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Mathematics of the Parthenon

by Liliana Usvat

With the exception of the Great Pyramid in Egypt, the Parthenon of Athens has probably received more attention from archaeologists, historians, architects, painters and poets than any other structure on earth.

Built by the architects Ictinus and Callicrates under the supervision of the sculptor Phidias, the temple is generally considered to be the culmination of the development of the Doric order, the simplest of the three classical Greek architectural styles.

The ancient Greeks assigned various attributes to the Platonic solids and to certain geometrically-derived ratios, investing them with "meaning." For example, the cube symbolized kingship and earthly foundations, while the Golden Section was seen as a dynamic principle embodying philosphy and wisdom. Thus a building dedicated to a god-king might bear traces of cubic geometry, while one dedicated to a heavenly god might have been constructed using Golden Section proportions.

Phi = 1.618…
Phi is the Golden Section of the Greeks. It was said to be the first section in which the One became many.

It was not until about 300 BC that the Greek’s knowledge of the Golden Ratio was first documented in the written historical record by Euclid in “Elements.”  It states, “a straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less.”

The Parthenon is a temple on the Athenian Acropolis, Greece, dedicated to the goddess Athena, whom the people of Athens considered their patron. Its construction began in 447 BC when the Athenian Empire was at the height of its power.

It was completed in 438 BC, although decoration of the building continued until 432 BC. It is the most important surviving building of Classical Greece, generally considered the culmination of the development of the Doric order. Its decorative sculptures are considered some of the high points of Greek art.

The Parthenon is regarded as an enduring symbol of Ancient Greece, Athenian democracy, western civilization and one of the world's greatest cultural monuments. The Greek Ministry of Culture is currently carrying out a program of selective restoration and reconstruction to ensure the stability of the partially ruined structure.

Sacred Geometry

  • The Parthenon was built to extremely precise dimensions according to the mathematical ratios of sacred geometry.
  • The rectangular building (measured at the top step of its base to be 101.34 feet wide by 228.14 feet long) was constructed of brilliant white marble, surrounded by 46 great columns, roofed with tiles, and housed a nearly 40 foot tall statue of the goddess Athena. The statue, known as Athena Promachos, Athena the Champion, was made of wood, gold and ivory and could be seen from a distance of many miles.
  • Height of the columns – The structural beam on top of the columns is in a golden ratio proportion to the height of the columns.  Note that each of the grid lines is a golden ratio proportion of the one below it, so the third golden ratio grid line from the bottom to the top at the base of the support beam represents a length that is phi cubed, 0.236, from the top of the beam to the base of the column.

  • Dividing line of the root support beam - The structural beam on top of the columns has a horizontal dividing line that is in golden ratio proportion to the height of the support beam.

  • Width of the columns – The width of the columns is in a golden ratio proportion formed by the distance from the center line of the columns to the outside of the columns.

  • The golden ratio proportions that appear in the height of the roof support beam and in the decorative rectangular sections that run horizontally across it.  The gold colored grids below are golden rectangles, with a width to height ratio of exactly 1.618 to 1

Athena

  • The name Parthenon refers to the worship of Athena, the goddess and patroness of the city of Athens.
  • Athena issued fully grown from the head of her father Zeus (Jupiter).
  • She represents the highest order of spiritual development and the gifts of intellect and understanding. Athena is the symbol of the universal human aspiration for wisdom.

Purpose and History of the Parthenon

Long before the construction of the Parthenon the site had been a sacred place of other cultures. The Parthenon was built to supplant the temples of the earlier cultures and to both experience and praise the character of the Greek goddess Athena.

  • The origins of the sacred use of the great limestone rock rising from the Attic plain are unknown. They were forgotten long before the writing of the first recorded histories of Athens.
  • Neolithic remains discovered on the slopes of the Acropolis indicate a continuous settlement on the hill from at least 2800 BCE, well before the Minoan and Mycenaean cultures that later gave birth to the archaic Greek.
  • In the Mycenaean period (1600-1100 BCE) the summit was surrounded by a massive fortification wall, which protected the palace-temple of the Mycenaean priest-kings.
  • The earliest known Hellenistic structures, dating from the 6th century BCE, were two large temples dedicated to the goddess Athena, on hill top positions that had probably contained older shrines before them.
  • In 480 BCE the Persians destroyed these temples and in 447 BCE the Athenian leader Pericles initiated construction of the presently standing temple of Athena.
  • Built by the architects Ictinus and Callicrates under the supervision of the sculptor Phidias, the temple is generally considered to be the culmination of the development of the Doric order, the simplest of the three classical Greek architectural styles.
  • While much of the structure remains intact, the Parthenon has suffered considerable damage over the centuries. In 296 BCE the tyrant Lachares removed the gold from the statue of Athena in order to pay his army.
  • In the 5th century CE the Parthenon was converted into a Christian church.
  • In 1460 the Parthenon held a Turkish mosque.
  • In 1687 gunpowder stored by the Turks inside the temple exploded and destroyed the central area
  • In 1801 - 1803 parts of the temple’s remaining sculptures were sold by the Turks (who controlled Greece at the time) to the Englishman Lord Elgin. These sculptures were forcibly removed, sold to the British Museum and called the Elgin Marbles.
  • Greece has asked the British Museum to return the sculptures but it has refused to do so.
  • Francis Penrose, a British archaeologist studying the Parthenon in 1891, suggested that the site is oriented towards the rising of the Pleiades in the constellation of Taurus.
  • The Parthenon construction cost the Athenian treasury 469 silver talents. While it is almost impossible to create a modern equivalent for this amount of money, it might be useful to look at some facts. One talent was the cost to build one trireme, the most advanced warship of the era. “…one talent was the cost for paying the crew of a warship for a month” (D. Kagan, The Peloponnesian War, 61). According to Kagan, Athens at the beginning of the Peloponnesian war had 200 triremes in service, while the annual gross income of the city of Athens at the time of Perikles was 1000 talents, with another 6000 in reserve at its treasury.
"Chance favors the prepared mind." - Louis Pasteur