![Five Pointed Star Lined](https://upload.wikimedia.org/wikipedia/commons/6/6e/Five_Pointed_Star_Lined.svg)
A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed
star polygon, formed from the diagonal
line segments of a convex (or simple, or non-self-intersecting)
regular pentagon
In geometry, a pentagon (from the Greek πέντε ''pente'' meaning ''five'' and γωνία ''gonia'' meaning ''angle'') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°.
A pentagon may be simpl ...
. Drawing a circle around the five points creates a similar symbol referred to as the
pentacle
A pentacle (also spelled and pronounced as ''pantacle'' in Thelema, following Aleister Crowley, though that spelling ultimately derived from Éliphas Lévi) "The Pantacle of Frater V. I. O." is a talisman that is used in magical evocation, and ...
, which is used widely by
Wicca
Wicca () is a modern Pagan religion. Scholars of religion categorise it as both a new religious movement and as part of the occultist stream of Western esotericism. It was developed in England during the first half of the 20th century and w ...
ns and in
paganism, or as a sign of life and connections. The word "pentagram" refers only to the five-pointed star, not the surrounding circle of a pentacle.
Pentagrams were used symbolically in
ancient Greece
Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean Sea, Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of Classical Antiquity, classical antiquity ( AD 600), th ...
and
Babylonia. Christians once commonly used the pentagram to represent the
five wounds of Jesus. Today the symbol is widely used by the Wiccans, witches, and pagans. The pentagram has
magical associations. Many people who practice
neopaganism wear jewelry incorporating the symbol.
The word ''pentagram'' comes from the
Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
word πεντάγραμμον (''pentagrammon''), from πέντε (''pente''), "five" + γραμμή (''grammē''), "line".
Pentagram refers to just the star and
pentacle
A pentacle (also spelled and pronounced as ''pantacle'' in Thelema, following Aleister Crowley, though that spelling ultimately derived from Éliphas Lévi) "The Pantacle of Frater V. I. O." is a talisman that is used in magical evocation, and ...
refers to the star within the circle specifically although there is some overlap in usage. The word ''pentalpha'' is a 17th-century revival of a post-classical Greek name of the shape.
History
Early history
![Hugieia-pentagram](https://upload.wikimedia.org/wikipedia/commons/b/b4/Hugieia-pentagram.svg)
Pentagram symbols from about 5,000 years ago were found in the Liangzhu culture of China.
Early pentagrams have been found on Sumerian pottery from Ur circa 3500 BCE, and the five-pointed star was at various times the symbol of
Ishtar
Inanna, also sux, 𒀭𒊩𒌆𒀭𒈾, nin-an-na, label=none is an ancient Mesopotamian goddess of love, war, and fertility. She is also associated with beauty, sex, divine justice, and political power. She was originally worshiped in Su ...
or
Marduk.
The pentagram was known to the
ancient Greeks
Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of cult ...
, with a depiction on a vase possibly dating back to the 7th century BC.
Pythagoreanism
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the ancient Greek colony of Kroton, ...
originated in the 6th century BC and used the pentagram as a symbol of mutual recognition, of wellbeing, and to recognize good deeds and charity.
From around 300-150 BCE the pentagram stood as the symbol of Jerusalem, marked by the 5 Hebrew letters ירשלם spelling its name.
The word ''Pentemychos'' ( lit. "five corners" or "five recesses") was the title of the
cosmogony of
Pherecydes of Syros
Pherecydes of Syros (; grc-gre, Φερεκύδης ὁ Σύριος; fl. 6th century BCE) was an Ancient Greek mythographer and proto- philosopher from the island of Syros. Little is known about his life and death. Some ancient testimonies cou ...
.
Here, the "five corners" are where the seeds of
Chronos
Chronos (; grc-gre, Χρόνος, , "time"), also spelled Khronos or Chronus, is a personification of time in pre-Socratic philosophy and later literature.
Chronos is frequently confused with, or perhaps consciously identified with, the Tita ...
are placed within the Earth in order for the
cosmos
The cosmos (, ) is another name for the Universe. Using the word ''cosmos'' implies viewing the universe as a complex and orderly system or entity.
The cosmos, and understandings of the reasons for its existence and significance, are studied in ...
to appear.
["the divine products of ]Chronos
Chronos (; grc-gre, Χρόνος, , "time"), also spelled Khronos or Chronus, is a personification of time in pre-Socratic philosophy and later literature.
Chronos is frequently confused with, or perhaps consciously identified with, the Tita ...
' seed, when disposed in five recesses, were called πεντέμυχος (Pentemychos)"
In
Neoplatonism
Neoplatonism is a strand of Platonic philosophy that emerged in the 3rd century AD against the background of Hellenistic philosophy and religion. The term does not encapsulate a set of ideas as much as a chain of thinkers. But there are some i ...
, the pentagram was said to have been used as a symbol or sign of recognition by the
Pythagoreans
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the ancient Greek colony of Kroton, ...
, who called the pentagram "health"
Western symbolism
Middle Ages
The pentagram was used in ancient times as a Christian symbol for the five
sense
A sense is a biological system used by an organism for sensation, the process of gathering information about the world through the detection of stimuli. (For example, in the human body, the brain which is part of the central nervous system re ...
s, or of the
five wounds of Christ
In Catholic tradition, the Five Holy Wounds, also known as the Five Sacred Wounds or the Five Precious Wounds, are the five piercing wounds that Jesus Christ suffered during his crucifixion. The wounds have been the focus of particular devotions, ...
. The pentagram plays an important symbolic role in the 14th-century English poem ''
Sir Gawain and the Green Knight
''Sir Gawain and the Green Knight'' is a late 14th-century chivalric romance in Middle English. The author is unknown; the title was given centuries later. It is one of the best-known Arthurian stories, with its plot combining two types of ...
'', in which the symbol decorates the shield of the hero,
Gawain
Gawain (), also known in many other forms and spellings, is a character in Arthurian legend, in which he is King Arthur's nephew and a Knight of the Round Table. The prototype of Gawain is mentioned under the name Gwalchmei in the earliest ...
. 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
Mary may refer to:
People
* Mary (name), a feminine given name (includes a list of people with the name)
Religious contexts
* New Testament people named Mary, overview article linking to many of those below
* Mary, mother of Jesus, also calle ...
had of Jesus, and exemplifies the five virtues of
knight
A knight is a person granted an honorary title of knighthood by a head of state (including the Pope) or representative for service to the monarch, the church or the country, especially in a military capacity. Knighthood finds origins in the Gr ...
hood, which are generosity, friendship, chastity, chivalry, and piety.
![Amiens Rose Nord 1](https://upload.wikimedia.org/wikipedia/commons/1/1d/Amiens_Rose_Nord_1.jpg)
The North rose of
Amiens cathedral
, image = 0 Amiens - Cathédrale Notre-Dame (1).JPG
, imagesize = 200px
, img capt = Amiens Cathedral
, pushpin map = France
, pushpin label position = below
, coordinates =
, country ...
(built in the 13th century) exhibits a pentagram-based motif. Some sources interpret the unusual downward-pointing star as symbolizing the Holy Spirit descending on people.
Renaissance
Heinrich Cornelius Agrippa
Heinrich Cornelius Agrippa von Nettesheim (; ; 14 September 1486 – 18 February 1535) was a German polymath, physician, legal scholar, soldier, theologian, and occult writer. Agrippa's '' Three Books of Occult Philosophy'' published in 1533 dre ...
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.
Romanticism
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 but controversial writer
Éliphas Lévi
Éliphas Lévi Zahed, born Alphonse Louis Constant (8 February 1810 – 31 May 1875), was a French esotericist, poet, and author of more than 20 books on magic, Kabbalah, alchemical studies, and occultism. He pursued an ecclesiastical career i ...
, known for believing that magic was a real science, had 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
Black magic, also known as dark magic, has traditionally referred to the use of supernatural powers or magic for evil and selfish purposes, specifically the seven magical arts prohibited by canon law, as expounded by Johannes Hartlieb in 14 ...
, 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 a 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."
File:Pentagram and human body (Agrippa).jpg, Man inscribed in a pentagram, from Heinrich Cornelius Agrippa
Heinrich Cornelius Agrippa von Nettesheim (; ; 14 September 1486 – 18 February 1535) was a German polymath, physician, legal scholar, soldier, theologian, and occult writer. Agrippa's '' Three Books of Occult Philosophy'' published in 1533 dre ...
's ''De occulta philosophia libri tres
''Three Books of Occult Philosophy'' (''De Occulta Philosophia libri III'') is Heinrich Cornelius Agrippa's study of occult philosophy, acknowledged as a significant contribution to the Renaissance philosophical discussion concerning the power ...
''. The five signs at the pentagram's vertices are astrological
Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Dif ...
.
File:Inverted pentacle.PNG, Another pentagram from Agrippa's book. This one has the Pythagorean letters inscribed around the circle.
File:Pentagram (Levi).jpg, The occultist and magician Éliphas Lévi
Éliphas Lévi Zahed, born Alphonse Louis Constant (8 February 1810 – 31 May 1875), was a French esotericist, poet, and author of more than 20 books on magic, Kabbalah, alchemical studies, and occultism. He pursued an ecclesiastical career i ...
's pentagram, which he considered to be a symbol of the microcosm, or human
The
apotropaic
Apotropaic magic (from Greek "to ward off") or protective magic is a type of magic intended to turn away harm or evil influences, as in deflecting misfortune or averting the evil eye. Apotropaic observances may also be practiced out of superst ...
use of the pentagram symbol in
German folklore
German folklore is the folk tradition which has developed in Germany over a number of centuries. Partially it can be also found in Austria.
Characteristics
It shares many characteristics with Nordic folklore and English folklore due to th ...
(called ''
Drudenfuss
In German folklore, a drude (german: Drude, plural, pl. ''Druden'') is a kind of malevolent nocturnal spirit (an elf (Alp (folklore), Alp) or kobold or a hag) associated with nightmares, prevalent especially in Southern Germany. Druden were said ...
'' in German) is referred to by
Goethe
Johann Wolfgang von Goethe (28 August 1749 – 22 March 1832) was a German poet, playwright, novelist, scientist, statesman, theatre director, and critic. His works include plays, poetry, literature, and aesthetic criticism, as well as tr ...
in ''
Faust
Faust is the protagonist of a classic German legend based on the historical Johann Georg Faust ( 1480–1540).
The erudite Faust is highly successful yet dissatisfied with his life, which leads him to make a pact with the Devil at a crossroa ...
'' (1808), where a pentagram prevents
Mephistopheles
Mephistopheles (, ), also known as Mephisto, is a demon featured in German folklore. He originally appeared in literature as the demon in the Faust legend, and he has since appeared in other works as a stock character (see: Mephistopheles i ...
from leaving a room (but did not prevent him from entering by the same way, as the outward pointing corner of the diagram happened to be imperfectly drawn):
East Asian symbolism
Wu Xing Wuxing may refer to:
Places in China Counties and districts
*Huzhou, formerly Wuxing County, Zhejiang, China
*Wuxing District (吴兴区), central district of Huzhou
Subdistricts (五星街道)
*Wuxing Subdistrict, Mudanjiang, in Dong'an District ...
() are the five phases, or five elements in
Taoists
Taoism (, ) or Daoism () refers to either a school of philosophical thought (道家; ''daojia'') or to a religion (道教; ''daojiao''), both of which share ideas and concepts of Chinese origin and emphasize living in harmony with the ''Tao ...
Chinese tradition. They are differentiated from the formative ancient
Japanese
Japanese may refer to:
* Something from or related to Japan, an island country in East Asia
* Japanese language, spoken mainly in Japan
* Japanese people, the ethnic group that identifies with Japan through ancestry or culture
** Japanese diaspor ...
or
Greek elements, due to their emphasis on cyclic transformations and change. The five phases are: Fire (火 ''huǒ''), Earth (土 ''tǔ''), Metal (金 ''jīn''), Water (水 ''shuǐ''), and Wood (木 ''mù''). The Wuxing is the fundamental philosophy and doctrine of
traditional Chinese Medicine
Traditional Chinese medicine (TCM) is an alternative medical practice drawn from traditional medicine in China. It has been described as "fraught with pseudoscience", with the majority of its treatments having no logical mechanism of acti ...
and
Acupuncture
Acupuncture is a form of alternative medicine and a component of traditional Chinese medicine (TCM) in which thin needles are inserted into the body. Acupuncture is a pseudoscience; the theories and practices of TCM are not based on scientif ...
.
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
Apotropaic magic (from Greek "to ward off") or protective magic is a type of magic intended to turn away harm or evil influences, as in deflecting misfortune or averting the evil eye. Apotropaic observances may also be practiced out of supers ...
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
The Hermetic Order of the Golden Dawn ( la, Ordo Hermeticus Aurorae Aureae), more commonly the Golden Dawn (), was a secret society devoted to the study and practice of occult Hermeticism and metaphysics during the late 19th and early 20th ...
developed the use of the pentagram in the
lesser banishing ritual of the pentagram
The Lesser Ritual of the Pentagram (or LRP) is a ceremonial magic ritual devised and used by the original order of the Golden Dawn that has become a mainstay in modern occultism. This ritual is considered by many to be a basic preliminary to any ...
, which is still used to this day by those who practice Golden Dawn-type magic.
Aleister Crowley
Aleister Crowley (; born Edward Alexander Crowley; 12 October 1875 – 1 December 1947) was an English occultist, ceremonial magician, poet, painter, novelist, and mountaineer. He founded the religion of Thelema, identifying himself as the pr ...
made use of the pentagram in his
Thelemic
Thelema () is a Western esoteric and occult social or spiritual philosophy and new religious movement founded in the early 1900s by Aleister Crowley (1875–1947), an English writer, mystic, occultist, and ceremonial magician. The word '' ...
system of
magick: an adverse or inverted pentagram represents the descent of spirit into matter, according to the interpretation of
Lon Milo DuQuette
Lon Milo DuQuette (born July 11, 1948), also known as Rabbi Lamed Ben Clifford and by his neo-Gnostic bishop title of Tau Lamed, is an American writer, lecturer, musician, and occultist, best known as an author who applies humor in the field of ...
. Crowley contradicted his old comrades in the
Hermetic Order of the Golden Dawn
The Hermetic Order of the Golden Dawn ( la, Ordo Hermeticus Aurorae Aureae), more commonly the Golden Dawn (), was a secret society devoted to the study and practice of occult Hermeticism and metaphysics during the late 19th and early 20th ...
, who, following Levi, considered this orientation of the symbol
evil
Evil, in a general sense, is defined as the opposite or absence of good. It can be an extremely broad concept, although in everyday usage it is often more narrowly used to talk about profound wickedness and against common good. It is general ...
and associated it with the triumph of matter over spirit.
Use in new religious movements
Baháʼí Faith
![Bab-Star-Tablet-Haykal](https://upload.wikimedia.org/wikipedia/commons/9/9b/Bab-Star-Tablet-Haykal.jpg)
The five-pointed star is a symbol of the
Baháʼí Faith
The Baháʼí Faith is a religion founded in the 19th century that teaches the essential worth of all religions and the unity of all people. Established by Baháʼu'lláh in the 19th century, it initially developed in Iran and parts of the ...
. In the Baháʼí Faith, the star is known as the ''Haykal'' ( ar, "temple"), and it was initiated and established by the
Báb
The Báb (b. ʿAlí Muḥammad; 20 October 1819 – 9 July 1850), was the messianic founder of Bábism, and one of the central figures of the Baháʼí Faith. He was a merchant from Shiraz in Qajar Iran who, in 1844 at the age of 25, claimed ...
. The Báb and
Bahá'u'lláh wrote various works in the form of a pentagram.
Moojan Momen
Moojan Momen is a retired physician and historian specializing in Baháʼí studies who has published numerous books and articles about the Baháʼí Faith and Islam, especially Shia Islam, including for Encyclopædia Iranica*
*
* the British L ...
(2019).
The Star Tablet of the Bab
'' British Library Blog.[Bayat, Mohamad Ghasem (2001). ]
An Introduction to the Súratu'l-Haykal (Discourse of The Temple)
' in Lights of Irfan, Book 2.
The Church of Jesus Christ of Latter-day Saints
The Church of Jesus Christ of Latter-day Saints
The Church of Jesus Christ of Latter-day Saints, informally known as the LDS Church or Mormon Church, is a nontrinitarian Christian church that considers itself to be the restoration of the original church founded by Jesus Christ. The ch ...
is theorized to have began using both upright and inverted five-pointed stars in
Temple
A temple (from the Latin ) is a building reserved for spiritual rituals and activities such as prayer and sacrifice. Religions which erect temples include Christianity (whose temples are typically called churches), Hinduism (whose temples ...
architecture, dating from the
Nauvoo Illinois Temple
The Nauvoo Illinois Temple is the 113th dedicated temple of the Church of Jesus Christ of Latter-day Saints (LDS Church). It is the third such temple that has been built in Illinois (the original Nauvoo Temple and Chicago Illinois Temple bein ...
dedicated on 30 April 1846. Other temples decorated with five-pointed stars in both orientations include the
Salt Lake Temple
The Salt Lake Temple is a temple of the Church of Jesus Christ of Latter-day Saints on Temple Square in Salt Lake City, Utah, United States. At , it is the largest Latter-day Saint temple by floor area. Dedicated in 1893, it is the sixth templ ...
and the
Logan Utah Temple
The Logan Utah Temple (formerly the Logan Temple) was completed in 1884, and is the fourth temple built by the Church of Jesus Christ of Latter-day Saints. Located in the city of Logan, Utah, it was the second temple built in the Rocky Mountain ...
. These usages come from the symbolism found in
Revelation
In religion and theology, revelation is the revealing or disclosing of some form of truth or knowledge through communication with a deity or other supernatural entity or entities.
Background
Inspiration – such as that bestowed by God on the ...
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
First or 1st is the ordinal form of the number one (#1).
First or 1st may also refer to:
*World record, specifically the first instance of a particular achievement
Arts and media Music
* 1$T, American rapper, singer-songwriter, DJ, and reco ...
right to
free exercise of religion
Freedom of religion or religious liberty is a principle that supports the freedom of an individual or community, in public or private, to manifest religion or belief in teaching, practice, worship, and observance. It also includes the freedom ...
.
The encircled pentagram (referred to as a
pentacle
A pentacle (also spelled and pronounced as ''pantacle'' in Thelema, following Aleister Crowley, though that spelling ultimately derived from Éliphas Lévi) "The Pantacle of Frater V. I. O." is a talisman that is used in magical evocation, and ...
by the plaintiffs) was added to the list of 38 approved religious symbols to be placed on the tombstones of fallen service members at
Arlington National Cemetery
Arlington National Cemetery is one of two national cemeteries run by the United States Army. Nearly 400,000 people are buried in its 639 acres (259 ha) in Arlington, Virginia. There are about 30 funerals conducted on weekdays and 7 held on Sa ...
on 24 April 2007. The decision was made following ten applications from families of fallen soldiers who practiced
Wicca
Wicca () is a modern Pagan religion. Scholars of religion categorise it as both a new religious movement and as part of the occultist stream of Western esotericism. It was developed in England during the first half of the 20th century and w ...
. The government paid the families to settle their pending lawsuits.
Other religious use
Satanism
The inverted pentagram is the symbol used for
Satanism, sometimes depicted with the
goat
The goat or domestic goat (''Capra hircus'') is a domesticated species of goat-antelope typically kept as livestock. It was domesticated from the wild goat (''C. aegagrus'') of Southwest Asia and Eastern Europe. The goat is a member of the a ...
's head of
Baphomet
Baphomet is a deity allegedly worshipped by the Knights Templar. that subsequently became incorporated into various occult and Western esoteric traditions. The name ''Baphomet'' appeared in trial transcripts for the Inquisition of the Knights ...
within it, which originated from the
Church of Satan
The Church of Satan is a religious organization dedicated to the religion of LaVeyan Satanism as codified in '' The Satanic Bible''. The Church of Satan was established at the Black House in San Francisco, California, on Walpurgisnacht, A ...
. In some depictions
the devil
Satan,, ; grc, ὁ σατανᾶς or , ; ar, شيطانالخَنَّاس , also known as the Devil, and sometimes also called Lucifer in Christianity, is an entity in the Abrahamic religions that seduces humans into sin or falsehood ...
is depicted, like Baphomet, as a goat, therefore the goat and goat's head is a significant symbol throughout Satanism. The pentagram is also used as the logo for
The Satanic Temple
The Satanic Temple, often abbreviated TST, is a nontheistic religious organization that is primarily based in the United States, with additional congregations in Canada, Australia, and the United Kingdom. Co-founded by Lucien Greaves, the or ...
, which also featured a depiction of Baphomet's head.
Serer religion
The five-pointed star is a symbol of the
Serer religion
The Serer religion, or ''a ƭat Roog'' ("the way of the Divine"), is the original religious beliefs, practices, and teachings of the Serer people of Senegal in West Africa. The Serer religion believes in a universal supreme deity called Roog ...
and the
Serer people of West Africa. Called ''Yoonir'' in
their language, it symbolizes the universe in the
Serer creation myth
The Serer creation myth is the traditional creation myth of the Serer people of Senegal, the Gambia and Mauritania. Many Serers who adhere to the tenets of the Serer religion believe these narratives to be sacred. Some aspects of Serer religious a ...
, and also represents the star
Sirius
Sirius is the brightest star in the night sky. Its name is derived from the Greek word , or , meaning 'glowing' or 'scorching'. The star is designated α Canis Majoris, Latinized to Alpha Canis Majoris, and abbreviated Alpha CM ...
.
Judaism
The pentagram has been used in
Judaism
Judaism ( he, ''Yahăḏūṯ'') is an Abrahamic, monotheistic, and ethnic religion comprising the collective religious, cultural, and legal tradition and civilization of the Jewish people. It has its roots as an organized religion in t ...
since at least 300BCE when it first was used as the stamp of
Jerusalem
Jerusalem (; he, יְרוּשָׁלַיִם ; ar, القُدس ) (combining the Biblical and common usage Arabic names); grc, Ἱερουσαλήμ/Ἰεροσόλυμα, Hierousalḗm/Hierosóluma; hy, Երուսաղեմ, Erusałēm. i ...
. It is used to represent justice, mercy, and wisdom.
Other modern use
*The pentagram is featured on the national flags of
Morocco
Morocco (),, ) officially the Kingdom of Morocco, is the westernmost country in the Maghreb region of North Africa. It overlooks the Mediterranean Sea to the north and the Atlantic Ocean to the west, and has land borders with Algeria t ...
(adopted 1915) and
Ethiopia
Ethiopia, , om, Itiyoophiyaa, so, Itoobiya, ti, ኢትዮጵያ, Ítiyop'iya, aa, Itiyoppiya officially the Federal Democratic Republic of Ethiopia, is a landlocked country in the Horn of Africa. It shares borders with Eritrea to the ...
(adopted 1996 and readopted 2009)
Image:Flag of Morocco.svg, Morocco
Morocco (),, ) officially the Kingdom of Morocco, is the westernmost country in the Maghreb region of North Africa. It overlooks the Mediterranean Sea to the north and the Atlantic Ocean to the west, and has land borders with Algeria t ...
's flag
Image:Flag of Ethiopia.svg, Ethiopia
Ethiopia, , om, Itiyoophiyaa, so, Itoobiya, ti, ኢትዮጵያ, Ítiyop'iya, aa, Itiyoppiya officially the Federal Democratic Republic of Ethiopia, is a landlocked country in the Horn of Africa. It shares borders with Eritrea to the ...
's flag
*The
Order of the Eastern Star
The Order of the Eastern Star is a Masonic appendant body open to both men and women. It was established in by lawyer and educator Rob Morris, a noted Freemason, and adopted and approved as an appendant body of the Masonic Fraternity in 187 ...
, an organization (established 1850) associated with
Freemasonry
Freemasonry or Masonry refers to fraternal organisations that trace their origins to the local guilds of stonemasons that, from the end of the 13th century, regulated the qualifications of stonemasons and their interaction with authorities ...
, 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 pointing down, but in a few, it is pointing up. Grand Chapter officers often have a pentagon inscribed around the star(the emblem shown here is from the Prince Hall Association).
Image:OrderEasternStar logo from saucer.jpg, Order of the Eastern Star
The Order of the Eastern Star is a Masonic appendant body open to both men and women. It was established in by lawyer and educator Rob Morris, a noted Freemason, and adopted and approved as an appendant body of the Masonic Fraternity in 187 ...
emblem
*A pentagram is featured on the flag of the
Dutch
Dutch commonly refers to:
* Something of, from, or related to the Netherlands
* Dutch people ()
* Dutch language ()
Dutch may also refer to:
Places
* Dutch, West Virginia, a community in the United States
* Pennsylvania Dutch Country
People E ...
city of
Haaksbergen
Haaksbergen () is a Municipalities of the Netherlands, municipality and a town in the eastern Netherlands, in the province of Overijssel, in the Twente region.
The ''Buurserbeek'' flows through the municipality of Haaksbergen.
Population centre ...
, as well on its coat of arms.
Image:Flag of Haaksbergen.svg, Flag of Haaksbergen
*A pentagram is featured on the flag of the
Japanese city of
Nagasaki
is the capital and the largest Cities of Japan, city of Nagasaki Prefecture on the island of Kyushu in Japan.
It became the sole Nanban trade, port used for trade with the Portuguese and Dutch during the 16th through 19th centuries. The Hi ...
, as well on its emblem.
Image:Flag of Nagasaki, Nagasaki.svg, Flag of Nagasaki
Geometry
![Stellamerlata](https://upload.wikimedia.org/wikipedia/commons/2/2a/Stellamerlata.gif)
The pentagram is the simplest
regular star polygon. The pentagram contains ten points (the five points of the star, and the five vertices of the inner pentagon) and fifteen line segments. It is represented by the
Schläfli symbol . 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
In mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, ...
of order 10.
It can be seen as a net of a
pentagonal pyramid
In geometry, a pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point (the apex). Like any pyramid, it is self- dual.
The ''regular'' pentagonal pyramid has a base that is a regu ...
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
In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of face i ...
, like this one with equally spaced vertices. A truncated retro-pentagram t, or a quasitruncation, produces a
decagram, .
Golden ratio
The
golden ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0,
where the Greek letter phi ( ...
, ''φ'' = (1 + ) / 2 ≈ 1.618, satisfying
:
:
:
plays 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 (a side of the pentagon in the pentagram's center) is ''φ''. As the four-color illustration shows:
:
The pentagram includes ten
isosceles triangles: five
acute
Acute may refer to:
Science and technology
* Acute angle
** Acute triangle
** Acute, a leaf shape in the glossary of leaf morphology
* Acute (medicine), a disease that it is of short duration and of recent onset.
** Acute toxicity, the adverse eff ...
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 triangle
Golden Triangle may refer to:
Places
Asia
* Golden Triangle (Southeast Asia), named for its opium production
* Golden Triangle (Yangtze), China, named for its rapid economic development
* Golden Triangle (India), comprising the popular tourist ...
s. The obtuse isosceles triangle highlighted via the colored lines in the illustration is a
golden gnomon
A golden triangle, also called a sublime triangle,
is an isosceles triangle in which the duplicated side is in the golden ratio \varphi to the base side:
: = \varphi = \approx 1.618~034~.
Angles
* The vertex angle is:
::\theta = 2\arcsin = 2\ar ...
.
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
John Napier of Merchiston (; 1 February 1550 – 4 April 1617), nicknamed Marvellous Merchiston, was a Scottish landowner known as a mathematician, physicist, and astronomer. He was the 8th Laird of Merchiston. His Latinized name was Ioan ...
in his 1614 book ''Mirifici logarithmorum canonis descriptio'' (Description of the wonderful rule of logarithms) along with rules that link the values of trigonometric functions of five parts of a right spherical triangle (two angles and three sides). It was studied later by
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
.
Three-dimensional figures
Several
polyhedra
In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices.
A convex polyhedron is the convex hull of finitely many points, not all on ...
incorporate pentagrams:
Image:Pentagrammic prism.png, Pentagrammic prism
In geometry, the pentagrammic prism is one of an infinite set of nonconvex prisms formed by square sides and two regular star polygon caps, in this case two pentagrams.
It is a special case of a right prism with a pentagram as base, which in gene ...
Image:Pentagrammic antiprism.png, Pentagrammic antiprism
In geometry, the pentagrammic antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams.
It has 12 faces, 20 edges and 10 vertices. This polyhedron is iden ...
Image:Pentagrammic crossed antiprism.png, Pentagrammic crossed-antiprism
In geometry, the pentagrammic crossed-antiprism is one in an infinite set of nonconvex antiprisms formed by triangle sides and two regular star polygon caps, in this case two pentagrams.
It differs from the pentagrammic antiprism by having oppo ...
Image:Small_stellated_dodecahedron.png, Small stellated dodecahedron
In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol . It is one of four nonconvex regular polyhedra. It is composed of 12 pentagrammic faces, with five pentagrams meeti ...
Image:Great_stellated_dodecahedron.png, Great stellated dodecahedron
In geometry, the great stellated dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol . It is one of four nonconvex regular polyhedra.
It is composed of 12 intersecting pentagrammic faces, with three pentagrams meeting at each ve ...
Image:Small ditrigonal icosidodecahedron.png, Small ditrigonal icosidodecahedron
Image:Dodecadodecahedron.png, Dodecadodecahedron
In geometry, the dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U36. It is the rectification of the great dodecahedron (and that of its dual, the small stellated dodecahedron). It was discovered independently by , and .
The ed ...
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
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
Definitions
Take some corner or vertex of a polyhedron. Mark a point somewhere along each connected edge. Draw line ...
elements.
Pentagram of Venus
![Venus geocentric orbit curve simplified Line (pentagram)](https://upload.wikimedia.org/wikipedia/commons/8/89/Venus_geocentric_orbit_curve_simplified_Line_%28pentagram%29.svg)
The pentagram of Venus is the apparent path of the
planet
A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
Venus
Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never f ...
as observed from
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
. Successive
inferior conjunction
In astronomy, a conjunction occurs when two astronomical objects or spacecraft have either the same right ascension or the same ecliptic longitude, usually as observed from Earth.
When two objects always appear close to the ecliptic—such as t ...
s of Venus repeat with an
orbital resonance
In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly, this relationsh ...
of approximately 13:8—that is, Venus orbits the
Sun
The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
approximately 13 times for every eight orbits of Earth—shifting 144° at each inferior conjunction.
The tips of the five loops at the center of the figure have the same geometric relationship to one another as the five
vertices, or points, of a pentagram, and each group of five
intersections
equidistant
A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.
In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is the ...
from the figure's center have the same geometric relationship.
In computer systems
The pentagram has these
Unicode
Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, wh ...
code points that enable them to be included in documents:
*
*
*
*
See also
*
*
*
*
*
*
*
*
*
Pentachoron
In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol . It is a 5-vertex four-dimensional object bounded by five tetrahedral cells. It is also known as a C5, pentachoron, pentatope, pentahedroid, or tetrahedral pyramid. It is ...
– the 4-
simplex
*
*
*
*
*
*
*
*
*
References
Bibliography
*
*
*
*
*
*
External links
*
The Pythagorean Pentaclefrom the Biblioteca Arcana.
{{Authority control
Christian symbols
Golden ratio
Magic symbols
National symbols of Ethiopia
National symbols of Morocco
5 (number)
Pythagorean symbols
Religious symbols
05
Serer religious symbols
Wicca