The Pythagoreans were not the lone past Greeks who delved into ineffable geometry. Overall, it was a philosophical thought that the satellite shared a symbolic signifier of shapes that ceaselessly manifest successful nature, including plants, animals, the quality body, and mostly crossed the full universe.

Plato and his academy studied geometry chiefly for these philosophical purposes, and mathematics itself was to supply a representation of the quality psyche. At the entranceway to Plato’s Academy, determination is an inscription meaning “let nary 1 ignorant of geometry travel nether my roof” (Greek: “Mηδείς ἀγεωμέτρητος εἰσίτω μου τὴν στέγην”).

This survey of the philosophical worth inherent successful the basics of geometry was considered ineffable and became a cosmopolitan connection chiefly among philosophers.

The ellipse successful ineffable geometry

Apart from the triangle, recovered successful the ineffable geometry of past Greek temples, galore different shapes person been imbued with symbolic meaning. Greeks perceived the ellipse arsenic a awesome of unity, oneness, and indivisibility. The ellipse is astir universally employed arsenic a awesome for the Sun. It whitethorn beryllium repeated successful bid to make caller symbols, specified arsenic circles wrong larger circles oregon intertwining ones.

Aristotle wrote successful Physics that the ellipse is “the perfect, first, astir beauteous form.” In some geometry and ineffable geometry, the ellipse is considered to beryllium the astir indispensable shape, arsenic it symbolizes unity successful some the 2 and three-dimensional. Earth is simply a sphere arsenic are the different planets, moons, stars, galaxies, and astir cardinal forms of beingness specified arsenic atoms, molecules, seeds, and eggs.

The ellipse besides represents the cycles of beingness and is truthful connected to maturation and movement. Cyclical question patterns are indispensable to beingness and tin beryllium observed betwixt each the planets circling astir the sun, the moons revolving astir the planets, and the planets spinning connected their axis, starring to further cycles of days, months, and years.

Searching for the Golden Ratio

The Golden Ratio is important to ineffable geometry. It is known by galore different names, including phi (the Greek Φ), the divine proportion, and the aureate mean. Ιn Euclid’s Elements, you find 1 of the archetypal recorded definitions of this aureate ratio: “A consecutive enactment is said to person been chopped into utmost and mean ratio when, arsenic the full enactment is to the greater segment, truthful is the greater to the lesser.”

In simpler terms, the Golden Ratio refers to a perfectly symmetrical narration betwixt 2 proportions by which the narration betwixt the larger and smaller parts is the aforesaid arsenic that betwixt the full and the larger parts.

The mathematics of the Golden Ratio proportionality is generated by the look (√5+1/2) (or 1:1.618). Τhe past Greeks recovered that the Golden Ratio provided “the astir aesthetically pleasing proportionality of sides of a rectangle.” They are alleged to person applied it successful their architecture. This ratio is renowned for producing immoderate of the astir aesthetic shapes.

The Platonic Solids. Public Domain/Wikipedia

Platonic solids and ineffable geometry

According to the large Athenian philosopher Plato successful his dialog Timaeus, the Earth is composed of 4 basal elements—fire, air, water, and earth.

The Platonic solids are 5 three-dimensional shapes indispensable to ineffable geometry. These are the tetrahedron, hexahedron (or cube), octahedron, dodecahedron, and icosahedron, which person four, six, eight, twelve, and 20 sides, respectively.

Plato associated his solids with the 4 basal elements. The tetrahedron represented fire, owed to its crisp points and edge, whereas the hexahedron was linked with earth, owed to its four-square regularity. The octahedron and icosahedron, some of which are made up of triangles, correspond aerial and water, respectively.

Lastly, the dodecahedron was assigned by Plato to the heavens, arsenic its 12 pentagonal faces corresponded with the 12 constellations. Using these 5 solids, Plato created a mentation of the universe. Plato’s mentation was based connected the symbolic properties of the 5 solids, and mathematicians were little funny successful them.

However, his mentation was revived during the sixteenth period by the German astronomer Johannes Kepler. Since then, the Platonic solids person made their mode into ineffable geometry and acquired further symbolic value.