MYSTICAL SYMBOLS

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Mystic Symbols

Religious symbolism

Astrology and alchemy

Aum/Om syllable (sound symbol)

The most commonly used symbol is the nine-pointed star. No particular design is more desirable than others, as long as it has 9 points.

Conch shell

Crescent

Crucifix

Crux Gemmata

Dharmacakra

Seated Buddha, Gandhara, 1st-2nd century CE. Tokyo National Museum.

Footprint of the Buddha. 1st century, Gandhara, with depictions of the triratna and the Dharmacakra.

Divided line of Plato

Eight auspicious symbols of Tibetan Buddhism

Ek Onkar

Endless knot

Enneagram

D10

Flower of Life

Globus cruciger

Golden spiral [edit] H

Two quantities (positive numbers) a and b are said to be in the golden ratio $\varphi$ if

$\frac{a+b}{a} = \frac{a}{b} = \varphi\,.$

This equation unambiguously defines $\varphi\,$ .

The right equation shows that $a=b\varphi$ , which can be substituted in the left part, giving

$\frac{b\varphi+b}{b\varphi}=\frac{b\varphi}{b}\,.$

Canceling b yields

$\frac{\varphi+1}{\varphi}=\varphi.$

Multiplying both sides by $\varphi$ and rearranging terms leads to:

$\varphi^2 - \varphi - 1 = 0.$

The only positive solution to this quadratic equation is

$\varphi = \frac{1 + \sqrt{5}}{2} \approx 1.618\,033\,989\,.$

Holy Grail

[edit] I

Ichthys

Infinity

[edit] J

[edit] K

Khamsa/Hamesh Hand/Hand of Fatima

[edit] L

[edit] M

edit] N

Numbers as religious symbols

[edit] O

[edit] P

[edit] R

[edit] S

Shield of the Trinity

[edit] T

Triratna/Three Jewels

[edit] U

[edit] V

Vande matram [edit] W

Winged Self [edit] Y

[edit] Political symbols

Anarchist symbolism (including the circled "A")

Dove (used by the UK Liberal Democrats party)

Fasces (as a symbol of Fascism)

Hammer and sickle (as a symbol of Communism)

Nihilism Symbol (the nautica star or backwards "N")

Peace symbol

Pentacle of protection Paganism

Red rose (used by the UK Labour party)

Star (as a symbol of Communism)

Swastika (as used by Nazis and neo-Nazis)

Torch (used by the UK Conservative Party)

List of political party symbols in India

Elephant (used as Republican symbol in America)

Donkey (used as Democrat symbol in America)

Scientific and engineering symbols

Mathematical symbols

@ (At) Accounting Sign

Astronomical symbols

Chemical element symbols

Electrical symbols & electronic symbols [1]

Hazard warning symbols

Alchemical symbols

[edit] Heraldic symbols

[edit] Vexillological symbols (Flags)

Main article: Vexillological symbol

[edit] Pictograms

Main article: Pictogram

[edit] Other symbols

Chess symbols in Unicode

Japanese map symbols

Japanese typographic symbols

Olympic five rings symbol

Smiley Face

Period-after-opening symbol (on cosmetics as 6M, 12M, 18M etc.)

Agnus

Vicit agnus noster, eum sequamur ("Our Lamb has conquered, let us follow him.").

Agnus Dei, qui tollis peccata mundi, miserere nobis.

Agnus Dei, qui tollis peccata mundi, dona nobis pacem.

Lamb of God, who takes away the sins of the world, have mercy on us.

Lamb of God, who takes away the sins of the world, grant us peace. Historically, in Requiem Masses, the first two invocations ended with "dona eis requiem" (give them rest) instead of "miserere nobis", and the last with "dona eis requiem sempiternam" (give them rest eternal).

The priest again uses the phrase "Lamb of God", in a more complete quotation from John 1:29, when displaying the consecrated Host (or the Host and Chalice) to the people before giving them Holy Communion. He says: "Ecce Agnus Dei, ecce qui tollit peccata mundi" ("Behold the Lamb of God, behold him who taketh away the sins of the world.")

Libera meLibera me, Domine, de morte aeterna, in die illa tremenda, quando coeli movendi sunt et terra, dum veneris judicare saeculum per ignem. Tremens factus sum ego et timeo, dum discussio venerit atque ventura ira. Dies illa, dies irae, calamitatis, et miseriae, dies magna et amara valde. Requiem aeternam dona eis, Domine: et lux perpetua luceat eis.

("Deliver me, O Lord, from eternal death on that fearful day, when the heavens and the earth are moved, when you will come to judge the world with fire. I am made to tremble and I fear, because of the judgment that will come, and also the coming wrath. That day, day of wrath, calamity, and misery, day of great and exceeding bitterness. Grant them eternal rest, O Lord, and let perpetual light shine upon them.")

In paradisum

In paradisum deducant te Angeli; in tuo adventu suscipiant te martyres, et perducant te in civitatem sanctam Jerusalem. Chorus angelorum te suscipiat, et cum Lazaro quondam paupere aeternam habeas requiem. ("May angels lead you into Paradise; may the martyrs receive you at your coming and lead you to the holy city of Jerusalem. May a choir of angels receive you, and with Lazarus, who once was poor, may you have eternal rest.")

Pie Jesu

The Pie Jesu combines and paraphrases of the final verse of the Dies irae and the Agnus Dei.

Pie Jesu Domine, dona eis requiem. Dona eis requiem sempiternam.

("O sweet Lord Jesus, grant them rest; grant them everlasting rest.")

Anglican burial service

The Anglican Book of Common Prayer contains seven texts which are collectively known as "funeral sentences"; several composers have written settings of these seven texts, which are generally known collectively as a "burial service." Composers who have set the Anglican burial service to music include Thomas Morley, Orlando Gibbons, and Henry Purcell. The text of these seven sentences, from the 1662 Book of Common Prayer, is:

I am the resurrection and the life, saith the Lord: he that believeth in me, though he were dead, yet shall he live: and whosoever liveth and believeth in me shall never die.
I know that my Redeemer liveth, and that he shalt stand at the latter day upon the earth. And though after my skin worms destroy this body, yet in my flesh shall I see God: whom I shall see for myself, and mine eyes shall behold, and not another.
We brought nothing into this world, and it is certain we can carry nothing out. The Lord gave, and the Lord hath taken away; blessed be the Name of the Lord.
Man that is born of a woman hath but a short time to live, and is full of misery. He cometh up, and is cut down, like a flower; he fleeth as it were a shadow, and never continueth in one stay.
In the midst of life we are in death: of whom may we seek for succour, but of thee, O Lord, who for our sins art justly displeased? Yet, O Lord God most holy, O Lord most mighty, O holy and most merciful Saviour, deliver us not into the bitter pains of eternal death.
Thou knowest, Lord, the secrets of our hearts; shut not thy merciful ears to our prayer; but spare us, Lord most holy, O God most mighty, O holy and merciful Saviour, thou most worthy judge eternal, suffer us not, at our last hour, for any pains of death, to fall from thee.
I heard a voice from heaven, saying unto me, Write, From henceforth blessed are the dead which die in the Lord: even so saith the Spirit: for they rest from their labours.

Alchemical symbols in Torbern Bergman's 1775 Dissertation on Elective Affinities.

Alchemical symbol

http://en.wikipedia.org/wiki/Fire_%28classical_element%29

Chinese

Wood (木) | Fire (火)
Earth (土) |
Metal (金) | Water (水)

Japanese

Earth (地) | Water (水) | Fire (火) |
Air / Wind (風) | Void / Sky / Heaven (空)

Hinduism and Buddhism

Vayu / Pavan — Air / Wind
Agni / Tejas — Fire
Akasha — Aether
Prithvi / Bhumi — Earth
Ap / Jala — Water

Tetrahedron

http://en.wikipedia.org/wiki/Tetrahedron

(Click here for rotating model)

Type	Platonic solid
Elements	F = 4, E = 6, V = 4 (χ = 2)
Faces by sides	4{3}
Schläfli symbol	{3,3}
Wythoff symbol	3 \| 2 3
Coxeter-Dynkin
Symmetry	T_d
References	U₀₁, C₁₅, W₁
Properties	Regular convex deltahedron
Dihedral angle	70.528779° = arccos(1/3)

Compound of ten tetrahedra

Compound of five tetrahedra

Two tetrahedra in a cube

Truncated tetrahedron

3.3.3
(Vertex figure)

Self-dual
(dual polyhedron)

http://en.wikipedia.org/wiki/Fire_%28classical_element%29

Prometheus

http://en.wikipedia.org/wiki/Prometheus

Prométhée enchaîné (Prometheus Bound) by Nicolas-Sébastien Adam (1762)

http://en.wikipedia.org/wiki/Epimetheus_%28mythology%29

Epimetheus

http://en.wikipedia.org/wiki/Pandora_%28mythology%29

http://en.wikipedia.org/wiki/Alchemical_symbol

Astrological

Gold dominated by Sol ☉ ☼ ( )

Silver dominated by Luna ☽ ( )

Copper dominated by Venus ♀ (also: )

Iron dominated by Mars ♂ ( )

Tin dominated by Jupiter ♃ ( )

Mercury (Quicksilver) dominated by Mercury ☿ ( )

Lead dominated by Saturn ♄ ( )

Mundane Elements

Antimony ♁

Magnesium ⊛

Platinum ☾ ☉

Alchemical Compounds

Aqua Fortis A.F.

Aqua Regia A.R.

Spirit of Wine S.V.

Amalgama*Cinnabar (Mercury sulfide)

12 Core Alchemical processes

The 12 Alchemical processes are considered to be the basis of modern Chemical processes. Each of these processes is "dominated" or "ruled" by one of the 12 Zodiac signs.

Decomposition through Calcination (Aries )

Decomposition through Digestion (Leo )

Decomposition through Fermentation/Putrefaction (Capricorn )

Modification through Congelation/Coagulation (Taurus )

Modification through Fixation (Gemini )

Modification through Ceration (Sagittarius )

Separation through Distillation (Virgo )

Separation through Sublimation (Libra )

Separation through Filtration (Scorpio )

Union through Solution (Cancer )

Union through Multiplication (Aquarius )

Union through Projection (Pisces )

The word Allāh is always written without an alif to spell the ā vowel. This is because the spelling was settled before Arabic spelling started habitually using alif to spell ā. However, in vocalized spelling, a small diacritic alif is added on top of the shaddah to indicate the pronunciation.

One exception may be in the pre-Islamic Zabad inscription, where it ends with an ambiguous sign that may be a lone-standing h with a lengthened start, or may be a non-standard conjoined l-h:-

as الاه : This reading would be Allāh spelled phonetically with alif for the ā.

as الاله : This reading would be Al-'ilāh = "the god", uncontracted, by older spelling practice without alif for ā.

The form in the inscription is shown at.^[6]

Unicode has a glyph reserved for Allāh, ﷲ‎ = U+FDF2, which can be combined with an alif to yield the post-consonantal form, اﷲ‎, as opposed to the full spelling alif-lām-lām-hā الله‎ which may be rendered slightly differently, in particular featuring a diacritic alif on top of the shadda. In this, Unicode imitates traditional Arabic typesetting, which also frequently featured special llāh types.

In Abjad numerals, numeric value of الله is 66.

http://en.wikipedia.org/wiki/Ankh

- Aries (The Ram)(cardinal, fire, personal): Keyword: "I am". Assertive, individualistic, impulsive, energetic, headstrong, pioneering, leader, competitive, action-oriented, aggressive, intemperate, violent, fiery, extreme, arrogant, quick, passionate, powerful, loner, freedom-loving. Part of body: head/skull

- Taurus (The Bull) (fixed, earth, personal): Keyword: "I have". Resourceful, thorough, devotedly, patient, indulgent, sensual, affectionate, possessive, cautious, acquisitive, musical, artistic, stubborn, solid, earthly, strong, sturdy, slow, kind, just. Part of body: throat/neck

- Gemini (The Twins)(mutable, air, personal): Keyword: "I think". Logical, inquisitive, lively, active, curious, multi-tasking, talkative, sociable, duality, mercurial, whimsical, restless, informed. Part of body: hands/lungs,

- Cancer (The Crab) (cardinal, water, personal): Keyword: "I feel". Protective, sensitive, clinging, tenacious, family and home oriented, helpful, nurturing, moody, watery, emotional, crabby, loving. Part of body: stomach/breasts

- Leo (The Lion)(fixed, fire, social): Keyword: "I will". Generous, proud, theatrical, passionate, bossy, loves attention, dramatic, independent, noble, creative, leader, egotistic, sunny, bright, kingly, powerful. Part of body: heart/back

- Virgo (The Virgin) (mutable, earth, social): Keyword: "I analyze". Practical, efficient, critical, work and service oriented, common sense, modest, health conscious, mentally active, fussy, helpful, loving, flexible. Part of body: intestines/digestion

- Libra (The Scales) (cardinal, air, social): Keyword: "I balance". Co-operative, fair, lazy, partnerships, balance, grace, charm, debative, open-minded, social, ideas. Part of body: kidneys/lumbar

- Scorpio (The Scorpion) (fixed, water, social): Keyword: "I desire". Passionate, secretive, powerful, keenly perceptive, deep, complex, analytical, inquisitive, resourceful, evolutionary, magnetic, intense, hypnotic, perspicacious, creative, vigorous, untameable, cunning, ambitious, aggressive, tyrannical, sadistic, mysterious, transformation. Part of body: Pelvis/reproductive organs

- Sagittarius (The Archer) (mutable, fire, universal): Keyword: "I perceive". Free, straightforward, careless, philosophic, intellectual, fun-loving, arrogant, adventurous, expansive, optimistic, blundering, believer, scattered. Part of body: hips/thighs

- Capricorn (The Sea-goat) (cardinal, earth, universal): Keyword: "I use". Prudent, cautious, suspicious, ambitious, rigid, authoritative, cunning, competent, saturnine. Part of body: knees/skeleton

- Aquarius (The Water Carrier) (fixed, air, universal): Keyword: "I know". Democratic, unconventional, detached, friendships, humanitarian, cause-oriented, the group, society, progressive, eccentric, elitist, sophisticated, objective. Part of body: nervous system/ankles

- Pisces (The Fishes)(mutable, water, universal): Keyword: "I believe". Imaginative, sensitive, distracted, feeling, duality, idealistic, spirituality, acceptance, undiscriminating, soul growth, martyrdom, artistic, neglectful, surrender, lazy, compassionate. Part of body: feet/immune system

Number	Sanskrit Name	Meaning	Western Name	Meaning
1	Mesha	Ram	Aries	Ram
2	Vrishabha	Bull	Taurus	Bull
3	Mithuna	Pair	Gemini	Twins
4	Karka	Crab	Cancer	Crab
5	Simha	Lion	Leo	Lion
6	Kanya	Girl	Virgo	Virgin
7	Tula	Balance	Libra	Scales
8	Vrishchika	Scorpion	Scorpio	Scorpion
9	Dhanus	Bow, Arc	Sagittarius	Archer
10	Makara	Sea-monster	Capricorn	Sea-goat
11	Kumbha	Pitcher, Water-pot	Aquarius	Water-carrier
12	Meena	Fish	Pisces	Fish

http://en.wikipedia.org/wiki/Aum

Simple Ek Onkar

Stylised Ek Onkar

Upanishads and Sutra literatureFurther information: Mandukya Upanishad

The syllable is mentioned in all the Upanishads, specially elaborated upon in the Taittiriya, Chandogya and Mundaka Upanishads. set forth as the object of profound religious meditation, the highest spiritual efficacy being attributed not only to the whole word but also to the three sounds a (a-kāra), u (u-kāra), m (ma-kāra), of which it consists.

The Katha Upanishad has:

"The goal, which all Vedas declare, which all austerities aim at, and which humans desire when they live a life of continence, I will tell you briefly it is Aum"

"The one syllable [evākṣara, viz. Aum] is indeed Brahma. This one syllable is the highest. Whosoever knows this one syllable obtains all that he desires.

"This is the best support; this is the highest support. Whosoever knows this support is adored in the world of Brahma." (1.2.15-17)^[2]

The Chandogya Upanishad (1.1.1-1) states:

om ity etad akṣaram udgītham upāsīta / om iti hy udgāyati / tasyopavyākhyānam

"The udgitha ["the chanting", that is, the syllable om] is the best of all essences, the highest, deserving the highest place, the eighth."

The Bhagavad Gita (8.13) has:

Uttering the monosyllable Aum, the eternal world of Brahman, One who departs leaving the body (at death), he attains the superior goal.

The Yoga Sutras of Patanjali states in verse (1:27):

"tasya vacakah pranavah" which translates as, "God's voice is Aum."

In the following sutra it emphasizes, "The repetition of Om should be made with an understanding of its meaning".

http://en.wikipedia.org/wiki/Axis_mundi

Axis Mundi

The Caduceus

http://en.wikipedia.org/wiki/Palmette

Nike before the altar

Tree of life

http://en.wikipedia.org/wiki/Tree_of_life

The Norse Yggdasil

The Kabbalah Tree of Life derived from the Flower of Life.

http://en.wikipedia.org/wiki/Fleur-de-lis

http://en.wikipedia.org/wiki/Annunciation

Today is the beginning of our salvation,

The revelation of the eternal mystery!

The Son of God becomes the Son of the Virgin

As Gabriel announces the coming of Grace.

Together with him let us cry to the Theotokos:

Rejoice, O Full of Grace,

The Lord is with You!

Annunciation is also cited in the Quran, in chapters 3 (Aal 'Imran - The family of Imran) verses 45-51 and 19 (Maryam - Mary) verses 16-26, although never with the mention or insinuation that Jesus is the son of God.

From chapter 3

[45] (Remember) when the angels said: "O Maryam (Mary)! Verily, Allâh gives you the glad tidings of a Word ("Be!" - and he was! i.e. 'Isâ (Jesus) the son of Maryam (Mary)) from Him, his name will be the Messiah 'Isâ (Jesus), the son of Maryam (Mary), held in honor in this world and in the Hereafter, and will be one of those who are near to Allâh."

[46] "He will speak to the people in the cradle and in manhood, and he will be one of the righteous."

[47] She said: "O my Lord! How shall I have a son when no man has touched me." He said: "So (it will be) for Allâh creates what He wills. When He has decreed something, He says to it only: "Be!" - and it is.

[48] And He (Allâh) will teach him ('Isâ (Jesus)) the Book and Al-Hikmah (i.e. the Sunnah, the faultless speech of the Prophets, wisdom), (and) the Taurât (Torah) and the Injeel (Gospel).

[49] And will make him ('Isâ (Jesus)) a Messenger to the Children of Israel (saying): "I have come to you with a sign from your Lord, that I design for you out of clay, a figure like that of a bird, and breathe into it, and it becomes a bird by Allâh's Leave; and I heal him who was born blind, and the leper, and I bring the dead to life by Allâh's Leave. And I inform you of what you eat, and what you store in your houses. Surely, therein is a sign for you, if you believe.

[50] And I have come confirming that which was before me of the Taurât (Torah), and to make lawful to you part of what was forbidden to you, and I have come to you with a proof from your Lord. So fear Allâh and obey me.

[51] Truly! Allâh is my Lord and your Lord, so worship Him (Alone). This is the Straight Path.

From chapter 19

[16] And mention in the Book (the Qur'ân, O Muhammad (peace be upon him) the story of) Maryam (Mary), when she withdrew in seclusion from her family to a place facing east.

[17] She placed a screen (to screen herself) from them; then We sent to her Our Ruh (angel Jibrîl (Gabriel)) and he appeared before her in the form of a man in all respects.

[18] She said: "Verily! I seek refuge with the Most Gracious (Allâh) from you, if you do fear Allâh."

[19] (The angel) said: "I am only a Messenger from your Lord, (to announce) to you the gift of a righteous son."

[20] She said: "How can I have a son, when no man has touched me, nor am I unchaste?"

[21] He said: "So (it will be), your Lord said: 'That is easy for Me (Allâh): And (We wish) to appoint him as a sign to mankind and a mercy from Us (Allâh), and it is a matter (already) decreed, (by Allâh).' "

[22] So she conceived him, and she withdrew with him to a far place (i.e. Bethlehem valley about 4-6 miles from Jerusalem).

[23] And the pains of childbirth drove her to the trunk of a date-palm. She said: "Would that I had died before this, and had been forgotten and out of sight!"

[24] Then (the babe 'Iesa (Jesus) or Jibrîl (Gabriel)) cried unto her from below her, saying: "Grieve not: your Lord has provided a water stream under you.

[25] "And shake the trunk of date-palm towards you, it will let fall fresh ripe-dates upon you."

[26] "So eat and drink and be glad. And if you see any human being, say: 'Verily! I have vowed a fast unto the Most Gracious (Allâh) so I shall not speak to any human being this day.'

http://en.wikipedia.org/wiki/Nymphaea_caerulea

Egyptian blue lily or sacred blue lily,

http://en.wikipedia.org/wiki/Gravity%27s_Rainbow

http://en.wikipedia.org/wiki/Bagua_%28concept%29

Bagua

無極生有極, 有極是太極,
太極生兩儀, 即陰陽;
兩儀生四象: 即少陰、太陰、少陽、太陽,
四象演八卦，八八六十四卦

The Eight Trigrams (Pre-King Wen "Earlier Heaven" order)

卦 Name	自然 Nature	Season	性情 Personality	家族 Family	方位 Direction	意義 Meaning
乾Qian	天 Heaven	Summer	Creative	父 Father	南 South	Expansive energy, the sky.
巽Xun	風 Wind		Gentle	長女 Eldest Daughter	西南 Southwest	Gentle penetration, flexibility.
坎Kan	水 Water	Autumn	Abysmal	中男 Middle Son	西 West	Danger, rapid rivers, the abyss, the moon.
艮Gen	山 Mountain		Mountain	少男 Youngest Son	西北 Northwest	Stillness, immovability.
坤Kun	地 Earth	Winter	Receptive	母 Mother	北 North	Receptive energy, that which yields.
震Zhen	雷 Thunder		Arousing	長男 Eldest Son	東北 Northeast	Excitation, revolution, division.
離Li	火 Fire	Spring	Clinging	中女 Middle Daughter	東 East	Rapid movement, radiance, the sun.
兌Dui	泽 Lake		Joyous	少女 Youngest Daughter	東南 Southeast	Joy, satisfaction, stagnation.

The Eight Trigrams (King Wen "Later Heaven" order)

卦名 Name	自然 Nature	Season	性情 Personality	家族 Family	方位 Direction	意義 Meaning
離Li	火 Fire	Summer	Clinging	中女 Middle Daughter	南 South	Rapid movement, radiance, the sun.
坤Kun	地 Earth		Receptive	母 Mother	西南 Southwest	Receptive energy, that which yields.
兌Dui	泽 Lake	Autumn	Joyous	少女 Youngest Daughter	西 West	Joy, satisfaction, stagnation.
乾Qian	天 Heaven		Creative	父 Father	西北 Northwest	Expansive energy, the sky.
坎Kan	水 Water	Winter	Abysmal	中男 Middle Son	北 North	Danger, rapid rivers, the abyss, the moon.
艮Gen	山 Mountain		Mountain	少男 Youngest Son	東北 Northeast	Stillness, immovability.
震Zhen	雷 Thunder	Spring	Arousing	長男 Eldest Son	東 East	Excitation, revolution, division.
巽Xun	風 Wind		Gentle	長女 Eldest Daughter	東南 Southeast	Gentle penetration, flexibility.

The Greatest Name, or more fully, the calligraphy of the Greatest Name of God, is an Arabic calligraphic rendering of "Yá Bahá'u'l-

Designed by `Abdu'l-Bahá , the ringstone symbol, as its name implies, is the most common symbol found on rings worn by Bahá'ís, but it is also used on necklaces, book covers, and paintings. It consists of two stars (haykal) interspersed with a stylized Bahá’. The lower line is said to represent humanity, the upper line God, and the middle line represents the special station of

http://en.wikipedia.org/wiki/Bhavacakra

Wheel of life

Wheel of existence

Wheel of rebirth

Wheel of saṃsāra

Wheel of suffering

Wheel of transformation

http://en.wikipedia.org/wiki/Bindi_%28decoration%29

http://en.wikipedia.org/wiki/Caduceus

Two caduceuses without wings as decoration of door portal in Ztracená street in Olomouc (Czech Republic).

Chiron and Achilles

satyrs (in Greek, Σάτυροι — Sátyroi

A child satyr (center) depicted in Titian's painting Bacchus and Ariadne c.1520-1523

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Satyr

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Ancient Greek Satyr statuette

In Greek mythology, satyrs (in Greek, Σάτυροι — Sátyroi) are young humans, possibly with horse ears, that roamed the woods and mountains, and were the companions of Pan and Dionysus. In mythology they are often associated with male sex drive and Greco-Roman art often portrays them with erections.

Mythology

Satyrs were originally imagined as small, human-like creatures with very big erections that could balance a brick. Their chief was called Silenus, a minor deity associated (like Hermes and the later 'Roman' god Priapus) with fertility. These characters can be found in the remaining Satyr plays: Cyclops by Euripedes and Sophocles' The Searching Satyrs. The satyr play was a lighthearted follow-up attached to the end of each trilogy of tragedies in Athenian festivals honoring Dionysus. These plays would take a lighthearted approach to the heavier subject matter of the tragedies in the series, featuring heroes speaking in tragic iambic verse and taking their situation seriously as "straight men" to the flippant, irreverent and obscene remarks and antics of the satyrs.

Image from a Greek chalice depicting a satyr with a tail and erect penis, Euphronios, 510–500 BC, Athens

The groundbreaking tragic playwright Aeschylus is said to have been especially loved for his satyr plays, but none of them survived.

A bald, bearded, horse-tailed satyr balances a winecup on his erect phallus, on an Attic red-figured psykter, ca. 500-490 BC.

Satyrs acquired their goat aspect through later conflation with the Roman Faunus, a carefree nature spirit of similar temperament. Hence satyrs are most commonly described as having the upper half of a man and the lower half of a goat. They are also described as possessing a long, thick tail, either that of a goat or a horse. Mature satyrs are often depicted with goat's horns, while juveniles are often shown with bony nubs on their foreheads. Attic painted vases depict satyrs as being strongly built with flat noses, large pointed ears, long curly hair, and full beards, with wreaths of vine or ivy circling their heads. Satyrs often carry the thyrsus: the rod of Dionysus tipped with a pine cone.

In some recent works satyrs have become more human, with fewer animal characteristics, until only the tail remains to show that they are satyrs. In most books, drawings, etc., however, they still have their general half-goat, half-man appearance.

They are described as roguish but faint-hearted folk — subversive and dangerous, yet shy and cowardly. As Dionysiac creatures they are lovers of wine, women and boys, and are ready for every physical pleasure. They roam to the music of pipes (auloi), cymbals, castanets, and bagpipes, and love to dance with the nymphs (with whom they are obsessed, and whom they often pursue), and have a special form of dance called sikinnis. Because of their love of wine, they are often represented holding winecups, and appear often in the decorations on winecups.

Satyrs are not immortal, but grow old. On painted vases and other Greek art, satyrs are represented in the three stages of a man's life: mature satyrs are bearded, and are shown as balding, a humiliating and unbecoming disfigurement in Greek culture.

In Greek mythology and art

Satyr and maenad, shown on a red-figure Attic cup, ca. 510 BC–500 BC., Louvre, Paris, France

In earlier Greek art, satyrs appear as old and ugly, but in later art, especially in works of the Attic school, this savage characteristic is softened into a more youthful and graceful aspect. There is a famous statue said to be a copy of a work of Praxiteles, representing a graceful satyr leaning against a tree with a flute in his hand.

Older satyrs were known as sileni, the younger as satyrisci. The hare was the symbol of the shy and timid satyr. Greek spirits known as Calicantsars have a noticeable resemblance to the ancient satyrs; they have goats' ears and the feet of donkeys or goats, are covered with hair, and love women and the dance.

Although they are not mentioned by Homer, in a fragment of Hesiod's works they are called brothers of the mountain nymphs and Kuretes, strongly connected with the cult of Dionysus, and are an idle and worthless race. In the Dionysus cult, male followers are known as satyrs and female followers as maenads.

In Attica there was a species of drama known as the legends of gods and heroes, and the chorus was composed of satyrs and sileni. In the Athenian satyr plays of the 5th century BC, the chorus commented on the action. This "satyric drama" burlesqued the serious events of the mythic past with lewd pantomime and subversive mockery. One complete satyr play from the 5th century survives, the Cyclops of Euripides.

A papyrus bearing a long fragment of a satyr play by Sophocles, given the title 'Tracking Satyrs' (Ichneutae), was found at Oxyrhynchus in Egypt, 1907.

In Roman mythology and art

A Satyr depicted on a Roman mosaic in Villa Romana del Casale, an archeological site near Piazza Armerina in Sicily, Italy

Roman satyrs were conflated in the popular and poetic imagination with Latin spirits of woodland and with the rustic spirit Pan, called the Panes

This satyr gargoyle, affixed to the Cathedral of St. Vincent (Bern, Switzerland), is posed in the act of choking a mermaid.

Roman satyrs were described as goatlike from the haunches to the hooves, and were often pictured with larger horns, even ram's horns. Roman poets often conflated them with the fauns.

Roman satire is a literary form, a poetic essay that was a vehicle for biting, subversive social and personal criticism. Though Roman satire is sometimes thoughtlessly linked to the Greek satyr plays, satire's only connection to the satyric drama is through the subversive nature of the satyrs themselves, as forces in opposition to urbanity, decorum, and civilization itself.

Other references

In the King James Version of the Bible, Isaiah 13:21 and 34:14, the English word "satyr" is used to represent the Hebrew sh'lrlm, "hairy ones". In Hebrew folklore, sh'lrlm are a type of demon or supernatural being which inhabits waste places. There is an allusion to the practice of sacrificing to the sh'lrlm (often translated as "devils") in Leviticus 17:7. They correspond to the "shaggy demon of the mountain-pass" (azabb al-akaba) of old Arab legend. Christian mythology demonised all pagan nature spirits such as satyrs by associating them with demons and devils, though they do resemble the Jewish goat-man demon Azazel to whom the scapegoats were sent.

Baby satyr

Baby satyrs, or child satyrs, are mythological creatures related to the satyr. They appear in popular folklore, classical artworks, film, and in various forms of local art.

Some classical works depict young satyrs being tended to by older, sober satyrs, while there are also some representations of child satyrs taking part in Bacchanalian/Dionysian rituals (including drinking alcohol, playing musical instruments, and dancing).

A child satyr (center) depicted in Titian's painting Bacchus and Ariadne c.1520-1523

A statue of a female satyr holding two infants

The presence of a baby or child satyr in a classical work, such as on a Greek vase, was mainly an aesthetic choice on the part of the artist. However, the role of a child in Greek art might imply a further meaning for baby satyrs: Eros, the son of Aphrodite, is consistently represented as a child or baby, and Bacchus, the divine sponsor of satyrs, is seen in numerous works as a baby, often in the company of the satyrs. A prominent instance of a baby satyr outside ancient Greece is Albrecht Dürer's 1505 engraving, "Musical Satyr and Nymph with Baby (Satyr's Family)". There is also a Victorian-era napkin ring depicting a baby satyr next to a barrel, which further represents the perception of baby satyrs as partaking in the Bacchanalian festivities. See Revivals, Reveries, and Reconstructions: Images of Antiquity in Prints from 1500 to 1800, an exhibition at the Philadelphia Museum of Art.

There are also many works of art of the rococo period depicting child or baby satyrs in Bacchanalian celebrations. Some works depict female satyrs with their children; others describe the child satyrs as playing an active role in the events, including one instance of a painting by Jean Raoux (1677–1735). "Mlle Prévost as a Bacchante" depicts a child satyr playing a tambourine while Mlle Prévost, a dancer at the Opéra, is dancing as part of the Bacchanal festivities. [1]

http://en.wikipedia.org/wiki/Celtic_cross

Celtic cross in Père Lachaise cemetery

Celtic cross

http://en.wikipedia.org/wiki/Chai_%28symbol%29

http://en.wikipedia.org/wiki/Tetragrammaton#Jewish_use_of_the_word

Tetragrammaton

Tetragrammaton at the Roman Catholic Church of Saint Germain in Paris, France.

Afrikaans	Jehóva
Arabic	يهوه
Awabakal	Yehóa
Bosnian	Jehova
Bugotu	Jihova
Bulgarian	Йехова
Croatian	Jahve / Jehova
Czech	Jehova / Jahve
Danish	Jahve (/ Jehova)
Dutch	Jahwe(h) / Jehovah
Efik	Jehovah
Ewe (Ʋegbe)	Yehowah
English	Jehovah / Yahweh
Fijian	Jiova
Finnish	Jahve / Jehova
French	Yahvé / Jéhovah
Futuna	Ihovah
Galician	Xeova
German	Jahwe / Jehova
Greek	Iehova / Yiahve Ιεχωβά / Γιαχβέ
Hungarian	Jahve / Jehova
Igbo	Jehova
Indonesian	Yehuwa
Inuktitut	Ayaaya / Ajaaja / YAHYAH
Isoko	eJehova
Italian	Geova / Jahve
Japanese	EHOBA/YAHAWE エホバ / ヤハウェ
Korean	Yeohowa 여호와 / Yahwe 야훼
Lithuanian	Jahveh,Jahvė
Mandarin in Traditional Chinese	Yéhéhuá / Yǎwēi / Yǎwēi 耶和華/雅威/雅巍
Cantonese	Yewowha 耶和華
Min Dong	Ià-huò-huà 耶和華
Mandarin in Simplified Chinese	Yéhéhuá / Yǎwēi / Yǎwēi 耶和华/雅威/雅巍

Maori	Ihowa
Motu	Iehova
Macedonian	Јахве
Narrinyeri	Jehovah
Nembe	Jihova
Norwegian	Jahve / Jehova
Petats	Jihouva
Polish	Jehowa / Jahwe
Persian	يهوه
Portuguese	Iavé / Javé / Yahweh / Jeová
Romanian	Iahve / Iehova
Russian	Иегова / Яхве
Samoan	Ieova
Serbian	Јахве / Jahve / Јехова / Jehova
Sotho	Jehova
Spanish	Yavé Yahveh /Jehová
Swahili	Yehova
Slovak	Jahve,Jehova
Slovenian	Jahve,Jehova
Swedish	Jehova / Jahve
Tagalog	Hehoba/Yawe
Tahitian	Jehovah
Tongan	Jihova
Turkish	Yehova
Venda	Yehova
Xhosa	u Yehova
Yoruba	Jehofah
Zulu	u Jehova

http://en.wikipedia.org/wiki/Tetractys

Symbol by early 17th-century Christian mystic Jakob Böhme, including a tetractys of flaming Hebrew letters of the Tetragrammaton.

Image:Tetragrammaton scripts.svg

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Tetragrammaton_scripts.svg‎

Judaism

Maltese cross

Typical St. Florian's cross

Loyalty

Piety

Frankness

Bravery

Glory and honour

Contempt of death

Helpfulness towards the poor and the sick

Respect for the church

The Tau cross

http://en.wikipedia.org/wiki/Category:Christian_symbols

Christian symbolism

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Old Roman Symbol

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Q

Quatrefoil

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Rose-Cross

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http://en.wikipedia.org/wiki/Category:Abrahamic_symbols

http://en.wikipedia.org/wiki/Category:Religious_symbols

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Flower of Life

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Pentagram

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Religious symbolism

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Atomic whirl

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Flaming chalice

Flaming Chalice.svg
4,518 bytes

http://en.wikipedia.org/wiki/Category:Symbols

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[+] Diacritics

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[+] Flags
[+] Formal insignia

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[+] Graphemes

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[+] Hammer & sickle

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[+] Images of symbols

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[+] LGBT symbols

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[+] National symbols

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[+] Peace symbols
[+] Punctuation

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[+] Religious symbols
[+] Ribbon symbolism

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[+] Star symbols
[+] Symbolic system

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[+] Typographical symbols

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[+] United States state insignia

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[+] Visual motifs

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French law on secularity and conspicuous religious symbols in schools

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Kteis

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Parodies of the ichthys symbol

P cont.

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Yellow Sign

http://en.wikipedia.org/wiki/Crescent

The origin of the Islamic crescent

MathWorld article on geometric "Lune"

Worldwide Moon Sighting Reports

http://en.wikipedia.org/wiki/Cross_and_Crown

Cross of Sacrifice

http://en.wikipedia.org/wiki/Cross_of_St._Peter

A famous khachkar at Goshavank (Notice the cross).

Cross Name	Description	Picture
Ankh	Also known as the Key of the Nile, the Looped Tau Cross, and the Ansated Cross. It was an Ancient Egyptian symbol of life. Sometimes given a Latin name if it appears in specifically Christian contexts, such as the *crux ansata* ("handled cross").
Canterbury cross	Used in the Anglican Churches. It has four arms of equal length, each widening at the outer end in a hammer shape so that their rims form a near circle. Each arm bears a triangular panel incised with a triquetra symbolizing the Trinity. In the center of the cross is a small square. The Saxon original dates from c. 850 A.D. and was excavated in 1867 in Canterbury, England. A stone replica can be found in Canterbury Cathedral and in several other Anglican cathedrals around the world. [1] [2]
Christian cross	Also known as the Latin cross or *crux ordinaria*. It is the most common symbol of Christianity, intended to represent the redeeming martyrdom of Jesus when he was crucified on the True Cross in the New Testament.
Coptic Cross	A small circle from which emanate four arms of equal length, with angled T shapes in the corner, cross-pieces outward, representing the nails used in Jesus' crucifixion. This cross receives its name from Coptic Christianity, which centered around Alexandria, Egypt.
Greek cross	Also known as the *crux immissa quadrata*. Has all arms of equal length.
Eastern cross	Used in the Eastern Orthodox Church. The top line is said to represent the headboard, and the bottom, slanted line represents the footrest, wrenched loose by Jesus' writhing in intense agony. The letters IC XC found at the end of the main arm of most Eastern Orthodox Crosses are a Christogram, representing the name of Jesus Christ.
High cross	Free-standing Celtic crosses commonly found in Ireland and to a lesser extent in Great Britain, very common in churches and graveyards.
St. Brigid's Cross	This cross is found throughout Ireland. It is told that the cross was made by Brigid, daughter of a Pagan King from reeds to be used as an instrument of conversion. However, Brigid's name is derived from Brigit (also spelled Brigid, Brìghde, Brìde, and Bríde), a Celtic Goddess of fire, poetry, and smithcraft, and today the cross is used to protect houses from fire. This is an example of the integration of religious traditions. The cross itself derives from the Indo-European Swastika, or Solar Wheel
Labarum	Constantine I's Labarum is also known as a Chrismon, Chi-Rho (from the two Greek letters that make it up) or monogram of the name Jesus Christ. Several other forms of Chrismons exist.
Lebanese Forces Cross	Inspired from the eastern crosses it symbolizes 3 things: 1- The Cross of the savior Jesus Christ In red, the sign of martyrdom and glory. 2- The bearing cross of the Lebanese Christians The sign of their suffering throughout history. 3- The Diagonal cut at the base of the cross It symbolizes the strength of the Lebanese Christians’ will and their determination to keep the cross planted in their region of the world.
Lorraine Cross	Used in heraldry. It is similar to a patriarchal cross, but usually has one bar near the bottom and one near the top, rather than having both near the top.
Marian Cross	Etched on the casket of Pope John Paul II, the Marian Cross is a Catholic adaptation of the traditional Latin cross to emphasize Catholic devotion to Mary.
Nordic Cross	Used in flags descended from the Dannebrog.
Papal Cross	The three cross-bars represent the Roman Catholic Pope's triple role as Bishop of Rome, Patriarch of the West, and successor of St. Peter, Chief of the Apostles.
Patriarchal cross	Similar to a traditional Christian cross, but with an additional, smaller crossbar above the main one meant to represent all the Orthodox Christian Archbishops and Patriarchs. In the Eastern Orthodox Church, this cross is sometimes seen with an additional, slanted bar near the foot of the cross (see Byzantine Cross). This cross is similar to the Lorraine Cross and the Caravaca Cross.
Presbyterian Cross	Used by Presbyterian denominations.
Red Cross	Used as a symbol for medical care in most of the world, the Red Crescent being used in Islamic countries and the Magen David Adom in Israel.
Cross of Sacrifice	A Latin cross with a superimposed sword, blade down. It is a symbol used by the Commonwealth War Graves Commission at the site of many war memorials.
Flag of Queen Tamar	Used in Georgia as national flag, first used by Georgian King Vakhtang Gorgasali in 5th century and later adopted by Queen Tamar of Georgia in 13th century. The flag depicts a Jerusalem cross, adopted during the reign of George V of Georgia who drove out the Mongols from Georgia in 1334.
Saint Andrew's Cross	Used in Scotland's national flag and the naval ensign of the Russian Navy, it is also called the Saltire, the Boundary Cross (because it was used by the Romans as a barrier) and the *crux decussata*. Saint Andrew is believed to have suffered a martyr's death on such a cross, hence its name. The cross does not have to be at this particular angle to qualify as a saltire; the symbol X can also be considered a St. Andrew's Cross.
St George's Cross	Used in England's national flag.
Saint Peter's Cross	An upside-down Latin cross, based on a tradition that holds that Saint Peter was martyred by being crucified upside-down. Today it is often associated with anti-Christian or Satanic groups.
Skull and crossbones	Not a cross as such, but a saltire made of bones, with an overlaid skull. Traditionally used by pirates. It was actually relatively rarely used by pirates, each ship having its own design, often involving an hourglass.
Sun cross	Also known as the Sunwheel, solar cross or Odin's cross, because Odin's symbol in Norse mythology was a cross in a circle.
Tau Cross	Also known as Saint Anthony's Cross, the Egyptian Cross and the *crux commissa*. It is shaped like the letter T. Francis of Assisi used it as his signature.
Thieves' Cross	Also known as the Furka Cross. The fork, shaped like the letter Y. [3]
Mariner's Cross	The Mariner's Cross is a stylized cross in the shape of an anchor. The Mariner's Cross is also referred to as St. Clement's Cross in reference to the way he was martyred.
Bent cross	Also known as the swastika, it is an equilateral cross with its arms bent at right angles in either left-facing or right-facing direction. The swastika is a holy symbol in Hinduism, Jainism and Buddhism. In the West, it is more widely known as a symbol of Nazism. It is also used in Heathenry. It is traditionally oriented so that a main line is horizontal, though it is occasionally rotated at forty-five degrees, and the Hindu version is often decorated with a dot in each quadrant. The Nazi swastika always faces right, which has led to the decreased use of the right-facing version of this cross as religious symbols outside of India. They are now mostly left-facing.
Persian cross	Carved into mountainside at the site of the tombs of the Achaemenian Kings

Written crosses are used for many different purposes, particularly in mathematics.

The Roman numeral for ten is X.

In the Latin alphabet, the letter X and the minuscule form of t are crosses.

The Chinese character for ten is 十; (see Chinese numerals).

The dagger or obelus (†)

The addition (or plus) sign (+) and the multiplication (or times) sign (×).

If n≥1 is an integer, the numbers coprime to n, taken modulo n, form a group with multiplication as operation; it is written as (Z/nZ)^× or Z_n^*.

A cross is often used as a check mark because it can be clearer, easier to create with an ordinary pen or pencil, and less obscuring of the text or image that is already present than a large dot. It also allows marking a position more accurately than a large dot.

A large cross through a text often means that it is wrong or should be considered deleted.

http://en.wikipedia.org/wiki/Crucifix

Michelangelo's Creation of Adam, from the Sistine Chapel. Michelangelo shows God creating Adam, with Eve in His arm. While not strictly true to the Genesis account, this is one of the most famous depictions of the creation of Adam and Eve in Western art.

Adam (Hebrew: אָדָם, "man"; Arabic: آدم; Ge'ez:) and Eve (Hebrew: חַוָּה, Ḥavva, "living one"; Arabic: حواء, Hawwa; Ge'ez: ሕይዋን, Hiywan) were the first man and woman created by God according to the Bible and the Qur'an.

A Crux gemmata

http://en.wikipedia.org/wiki/Category:Christian_iconography

http://en.wikipedia.org/wiki/Iconography

http://en.wikipedia.org/wiki/Dharmacakra

http://en.wikipedia.org/wiki/The_divided_line_of_Plato

http://en.wikipedia.org/wiki/Endless_knot

"an ancient symbol representing the interweaving of the Spiritual Path, the flowing of Time and Movement within That Which is Eternal. All existence, it says, is bound by time and change, yet ultimately rests serenely within the Divine, the Eternal, Buddha, the Mind of God."

"Addiction and aversion lead to delusion, which is the ongoing source of all suffering."

The inter-twining of wisdom and compassion; represents the mutual dependence of religious doctrine and secular affairs

The union of wisdom and method

The inseparability of emptinesss (shunyata) and Dependent Co-arrising (Pratitya-samutpada at the time of the path)

At the time of enlightenment the union of wisdom and great compassion

Symbolic of knot symbolism in linking ancestors and omnipresence and the magical ritual and meta-process of binding (refer etymology of Tantra, Yoga and religion) (see Namkha)

Since the knot has no beginning or end it also symbolizes the infinite wisdom of the Buddha.

http://en.wikipedia.org/wiki/Gordian_knot

Some brief descriptions of the Enneatypes are as follows:

One: Reformer, Critic, Perfectionist - This type focuses on integrity. Ones can be wise, discerning and inspiring in their quest for the truth. They also tend to dissociate themselves from their flaws or what they believe are flaws (such as negative emotions) and can become hypocritical and hyper-critical of others, seeking the illusion of virtue to hide their own vices. The One's greatest fear is to be flawed and their ultimate goal is perfection. The corresponding "deadly sin" Ones is Anger and their "holy idea" or essence is Holy Perfection. Under stress Ones express qualities of Fours and when relaxed qualities of Sevens.

Two: Helper, Giver, Caretaker - Twos, at their best, are compassionate, thoughtful and astonishingly generous; they can also be prone to passive-aggressive behavior, clinginess and manipulation. Twos want, above all, to be loved and needed and fear being unworthy of love. The corresponding "deadly sin" of Twos is Pride and their "holy idea" or essence is Holy Will. Under stress Twos express qualities of Eights and when relaxed qualities of Fours.

Three: Achiever, Performer, Succeeder - Highly adaptable and changeable. Some walk the world with confidence and unstinting authenticity; others wear a series of public masks, acting the way they think will bring them approval and losing track of their true self. Threes are motivated by the need to succeed and to be seen as successful. The corresponding "deadly sin" of Threes is Deceit and their "holy idea" or essence is Holy Law. Under stress Threes express qualities of Nines and when relaxed qualities of Sixes.

Four: Romantic, Individualist, Artist - Driven by a desire to understand themselves and find a place in the world they often fear that they have no identity or personal significance. Fours embrace individualism and are often profoundly creative and intuitive. However, they have a habit of withdrawing to internalize, searching desperately inside themselves for something they never find and creating a spiral of depression. The corresponding "deadly sin" of Fours is Envy and their "holy idea" or essence is Holy Origin. Under stress Fours express qualities of Twos and when relaxed qualities of Ones.

Five: Observer, Thinker, Investigator - Fives are motivated by the desire to understand the world around them, specifically in terms of facts. Believing they are only worth what they contribute, Fives have learned to withdraw, to watch with keen eyes and speak only when they can shake the world with their observations. Sometimes they do just that. However, some Fives are known to withdraw from the world, becoming reclusive hermits and fending off social contact with abrasive cynicism. Fives fear incompetency or uselessness and want to be capable and knowledgeable above all else. The corresponding "deadly sin" of the Five is Avarice and their "holy idea" or essence is Holy Omniscience. Under stress Fives express qualities of Sevens and when relaxed qualities of Eights.

Six: Loyalist, Devil's Advocate, Defender - Sixes long for stability above all else. They exhibit unwavering loyalty and responsibility, but once betrayed, they are slow to trust again. They are prone to extreme anxiety and passive-aggressive behavior. Their greatest fear is to lack support and guidance. The corresponding "deadly sin" of the Six is Cowardice and their "holy idea" or essence is Holy Faith and Strength. Under stress Sixes express qualities of Threes and when relaxed qualities of Nines. There are two kinds of Sixes - phobic and counterphobic. Phobic Sixes have a tendency to run or hide from things they fear while counterphobic Sixes are more likely to confront their fears.

Seven: Enthusiast, Adventurer, Materialist, Epicure - Sevens are adventurous, and busy with many activities with all the energy and enthusiasm of the Puer Aeternus. At their best they embrace life for its varied joys and wonders and truly live in the moment; but at their worst they dash frantically from one new experience to another, too scared of disappointment to actually enjoy themselves. Sevens fear being unable to provide for themselves or to experience life in all of its richness. The corresponding "deadly sin" of Sevens is Gluttony and their "holy idea" or essence is Holy Wisdom". Under stress Sevens express qualities of Ones and when relaxed qualities of Fives.

Eight: Leader, Protector, Challenger - Eights value personal strength and they desire to be powerful and in control. They concern themselves with self-preservation. They are natural leaders, who can be either friendly and charitable or dictatorially manipulative, ruthless, and willing to destroy anything in their way. Eights seek control over their own lives and destinies, and fear being harmed or controlled by others. The corresponding "deadly sin" of the Eight is Lust and their "holy idea" or essence is Holy Truth. Under stress Eights express qualities of Fives and when relaxed qualities of Twos.

Nine: Mediator, Peacemaker, Preservationist - Nines are ruled by their empathy. At their best they are perceptive, receptive, gentle, calming and at peace with the world. On the other hand, they prefer to dissociate from conflicts; they indifferently go along with others' wishes, or simply withdraw, acting via inaction. They fear the conflict caused by their ability to simultaneously understand opposing points of view and seek peace of mind above all else. The corresponding "deadly sin" of the Nine is Sloth and their "holy idea" or essence is Holy Love. Under stress Nines express qualities of Sixes and when relaxed qualities of Threes.

The circled dot, circumpunct, or circle with a point at its centre. It is an ancient symbol.

It can symbolize:

The sun: See also Solar symbol

http://en.wikipedia.org/wiki/Eye_of_Providence

Aachen Cathedral

Emblem of the Parc naturel régional du Queyras

Octahedron (Animation)

The vesica piscis

http://en.wikipedia.org/wiki/Sacred_geometry

Hexahedron
or Cube

http://en.wikipedia.org/wiki/Globus_cruciger

The globus cruciger was used in the Byzantine Empire, as shown in this coin of Emperor Leontius (d. 705).

http://en.wikipedia.org/wiki/Golden_ratio

The golden section is a line segment sectioned into two according to the golden ratio. The total length a+b is to the longer segment a as a is to the shorter segment b.

$\varphi = \frac{1 + \sqrt{5}}{2}\approx 1.618\,033\,989\,.$

$\frac{a+b}{a} = \frac{a}{b} = \varphi\,.$

The golden ratio is defined algebraically as

$\frac{a+b}{a} = \frac{a}{b} = \varphi\,.$

The right equation shows that $a=b\varphi$ , which can be substituted in the left part, giving

$\frac{b\varphi+b}{b\varphi}=\frac{b\varphi}{b}\,.$

Canceling b yields

$\frac{\varphi+1}{\varphi}=\varphi.$

Multiplying both sides by $\varphi$ and rearranging terms leads to:

$\varphi^2 - \varphi - 1 = 0.$

The only positive solution to this quadratic equation is

$\varphi = \frac{1 + \sqrt{5}}{2} \approx 1.618\,033\,989\,.$

Mathematician Mark Barr proposed using the first letter in the name of Greek sculptor Phidias, phi, to symbolize the golden ratio. Usually, the lowercase form (φ) is used. Sometimes, the uppercase form (Φ) is used for the reciprocal of the golden ratio, 1/φ .

Depiction of the proportions in a medieval manuscript, that according to Jan Tschichold feature a "Page proportion 2:3. Margin proportions 1:1:2:3. Text area proportioned in the Golden Section."^[23]

Australian sculptor Andrew Rogers's 50-ton stone and gold sculpture, entitled Golden Ratio, is installed outdoors in Jerusalem. Rogers donated the sculpture. The height of each stack of stones, beginning from either end and moving toward the center, is the beginning of the Fibonacci sequence: 1, 1, 2, 3, 5, 8.

Conjugate golden ratio

The negative root of the quadratic equation for φ (the "conjugate root") is $1 - \varphi \approx -0.618$ . The negative of this quantity corresponds to the length ratio taken in reverse order (shorter segment length over longer segment length, b/a), and is sometimes referred to as the golden ratio conjugate.[1] It is denoted here by the capital Phi ( $Φ$ ):

$\Phi = {1 \over \varphi} \approx 0.618\,033\,989\,.$

Alternatively, $Φ$ can be expressed as

$\Phi = \varphi -1\,.$

This illustrates the unique property of the golden ratio among positive numbers, that

${1 \over \varphi} = \varphi - 1\,$

or its inverse:

${1 \over \Phi} = \Phi + 1\,.$

Short proofs of irrationality

Recall that we denoted the "larger part" by a and the "smaller part" by b, and defined:

$\frac{a+b}{a} = \frac{a}{b}\,.$

Multiplying both sides by ab leads to:

$ab+b^2 = a^2\,.$

Subtracting ab from both sides and factoring out a gives:

$b^2 = a(a-b)\,.$

Finally reversing sides and dividing both by b(a-b) delivers the equivalent form:

$\frac{a}{b} = \frac{b}{a-b}\,.$

This gives a short proof that the golden ratio is an irrational number. An irrational number is one that cannot be written as a/b where a and b are integers. If a/b is such a fraction, in lowest terms, then b/(a − b) is an equivalent fraction with a smaller numerator, which is a contradiction. Thus this number cannot be written in this form, and is therefore irrational.

Another short proof — perhaps more commonly known — of the irrationality of the golden ratio makes use of the closure of rational numbers under addition and multiplication. If $\frac{1 + \sqrt{5}}{2}$ is rational, then $2\left(\frac{1 + \sqrt{5}}{2} - \frac{1}{2}\right) = \sqrt{5}$ is also rational, which is a contradiction if it is already known that the square root of a non-square natural number is irrational.

Alternate forms

The formula $\varphi = 1 + 1/\varphi$ can be expanded recursively to obtain a continued fraction for the golden ratio:

$\varphi = [1; 1, 1, 1, \dots] = 1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \cdots}}}$

and its reciprocal:

$\varphi^{-1} = [0; 1, 1, 1, \dots] = 0 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \cdots}}}\,.$

The convergents of these continued fractions (1, 2, 3/2, 5/3, 8/5, 13/8, ..., or 1, 1/2, 2/3, 3/5, 5/8, 8/13, ...) are ratios of successive Fibonacci numbers.

The equation $\varphi^2 = 1 + \varphi$ likewise produces the continued square root form:

$\varphi = \sqrt{1 + \sqrt{1 + \sqrt{1 + \sqrt{1 + \cdots}}}}\,.$

Also:

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

$\varphi = {1 \over 2}\csc(\pi/10) = {1 \over 2}\csc 18^\circ$

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

These correspond to the fact that the length of the diagonal of a regular pentagon is φ times the length of its side, and similar relations in a pentagram.

If x agrees with $\varphi$ to n decimal places, then $\frac{x^2+2x}{x^2+1}$ agrees with it to 2n decimal places.

An equation derived in 1994 connects the golden ratio to the Number of the Beast (666):^[1]

$-\frac{\varphi}{2}=\sin666^\circ=\cos(6\cdot 6 \cdot 6^\circ).$

Which can be combined into the expression:

$-\varphi=\sin666^\circ+\cos(6\cdot 6 \cdot 6^\circ).$

Ptolemy's theorem

The golden ratio can also be found by applying Ptolemy's theorem to the quadrilateral formed by removing one vertex from a regular pentagon. If the quadrilateral's long edge and diagonals are b, and short edges are a, then Ptolemy's theorem says b² = a² + ab which yields

${b \over a}={{(1+\sqrt{5})}\over 2}\,.$

Geometry

Slavic solar symbol found on the Zbruch Idol

Some forms of the triple spiral or triskelion signs are sometimes considered to be solar symbols. The triskelion on the flag of Ingushetia is given this meaning.

The swastika can be derived from the sun cross, and is another solar symbol in some contexts.^{[citation
needed]} It is used (not as a solar symbol in particular) among Buddhists, Jains, and Hindus (see manji) in addition to its infamous Nazi associations.

High Cross, Dysert, Co. Clare, Ireland

Cross of the Scriptures, Clonmacnoise, Ireland

Kildalton Cross, Islay Scotland AD 800

Muiredach's Cross and West Cross at Monasterboice, Co Louth, Ireland

http://en.wikipedia.org/wiki/Holy_Grail

How at the Castle of Corbin a Maiden Bare in the Sangreal and Foretold the Achievements of Galahad: illustration by Arthur Rackham, 1917

The Damsel of the Sanct Grael by Dante Gabriel Rossetti

(16th century illuminated, heraldic, stained glass panel, depicting the Holy Grail) and the coat of arms of Sir Robert Bell

Infinity is often used not only to define a limit but as if it were a value in the extended real numbers in real analysis; if f(t) ≥ 0 then

$\int_{0}^{1} \, f(t)\ dt \ = \infty$ means that f(t) does not bound a finite area from 0 to 1

$\int_{0}^{\infty} \, f(t)\ dt \ = \infty$ means that the area under f(t) is infinite.

$\int_{0}^{\infty} \, f(t)\ dt \ = 1$ means that the area under f(t) equals 1 Infinity is also used to describe infinite series:

$\sum_{i=0}^{\infty} \, f(i) = x$ means that the sum of the infinite series converges to some real value x.

$\sum_{i=0}^{\infty} \, f(i) = \infty$ means that the sum of the infinite series diverges in the specific sense that the partial sums grow without bound.