Pentagram

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For other uses, see Pentagram (disambiguation).

A pentagram

A pentagram (sometimes known as pentalpha or pentangle) is the shape of a five-pointed star drawn with five straight strokes. The word pentagram comes from the Greek word πεντάγραμμον (pentagrammon), a noun form of πεντάγραμμος (pentagrammos) or πεντέγραμμος (pentegrammos), a word meaning roughly "five-lined" or "five lines".

[edit] History

Pentagrams were used symbolically in ancient Greece and Babylonia. The Pentagram has magical associations, and many people who practice neopagan faiths wear jewelry incorporating the symbol. Christians once more commonly used the pentagram to represent the five wounds of Jesus,^[1]^[2] and it also has associations within Freemasonry.

The pentagram has long been associated with the planet Venus, and the worship of the goddess Venus, or her equivalent. It is also associated with the Roman Lucifer, who was Venus as the Morning Star, the bringer of light and knowledge. It is most likely to have originated from the observations of prehistoric astronomers.^{[citation needed]} When viewed from Earth, successive inferior conjunctions of Venus plot a nearly perfect pentagram shape around the zodiac every eight years.

The word "pentacle" is sometimes used synonymously with "pentagram", although their technical usages are different, and their etymologies may be unrelated.^[3]

[edit] Early history

Man inscribed in a pentagram, from Heinrich Cornelius Agrippa's Libri tres de occulta philosophia. The five signs at the pentagram's vertices are astrological.

The occultist and magician Eliphas Levi's pentagram, which he considered to be a symbol of the microcosm, or human.

[edit] Sumer

The first known uses of the pentagram are found in Mesopotamian writings dating to about 3000 BC. The Sumerian pentagrams served as pictograms for the word "UB," meaning "corner, angle, nook; a small room, cavity, hole; pitfall," suggesting something very similar to the pentemychos (see below on the Pythagorean use for what pentemychos means). In René Labat's index system of Sumerian hieroglyphs/pictograms it is shown with two points up.^[4] In the Babylonian context, the edges of the pentagram were probably orientations: forward, backward, left, right, and "above".^{[citation needed]} These directions also had an astrological meaning, representing the five planets Jupiter, Mercury, Mars and Saturn, and Venus as the "Queen of Heaven" (Ishtar) above.^{[citation needed]}

[edit] Pythagoreans

The Pythagoreans called the pentagram ύγιεια Hygieia ("health"; also the Greek goddess of health, Hygieia), and saw in the pentagram a mathematical perfection (see Geometry section below).

The five vertices were also used by the medieval neo-pythagoreans (whom one could argue were not pythagoreans at all) to represent the five classical elements:

ύδωρ, Hydor, water
Γαια, Gaia earth
ίδέα, Idea or ίερόν, Hieron "a divine thing"
έιλή, Heile, heat (fire)
άήρ, Aer, air

The vertices were labeled in the letters of υ-γ-ι-ει-α. The ordering (clockwise or counter-clockwise) and starting vertex varied.

Heinrich Cornelius Agrippa and others, recognised the letters as being the five beginning letters of the words: udor (water, often transliterated as hydor), ge (earth; Agrippa used gaia), idea (idea, as in the Platonic Idea), eile (heat, sometimes written as heile), and aer (air). However, even if one uses the "elemental" scheme that Agrippa used, it's a definite stretch because it uses heat (heile), which is not an element but a quality of the element fire. Had Agrippa used the Attic Greek, which is the language Pythagoreans back then actually spoke and wrote, he could have used (phonetic) "empreesis" for fire or conflagration.

Another pentagram from Agrippa's book. This one has the Pythagorean letters inscribed around the circle.

The ancient Pythagorean pentagram was drawn with two points up and represented the doctrine of Pentemychos. Pentemychos means "five recesses" or "five chambers", also known as the pentagonas — the five-angle, and was the title of a work written by Pythagoras's teacher and friend Pherecydes of Syros.^[5] It was also the "place" where the first pre-cosmic offspring had to be put in order for the ordered cosmos to appear. The pentemychos is in Tartaros.^{[citation needed]}

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In very early Greek thought, Tartaros (or Chaos, according to Hesiod) was the primordial Darkness from which the cosmos is born. While it was locked away after the emergence and ordering of the cosmos, it still continued to have an influence. In fact, it was known as "the subduer of both gods and men" (Homer), and it was from this that the world got its "psyche" (soul) and its "daimon". The Boundless Darkness held influence through Mychos or Krater. Apart from being the gateway from "there" to "here" it was also a way in the opposite direction, from "here" to "there", as is evident in the many tales about how Greek heroes, philosophers and mystics descended through Krater to Tartaros/Hades (the distinction between the two was very optional back then) in quest for Wisdom. The Underworld as the source of wisdom was the rule.

Tartaros was also later seen as the "chthonic realm" where all the enemies of the cosmic order were locked away, also called the "prison-house" of Zeus. It was said to lay outside of the aither over which Zeus had lordship; what we today would call space, back then called "Zeus' defense-wall," yet it was also beneath the earth. Plato (in Cratylus) said that the aither had a penetrating power that permeates the whole world, and he found it both inside and outside of our bodies. The pentemychos is outside, or in-side, of the aither.

In the play Medea by Euripides, the sorceress Medea calls upon Hecate with the words, "By that dread queen whom I revere before all others and have chosen to share my task, by Hecate who dwells within my inmost chamber, not one of them shall wound my heart and rue it not." Note that she speaks of the Heart. The inmost chamber is the Mychos. Normally, Hecate and Persephone are portrayed solely as the rulers of the Underworld. In Medea, however, Hecate is called the Lady of Tartaros, Phulada (Guardian), Propulaia (Before the Gates), Kleidophoros (Key-bearer) and Kleidoukhos (Key-holder, Priestess). This Underworld of the Greeks and Pythagoreans is also the "inmost chamber" and the Core of Inner Being.

This is an esoteric connection, but the Core is the Greek Goddess Kore (another name for Persephone, alongside Hecate queen of the underworld), whose symbol was the apple. If an apple is cut transversally through its core, it reveals a pentagram. The apple remains a symbol of health ("An apple a day keeps the doctor away").

[edit] Religious symbolism

[edit] Christianity

A goat's head inscribed in a pentagram, from La Clef de la Magie Noire by the Rosicrucian Stanislas de Guaita (1897). The epigraph reads "Leviathan" (outer circle) and "Samael" and "Lilith" (inner circle).

The pentagram was a Christian symbol for the five senses,^[6] and if the letters S, A, L, V, and S are inscribed in the points, it is a symbol of health (Latin salūs).^{[citation needed]}

The Pentagram can be displayed in two other ways with two different meanings according to certain beliefs. If the Pentagram is displayed as a star with 1 point facing up then it represents God ruling over mortals but if displayed upside down it symbolizes the devil or satan ruling over the world of mortals and god. Also in several occult religions and beleifs displaying the pentagram upside down is an act of satanism and it is said to attract evil spirits.

Medieval Christians believed it to symbolise the five wounds of Christ. The pentagram was believed to protect against witches and demons.^[7]

The pentagram figured in the heavily symbolic Arthurian romances.^[7] It appears on the shield of Sir Gawain in the 14th Century poem, Sir Gawain and the Green Knight. In the poem the five lines of the star are given multiple meanings: they represent the five senses, five fingers, the five wounds of Christ,^[8] the five joys that Mary had of Jesus (the Annunciation, the Nativity, the Resurrection, the Ascension and the Assumption), and the five virtues of knighthood which Gawain hopes to embody: frankness, fellowship, purity, courtesy and compassion.

Probably due to misinterpretation of symbols used by ceremonial magicians, it later became associated with Satanism and subsequently rejected by most of Christianity sometime in the twentieth century.^[7]

The Church of Jesus Christ of Latter-day Saints has used pentagrams and five-pointed stars in Temple architecture, particularly the Nauvoo Illinois Temple^[9] and the Salt Lake Temple. These symbols derived from traditional morning star pentagrams that are no longer commonly used in mainstream Christianity.[1]

[edit] Judaism

The pentagram was the official seal of the city of Jerusalem for a time.^[7]

[edit] Satanism

Satanists use a pentagram with two points up, often inscribed in a double circle, with the head of a goat inside the pentagram. This is referred to as the Sigil of Baphomet. They use it much the same way as the Pythagoreans, as Tartaros means Hell in Christian terminology (the word is used as such in the Bible, referring to the place where the fallen angels are fettered). The Pythagorean Greek letters are most often replaced by the Hebrew letters לויתן forming the name Leviathan. Less esoteric LaVeyan Satanists use it as a sign of rebellion or religious identification, the three downward points symbolising rejection of the holy Trinity.

[edit] Neopaganism

A typical Neopagan pentagram (circumscribed): a symbol used in many Neopagan traditions to represent earth, air, fire and water, plus the fifth element of quintessence or Spirit.

Many Neopagans, especially Wiccans, use the pentagram as a symbol of faith similar to the Christian cross or the Jewish Star of David. It is not, however, a universal symbol for Neopaganism, and is rarely used by Reconstructionists. Its religious symbolism is commonly explained by reference to the neo-Pythagorean understanding that the five vertices of the pentagram represent the four elements with the addition of Spirit as the uppermost point. As a representation of the elements, the pentagram is involved in the Wiccan practice of summoning the elemental spirits of the four directions at the beginning of a ritual.

The outer circle of the circumscribed pentagram is sometimes interpreted as binding the elements together or bringing them into harmony. The Neopagan pentagram is generally displayed with one point up, partly because of the "inverted" pentagram's association with Satanism; however, within traditional forms of Wicca a pentagram with two points up is associated with the Second Degree Initiation and in this context has no relation to Satanism.

Because of a perceived association with Satanism and also because of negative societal attitudes towards Neopagan religions and the "occult", many United States schools have sought to prevent students from displaying the pentagram on clothing or jewelry.^[10]^[11]^[12] In public schools, such actions by administrators have been determined to be in violation of students' First Amendment right to free exercise of religion.

[edit] Samael Aun Weor

Samael Aun Weor used the Pentagram to represent man's Atman, or Internal Christ. When a man's limbs are outstretched thus that his feet are planted on the ground while his head is situated atop his body it creates the omnipotent symbol of the pentagram. Through the Mantra "Klim, Krishna, Govindaya, Gopijana, Vallebayah, Swahah" one's inner being is said to be awakened and come to the initiate's aid. Aun Weor stated that no demon could resist the power of this mantra, since one's Logos cannot be overcome by a demon of any stature.

In contrast to representing one's Logos, the inverted pentagram represents one's Umbral Guardian, the malignant antithesis of the divine father. When the pentagram's inferior rays point upwards, it represents Satan. This symbol is therefore shown above as the goat of the Witches' Sabbath, which serves as a call to the vast columns of demons.

[edit] Political symbolism

[edit] Flags

The flag of Morocco

The flag of Ethiopia

While a solid five-pointed star is found on many flags, the pentagram is relatively rare. It appears on two national flags (those of Ethiopia and Morocco) and in some coats of arms. See gallery of flags by design.

According to Ivan Sache, on the Moroccan flags, the pentagram represents the link between God and the nation.^[13] It is also possible that both flags use the pentagram as a symbol of King Solomon (see Solomon's seal), the archetypal wise king of Jewish, Christian and Muslim lore.

The symbol also represents the five pillars of the Muslim faith and five daily times of prayer.

[edit] Other organizations

[edit] Order of the Eastern Star

Eastern Star General Grand Chapter emblem

The Order of the Eastern Star, a fraternal organization associated with Freemasonry, employs a point-down pentagram as its symbol, with the five isosceles triangles of the points colored red, blue, yellow, white and green.

[edit] Literature

In the medieval romance of Sir Gawain and the Green Knight, the pentagram on Gawain's shield is given a Christian interpretation (see above).

In Goethe's Faust, the pentagram prevents Mephistopheles from leaving a room.

Mephistopheles:

I must confess, my stepping o'er

Thy threshold a slight hindrance doth impede;

The wizard-foot doth me retain.

Faust:

The pentagram thy peace doth mar?

To me, thou son of hell, explain,

How earnest thou in, if this thine exit bar?

Could such a spirit aught ensnare?

In H.P. Lovecraft's Cthulhu Mythos stories, the version of The Elder Sign devised by August Derleth is a warped pentagram with a flaming eye or pillar of flame in the center. It was first described in Derleth's novel, The Lurker at the Threshold. (This was, however, different from the symbol that Lovecraft himself had envisaged.)

In Dan Brown's novel The Da Vinci Code, the pentagram represents Venus, based on the successive inferior conjunctions of Venus against the Zodiac.

In Japanese culture, the pentagram (五芒星 gobōsei) is a symbol of magical power, associated with the onmyoji Abe no Seimei; it is a diagram of the "overcoming cycle" of the five Chinese elements. As a predominantly non-Christian country, with a different set of associations attached to the symbol, there is no social stigma associated with it.

[edit] Popular Culture

Rush's albums such as 2112 has the Pentagram on it.

HIM uses the Heartagram, which is based on the Pentagram.

[edit] Geometry

Complete graph

The pentagram is represented by the Schlafli symbol {5/2}. It is the smallest star polygon.

The pentagram can be constructed by connecting alternate vertices of a pentagon. It can also be constructed as a stellation of a pentagon, by extending the edges of a pentagon until the lines intersect.

Like a regular pentagon, and a regular pentagon with a pentagram constructed inside it, the regular pentagram has as its symmetry group the dihedral group of order 10.

[edit] Golden ratio

A pentagram colored to distinguish its line segments of different lengths. The four lengths are in golden ratio to one another.

The golden ratio, φ = (1+√5)/2 ≈ 1.618, satisfying

$\varphi=1+2\sin(\pi/10)=1+2\sin 18^\circ\,$

$\varphi=1/(2\sin(\pi/10))=1/(2\sin 18^\circ)\,$

$\varphi=2\cos(\pi/5)=2\cos 36^\circ\,$

plays an important role in regular pentagons and pentagrams. Each intersection of edges sections the edges in 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 2 intersecting edges (a side of the pentagon in the pentagram's center) is φ. As the four-color illustration shows:

$\frac{\mathrm{red}}{\mathrm{green}} = \frac{\mathrm{green}}{\mathrm{blue}} = \frac{\mathrm{blue}}{\mathrm{magenta}} = \varphi .$

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.

[edit] Trigonometric values

See Exact trigonometric constants: Pentagon

$\sin \frac{\pi}{10} = \sin 18^\circ = \frac{\sqrt 5 - 1}{4}=\frac{\varphi-1}{2}=\frac{1}{2\varphi}$

$\cos \frac{\pi}{10} = \cos 18^\circ = \frac{\sqrt{2(5 + \sqrt 5)}}{4}$

$\tan \frac{\pi}{10} = \tan 18^\circ = \frac{\sqrt{5(5 - 2 \sqrt 5)}}{5}$

$\cot \frac{\pi}{10} = \cot 18^\circ = \sqrt{5 + 2 \sqrt 5}$

$\sin \frac{\pi}{5} = \sin 36^\circ = \frac{\sqrt{2(5 - \sqrt 5)} }{4}$

$\cos \frac{\pi}{5} = \cos 36^\circ = \frac{\sqrt 5+1}{4} = \frac{\varphi}{2}$

$\tan \frac{\pi}{5} = \tan 36^\circ = \sqrt{5 - 2\sqrt 5}$

$\cot \frac{\pi}{5} = \cot 36^\circ = \frac{ \sqrt{5(5 + 2\sqrt 5)}}{5}$

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.

[edit] Three dimensional figures

See Uniform polyhedron: Icosahedral symmetry

Several polyhedra incorporate pentagrams:

Pentagrammic prism	Pentagrammic antiprism	Pentagrammic crossed antiprism	Small stellated dodecahedron
Small ditrigonal icosidodecahedron	Small dodecahemicosahedron	Snub dodecadodecahedron	16th stellation of icosidodecahedron

[edit] See also

Wikimedia Commons has media related to:

Pentagrams

Bahá'í symbols
Command-at-Sea Pin
Complete graph; the complete graph on five vertices can be drawn as a pentagram
Heartagram
Heptagram
Hexagram and Seal of Solomon
magic and magick
Mullet (heraldry)
Pentagon
Pentad
Pentacle
Pythagoras
Red star
Five-pointed star
Star (glyph)
Stellone d'Italia
List of symbols
Nonconvex uniform polyhedra with full icosahedral symmetry (many show a pattern of pentagrams)
Order of the Eastern Star
Libri tres de occulta philosophia

[edit] References

^ "Pentagram" article in The Continuum Encyclopedia of Symbols Becker, Udo, ed., Garmer, Lance W. translator, New York: Continuum Books, 1994, p. 230.
^ Signs and Symbols in Christian Art Ferguson, George, Oxford University Press: 1966, p. 59.
^ "Pentacle", Oxford English Dictionary.
^ Labat, René. Manuel d'épigraphie akkadienne: Signes, Syllabaire, Idéogrammes. The pentagram is symbol number 306 in this system.
^ This is a lost book, but its contents are preserved in Damascius de principiis, quoted in Kirk and Raven, The Pre-Socratic Philosophers, Cambridge Univ. Press, 1956, p. 55.
^ Christian Symbols Ancient and Modern, Child, Heather and Dorothy Colles. New York: Charles Scribner's Sons, 1971, ISBN 0-7135-1960-6.
^ ^a ^b ^c ^d http://altreligion.about.com/library/glossary/symbols/bldefspentagram.htm
^ Christian Symbols and How To Use Them, Knapp, Justina; Milwaukee: The Bruce Publishing Company, 1955. Plate LXV, Plate LV (Imprimatur, Jos. F. Busch, Bishop of St. Cloud)
^ See the Nauvoo Temple website discussing its architecture, and particularly the page on Nauvoo Temple exterior symbolism. Retrieved 13 December 2006.
^ "Religious Clothing in School", Robinson, B.A., Ontario Consultants on Religious Tolerance, 20 August, 1999, updated 29 April, 2005. accessed 10 February, 2006.
^ "ACLU Defends Honor Student Witch Pentacle" press release, American Civil Liberties Union of Michigan, 10 February, 1999. accessed 10 February, 2006.
^ "Witches and wardrobes: Boy says he was suspended from school for wearing magical symbol" Rouvalis, Cristina; Pittsburgh Post-Gazette, September 27, 2000. accessed 10 February, 2006.
^ Moroccan flag on Flagspot.net accessed on 10 February, 2006.

[edit] External links

Eric W. Weisstein, Pentagram at MathWorld.
The Pythagorean Pentacle from the Biblioteca Arcana.
In-depth analysis of the Golden Ratio

The pentagram and Freemasonry

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