Pentagram
A pentagram is the shape of a five-pointed star polygon.
Pentagrams were used symbolically in ancient Greece and Babylonia, and are used today as a symbol of faith by many Wiccans, akin to the use of the cross by Christians. The pentagram has magical associations. Many people who practice Neopagan faiths wear jewelry incorporating the symbol. Christians once commonly used the pentagram to represent the five wounds of Jesus. The pentagram is also used as a symbol by other belief systems and is associated with Freemasonry.
The word pentagram comes from the Greek word πεντάγραμμον, from πέντε, "five" + γραμμή, "line".
The word "pentacle" is sometimes used synonymously with "pentagram". The word pentalpha is a learned modern revival of a post-classical Greek name of the shape.
History
Early history
In early monumental Sumerian script, or cuneiform, a pentagram glyph served as a logogram for the word ub, meaning "corner, angle, nook; a small room, cavity, hole; pitfall".The word Pentemychos was the title of the cosmogony of Pherecydes of Syros.
Here, the "five corners" are where the seeds of Chronos are placed within the Earth in order for the cosmos to appear.
In Neoplatonism, the pentagram was said to have been used as a symbol or sign of recognition by the Pythagoreans, who called the pentagram ὑγιεία Hygieia "health"
Western symbolism
The pentagram was used in ancient times as a Christian symbol for the five senses, or of the five wounds of Christ. The pentagram plays an important symbolic role in the 14th-century English poem Sir Gawain and the Green Knight, in which the symbol decorates the shield of the hero, Gawain. The unnamed poet credits the symbol's origin to King Solomon, and explains that each of the five interconnected points represents a virtue tied to a group of five: Gawain is perfect in his five senses and five fingers, faithful to the Five Wounds of Christ, takes courage from the five joys that Mary had of Jesus, and exemplifies the five virtues of knighthood.Heinrich Cornelius Agrippa and others perpetuated the popularity of the pentagram as a magic symbol, attributing the five neoplatonic elements to the five points, in typical Renaissance fashion. By the mid-19th century a further distinction had developed amongst occultists regarding the pentagram's orientation. With a single point upwards it depicted spirit presiding over the four elements of matter, and was essentially "good". However, the influential writer Éliphas Lévi called it evil whenever the symbol appeared the other way up.
- "A reversed pentagram, with two points projecting upwards, is a symbol of evil and attracts sinister forces because it overturns the proper order of things and demonstrates the triumph of matter over spirit. It is the goat of lust attacking the heavens with its horns, a sign execrated by initiates."
- "The flaming star, which, when turned upside down, is the sign of the goat of black magic, whose head may be drawn in the star, the two horns at the top, the ears to the right and left, the beard at the bottom. It is the sign of antagonism and fatality. It is the goat of lust attacking the heavens with its horns."
- "Let us keep the figure of the Five-pointed Star always upright, with the topmost triangle pointing to heaven, for it is the seat of wisdom, and if the figure is reversed, perversion and evil will be the result."
East Asian symbolism
are the five phases, or five elements in Chinese tradition They are similar to the ancient Greek elements, with more emphasis on their cyclic transformation than on their material aspects. The five phases are: Fire, Earth, Metal, Water, and Wood.Uses in modern occultism
Based on Renaissance-era occultism, the pentagram found its way into the symbolism of modern occultists. Its major use is a continuation of the ancient Babylonian use of the pentagram as an apotropaic charm to protect against evil forces. Éliphas Lévi claimed that "The Pentagram expresses the mind's domination over the elements and it is by this sign that we bind the demons of the air, the spirits of fire, the spectres of water, and the ghosts of earth." In this spirit, the Hermetic Order of the Golden Dawn developed the use of the pentagram in the lesser banishing ritual of the pentagram, which is still used to this day by those who practice Golden Dawn-type magic.Aleister Crowley made use of the pentagram in his Thelemic system of magick: an adverse or inverted pentagram represents the descent of spirit into matter, according to the interpretation of Lon Milo DuQuette. Crowley contradicted his old comrades in the Hermetic Order of the Golden Dawn, who, following Levi, considered this orientation of the symbol evil and associated it with the triumph of matter over spirit.
Use in new religious movements
Bahá'í
The five-pointed star is a symbol of the Bahá'í Faith. In the Bahá'í Faith, the star is known as the Haykal, and it was initiated and established by the Báb. The Báb and Bahá'u'lláh wrote various works in the form of a pentagram.The Church of Jesus Christ of Latter-day Saints
is theorized to have began using both upright and inverted five-pointed stars in Temple architecture, dating from the Nauvoo Illinois Temple dedicated on 30 April 1846. Other temples decorated with five-pointed stars in both orientations include the Salt Lake Temple and the Logan Utah Temple. These usages come from the symbolism found in Revelation chapter 12: "And there appeared a great wonder in heaven; a woman clothed with the sun, and the moon under her feet, and upon her head a crown of twelve stars."Wicca
Because of a perceived association with Satanism and occultism, many United States schools in the late 1990s sought to prevent students from displaying the pentagram on clothing or jewelry. In public schools, such actions by administrators were determined in 2000 to be in violation of students' First Amendment right to free exercise of religion.The encircled pentagram was added to the list of 38 approved religious symbols to be placed on the tombstones of fallen service members at Arlington National Cemetery on 24 April 2007. The decision was made following ten applications from families of fallen soldiers who practiced Wicca. The government paid the families to settle their pending lawsuits.
Other religious use
Serer religion
The five-pointed star is a symbol of the Serer religion and the Serer people of West Africa. Called Yoonir in their language, it symbolizes the universe in the Serer creation myth, and also represents the star Sirius.Druze
A multicolored version is used as symbol of the Druze religion.Other modern use
- The pentagram is featured on the national flags of Morocco and Ethiopia
- The Order of the Eastern Star, an organization associated with Freemasonry, uses a pentagram as its symbol, with the five isosceles triangles of the points colored blue, yellow, white, green, and red. In most Grand Chapters the pentagram is used point down, but in a few it is point up. Grand Chapter officers often have a pentagon inscribed around the star.
- A pentagram is featured on the flag of the Dutch city of Haaksbergen, as well on its coat of arms.
- A pentagram is featured on the flag of the Japanese city of Nagasaki, as well on its emblem.
Geometry
It can be seen as a net of a pentagonal pyramid although with isosceles triangles.
Construction
The pentagram can be constructed by connecting alternate vertices of a pentagon; see details of the construction. It can also be constructed as a stellation of a pentagon, by extending the edges of a pentagon until the lines intersect.Truncation
A uniform truncated pentagram t produces a doubly-wrapped pentagon with overlapping vertices and edges,. A shallower truncation produces an isogonal figure, like this one with equally spaced vertices. A truncated retro-pentagram t, or a quasitruncation, produces a decagram,.shallow t | t = |
Golden ratio
The golden ratio, φ = / 2 ≈ 1.618, satisfyingplays an important role in regular pentagons and pentagrams. Each intersection of edges sections the edges in the golden ratio: the ratio of the length of the edge to the longer segment is φ, as is the length of the longer segment to the shorter. Also, the ratio of the length of the shorter segment to the segment bounded by the two intersecting edges is φ. As the four-color illustration shows:
The pentagram includes ten isosceles triangles: five acute and five obtuse isosceles triangles. In all of them, the ratio of the longer side to the shorter side is φ. The acute triangles are golden triangles. The obtuse isosceles triangle highlighted via the colored lines in the illustration is a golden gnomon.
Trigonometric values
As a result, in an isosceles triangle with one or two angles of 36°, the longer of the two side lengths is φ times that of the shorter of the two, both in the case of the acute as in the case of the obtuse triangle.Spherical pentagram
A pentagram can be drawn as a star polygon on a sphere, composed of five great circle arcs, whose all internal angles are right angles. This shape was described by John Napier in his 1614 book Mirifici logarithmorum canonis descriptio along with rules that link the values of trigonometric functions of five parts of a right spherical triangle. It was studied later by Carl Friedrich Gauss.Three-dimensional figures
Several polyhedra incorporate pentagrams:Higher dimensions
Orthogonal projections of higher dimensional polytopes can also create pentagrammic figures:All ten 4-dimensional Schläfli–Hess 4-polytopes have either pentagrammic faces or vertex figure elements.