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Pi
ELEMENTS: The four basic elements to many pagans are earth, water, air (wind or spirit) and fire. Many consider the first two passive and feminine - and the last two active and masculine. In Wiccan or Native American rituals, the "quartered circle" (also the Medicine Wheel) represents a "sacred space" or the sacred earth. The four lines may represent the spirits of the four primary directions or the spirits of the earth, water, wind and fire.
ALCHEMY: This simple 17th century "sign" illustrates the blending of geometric shapes, elemental symbols and astrological signs. Each part representing the various "elements" and forces needed for magical work in the quest for physical transformation and spiritual illumination and immortality. Many medieval alchemists based their philosophies on mystical traditions rooted in the Kabbala (Jewish mysticism), Hermetic magic and the occult practices of ancient civilizations such as Egypt and China. See Philosopher's stone and phoenix.
CIRCLE (sacred hoop, ring): An ancient and universal symbol of unity, wholeness, infinity, the goddess, and female power. To earth-centered religions throughout history as well as to many contemporary pagans, it represents the feminine spirit or force, the cosmos or a spiritualized Mother Earth, and a sacred space. (See next item) Gnostic traditions linked the unbroken circle to the "world serpent" forming a circle as it eats its own tail. (See serpent)
SUN and SUN SIGN : The sun was worshipped as a personified, life-giving deity in Babylonian, Egyptian, Greek, Roman, and other major civilizations of history. The more common symbol is the familiar face in the center of the sun's rays. (This will be explained in our report on the Teletubbies. (See sun symbol below the picture of the Eye of Horus) A dot or point in the center of a circle symbolizes the blending of male and female forces. (See air, which also represents spirit, among the symbols for Elements) Hindus call the midpoint in a circle the bindu - the spark of (masculine) life within the cosmic womb.
This article is about the mathematical constant. For the Greek letter, see pi (letter). For other uses, see Pi (disambiguation).
When a circle's diameter is 1, its circumference is π.
List of numbers – Irrational numbers
ζ(3) – √2 – √3 – √5 – φ – α – e – π – δ
Binary
Hexadecimal 3.243F6A8885A308D31319…
Continued fraction 3 + \cfrac{1}{7 + \cfrac{1}{15 + \cfrac{1}{1 + \cfrac{1}{292 + \ddots}}}}
Note that this continued fraction is not periodic.
Pi or π is a mathematical constant whose value is the ratio of any circle's circumference to its diameter in Euclidean space; this is the same value as the ratio of a circle's area to the square of its radius. It is approximately equal to 3.14159 in the usual decimal notation (see the table for its representation in some other bases). π is one of the most important mathematical and physical constants: many formulae from mathematics, science, and engineering involve π.[1]
π is an irrational number, which means that its value cannot be expressed exactly as a fraction m/n, where m and n are integers. Consequently, its decimal representation never ends or repeats. It is also a transcendental number, which means that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) can be equal to its value; proving this was a late achievement in mathematical history and a significant result of 19th century German mathematics. Throughout the history of mathematics, there has been much effort to determine π more accurately and to understand its nature; fascination with the number has even carried over into non-mathematical culture.
The Greek letter π, often spelled out pi in text, was adopted for the number from the Greek word for perimeter "περίμετρος", first by William Jones in 1707, and popularized by Leonhard Euler in 1737.[2] The constant is occasionally also referred to as the circular constant, Archimedes' constant (not to be confused with an Archimedes number), or Ludolph's number (from a German mathematician whose efforts to calculate more of its digits became famous).
Fundamentals
The letter π
Main article: pi (letter)
Lower-case π is used to symbolize the constant.
The name of the Greek letter π is pi, and this spelling is commonly used in typographical contexts when the Greek letter is not available, or its usage could be problematic. It is not normally capitalised (Π) even at the beginning of a sentence. When referring to this constant, the symbol π is always pronounced like "pie" in English, which is the conventional English pronunciation of the Greek letter. In Greek, the name of this letter is pronounced /pi/.
The constant is named "π" because "π" is the first letter of the Greek words περιφέρεια (periphery) and περίμετρος (perimeter), probably referring to its use in the formula to find the circumference, or perimeter, of a circle. π is Unicode character U+03C0 ("Greek small letter pi").=
Definition
Circumference = π × diameter
In Euclidean plane geometry, π is defined as the ratio of a circle's circumference to its diameter:
\pi = \frac{C}{d}.
The ratio C/d is constant, regardless of a circle's size. For example, if a circle has twice the diameter d of another circle it will also have twice the circumference C, preserving the ratio C/d.
Area of the circle = π × area of the shaded square
Alternatively π can be also defined as the ratio of a circle's area (A) to the area of a square whose side is equal to the radius:
\pi = \frac{A}{r^2}.
These definitions depend on results of Euclidean geometry, such as the fact that all circles are similar. This can be considered a problem when π occurs in areas of mathematics that otherwise do not involve geometry. For this reason, mathematicians often prefer to define π without reference to geometry, instead selecting one of its analytic properties as a definition. A common choice is to define π as twice the smallest positive x for which cos(x) = 0.[6] The formulas below illustrate other (equivalent) definitions.
NOTICE HOW THE EYE OF HORUS AND MATHEMATICAL Pi SYMBOLS BOTH FAVOR EACH OTHER
HORUS
Horus was an ancient Egyptian sky god known as Re or Ra and was pictured in the form of a falcon. The right eye represents a Peregrine Falcon's eye and the markings around it, that includes the "teardrop" marking sometimes found below the eye. As the wedjet (also udjat or utchat), it also represented the sun, and was associated with Horus' mother, Isis, and with wedjet another goddess, as well as the sun deity Ra (Re). The mirror image, or left eye, sometimes represented the moon and the god Tehuti (Thoth). wedjet - Eye of Horus in hieroglyphs.
Eye of Horus, a hieroglyph and symbol
Seven different hieroglyphs are used to represent the "eye"-(human body parts). One is the common usage of the verb: to do, make, or perform. The other frequently used hieroglyph is the Wedjat, a sacred eye symbol that gives a mummy the ability "to see again", called the Eye of Horus after his cult rose to prominence as the son of Hathor.
In geometry, an equilateral triangle is a triangle in which all three sides are equal. In traditional or Euclidean geometry, equilateral triangles are also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. They are regular polygons, and can therefore also be referred to as regular triangles.
Hexagram
For other uses, see Hexagram (disambiguation).
For symbols used in the I Ching, see Hexagram (I Ching)
For a Jewish symbol, see Star of David.
For Occultic symbol see Unicursal hexagram
The regular hexagram 2{3}.
The unicursal hexagram is an irregular hexagram.
A hexagram is a six-pointed geometric star figure, {6/2} or 2{3}, the compound of two equilateral triangles. The intersection is a regular hexagon.
While generally recognized as a symbol of Jewish identity it is used also in other historical, religious and cultural contexts, for example in Islam, and Eastern Religions as well as in Occultism.
In mathematics, the G2 root system is in the form of a hexagram.
Origins and shape
The hexagram is a mandala symbol called satkona yantra or sadkona yantra found on ancient South Indian Hindu temples built thousands of years ago [1][2][3]. It symbolizes the nara-narayana, or perfect meditative state of balance achieved between Man and God, and if maintained, results in "moksha," or "nirvana" (release from the bounds of the earthly world and its material trappings).
Another theory about the origin of the shape is that it is simply 2 of the 3 letters in the name David: in its Hebrew spelling, David is transliterated as 'D-W-D'. In Biblical Hebrew, the letter 'D' (Dalet) was written in a form much like a triangle, similar to the Greek letter "Delta" (Δ). The symbol may have been a simple family crest formed by flipping and juxtaposing the two most prominent letters in the name. The letter "W" in this case could reference the compositing operation of the two Deltas.
Some researchers have theorized that the hexagram represents the astrological chart at the time of David's birth or anointment as king. The hexagram is also known as the "King's Star" in astrological circles.
In antique papyri, pentagrams, together with stars and other signs, are frequently found on amulets bearing the Jewish names of God, and used to guard against fever and other diseases. Curiously the hexagram is not found among these signs. In the great magic papyrus[citation needed](Wessely, l.c. pp. 31, 112) at Paris and London there are twenty-two signs side by side, and a circle with twelve signs, but neither a pentagram nor a hexagram.
Therefore, the syncretism of Hellenistic, Jewish, and Coptic influences probably did not originate the symbol.
It is also possible that as a simple geometric shape, like for example the triangle, circle, or square, the hexagram has been created by various different peoples with no connection to one another.
Usage by Jews
Main article: Star of David
The Star of David in the oldest surviving complete copy of the Masoretic text, the Leningrad Codex, dated 1008.
Equilateral triangle
Magen David is a generally recognized symbol of Judaism and Jewish identity and is also known colloquially as the Jewish Star or "Star of David". Its usage as a sign of Jewish identity began in the Middle Ages, though its religious usage began earlier, with the current earliest archeological evidence being a stone bearing the shield from the arch of a 3-4th century synagogue in the Galilee [1]. A more enduring symbol of Judaism, the menorah, has been in use since BCE.
Usage by Christians
The hexagram may be found in some Churches and stained-glass windows. An example of this is one embedded in the ceiling of the Washington National Cathedral. Because a similar-looking sign called the encircled pentagram is used in occultism, it was not used in church architecture until Christian architects, both Protestant and Catholic, began to accept the notion that the Star of David is an old Jewish sign.[citation needed] In Christianity it is often called the star of creation.
The Bible makes no direct mention of the Star of David, however, the Catechism of the Catholic Church of the year 528 refers to the star which led the Magi to Christ as "the Star of David". In the context, the phrase most likely meant "the star of the king of Israel" rather than the double triangle-shaped symbol used today.[citation needed]
Latter-day Saints (Mormons)
Star of David on the Salt Lake Assembly Hall
Main article: Mormonism and Judaism
The Star of David is also used less prominently by The Church of Jesus Christ of Latter-day Saints, chiefly in architecture. It symbolizes the Tribes of Israel and friendship and their claimed affinity towards the Jewish people. Additionally, some independent LDS theologians such as LDS Daniel Rona have further suggested the possibility that the Star of David was actually modeled after the Urim and Thummim, but this is not official doctrine of the Church.
Rastafari
A black star of David is used to identify the black population, in Africa or otherwise, with one of the Tribes of Israel.
Zion Christian Church
A Star of David badge is worn by members of the Zion Christian Church, which has over three million members and is the largest African Initiated Church in southern Africa.[citation needed]
Usage by Muslims
Hexagram in Islamic stonework at the Qutb complex, Delhi, India.
The symbol is known in Arabic as نجمة داوود, Najmat Dāwūd (Star of David) or خاتم سليمان Khātem Sulaymān (Seal of Solomon), but "Seal of Solomon" may also refer to a pentagram or a species of plant.
In various places in the Qur'an, it is written that David and King Solomon (Arabic, Suliman or Sulayman) were prophets and kings and therefore they are revered figures by Muslims. The Medieval pre-Ottoman Anatolian Turkish Beyliks of the Karamanoğlu and Candaroğlu used the star on their flag. Even today, the star can be found in mosques and on other Arabic and Islamic artifacts.
The Babylonian Talmud contains a legend about King Solomon being kidnapped by Ashmedai, the king of demons. He succeeded in kidnapping the king by stealing his "seal of Solomon", although according to the Talmud this seal was simply a metal coin with Hebrew letters meaning the name of God, inscribed on it. It is possible that the seal was altered in the Arab tales. The first appearance of the symbol in Jewish scriptures was in oriental Kabbalistic writings, so it is possible that it was an alteration of the pentagram under Arab influence.
Professor Gershom Sholem theorizes[citation needed] that the "Star of David" originates in the writings of Aristotle, who used triangles in different positions to indicate the different basic elements. The superposed triangles thus represented combinations of those elements. From Aristotle's writings those symbols made their ways into early, pre-Muslim Arab literature.
Usage by Hinduism and Eastern Religions
Diagram showing the two mystic syllables Om and Hrim
Six pointed stars have also been found in cosmological diagrams in Hinduism, Buddhism, and Jainism. The reasons behind this symbol's common appearance in Indic religions and the West are lost in the mists of antiquity. One possibility is that they have a common origin. The other possibility is that artists and religious people from several cultures independently created the Star of David shape, which after all is a relatively simple and obvious geometric design.
Within Indic lore, the shape is generally understood to consist of two triangles--one pointed up and the other down--locked in harmonious embrace. The two components are called 'Om' and the 'Hrim' in Sanskrit, and symbolize man's position between earth and sky. The downward triangle symbolizes Shakti, the sacred embodiment of femininity, and the upward triangle symbolizes Shiva, or Agni Tattva, representing the focused aspects of masculinity. The mystical union of the two triangles represents Creation, occurring through the divine union of male and female. The two locked triangles are also known as 'Shanmukha' - the six-faced, representing the six faces of Shiva & Shakti's progeny Kartikeya. This symbol is also a part of several yantras and has deep significance in Hindu ritual worship and mythology.
In Buddhism, some old versions of the Bardo Thodol, also known as The Tibetan Book of the Dead, contain a hexagram with a Swastika inside. It was made up by the publishers for this particular publication. In Tibetan, it is called the 'origin of phenomenon' (chos-kyi 'byung-gnas). It is especially connected with Vajrayogini, and forms the center part of Her mandala. In reality, it is in three dimensions, not two, although it may be portrayed either way.
Usage in heraldry
In heraldry and to a lesser extent vexillology a "star" is assumed to be a six-pointed figure, like a Star of David, but not hollow and with radiating wavy lines. The more familiar five-pointed star shape is known as a mullet or molet.
Usage in theosophy
The Star of David is used in the seal and the emblem of the Theosophical Society (founded in 1875). Although it is more pronounced, it is used along with other religious symbols. These include the Swastika, the Ankh, the Aum, and the Ouroborus. The star of David is also known as the Seal of Solomon that was its original name until around 50 years ago.
Usage in Raelism
The International Raelian Movement (IRM) uses a hexagram. The root of this symbol, according to the founder of the IRM, Rael, can be attributed to its use by genetic engineers from extrasolar planets who are allegedly the same entities referred to as Elohim. According to Rael, these space travellers came to Earth and synthesized life from non-living matter in 7 laboratory bases which contained the symbol.
Some meanings which involve particular variations of this symbol are supported by the IRM, such as "well being" (where "swastika" means "well being" in Sanskrit) and "infinity in time" (as Hindus see the swastika as a symbol for "eternal" cycles). In Raelism, the upper and lower triangles represent "as above, so below", which refers to either the likeness between the creators' past and created's future or the repeating fractal hierarchical structure in the universe. "As above so below" is also well known in Wicca as the last statement of an invocation or ritual in order to bring the change of events from the upper world to the lower world (our world).
The IRM has long-term plans to build a temple complex or embassy that would, at around the time of a Technological Singularity, and before 2035, support the arrival of prophets of major and some minor religions after a spectacular descent from an interstellar journey. Rael (or the Elohim, as Rael would put it) requires that the embassy contain the "symbol of the Elohim". The symbol initially used by the Raelian movement was the source of considerable controversy linked to a proposal to build the Raelian embassy in Israel since it resembled a hexagram with the image of a Swastika embedded in its center.
Usage in occultism
The hexagram, like the pentagram, was and is used in practices of the occult and is attributed to the 7 'old' planets outlined in astrology.
The six-pointed star is commonly used both as a talisman and for conjuring spirits in the practice of witchcraft. In the Book The History and Practice of Magic, Vol. 2, the six-pointed star is called the talisman of Saturn and it is also referred to as the Seal of Solomon.[1] Details are given in this book on how to make these symbols and the materials to use.
Dr. John Dee, the court astrologist of Queen Elizabeth I, in his book Hieroglyphic Monad, includes the following quote:
"'Mahatma Letters,' page 345: 'The double triangle viewed by the Jewish Kabbalists as Solomon's Seal is...the Sri--Antana of the Archaic Aryan Temple, the Mystery of Mysteries, a geometrical synthesis of the whole occult doctrine. The two interlaced triangles are the Buddham-Gums of Creation. They contain the 'squaring of the Circle,' the 'Philosophers' Stone,' the great problems of Life and Death--the mystery of Evil. The Chela who can explain this sign from every one of its aspects is virtually an Adept.'"[2]
Usage in Freemasonry
From the Encyclopedia of Freemasonry:
"The interlacing triangles or deltas symbolize the union of the two principles or forces, the active and passive, male and female, pervading the universe... The two triangles, one white and the other black, interlacing, typify the mingling of apparent opposites in nature, darkness and light, error and truth, ignorance and wisdom, evil and good, throughout human life."[3]
The hexagram is featured within and on the outside of many Masonic temples as a decoration. The hexagram, one of the world's most ancient symbols, may have been found within the structures of King Solomon's temple, from which Freemasons are inspired in their philosphies and studies.
