9

This article is about the number. For the years, see9 BCandAD 9.For other uses, see9 (disambiguation)andNumber nine (disambiguation).

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Cardinal	nine
Ordinal	9th (ninth)
Numeral system	nonary
Factorization	32
Divisors	1,3,9
Greek numeral	Θ´
Roman numeral	IX, ix
Greekprefix	ennea-
Latinprefix	nona-
Binary	10012
Ternary	1003
Senary	136
Octal	118
Duodecimal	912
Hexadecimal	916
Amharic	፱
Arabic,Kurdish,Persian,Sindhi,Urdu	٩
Armenian numeral	Թ
Bengali	৯
Chinese numeral	Cửu, cửu
Devanāgarī	९
Greek numeral	θ´
Hebrew numeral	ט
Tamil numerals	௯
Khmer	៩
Telugu numeral	౯
Thai numeral	๙
Malayalam	൯
Babylonian numeral	𒐝
Egyptian hieroglyph	𓐂
Morse code	____.

9(nine) is thenatural numberfollowing8and preceding10.

Evolution of the Hindu–Arabic digit

See also:Hindu–Arabic numeral system

Circa 300 BC, as part of theBrahmi numerals,various Indians wrote a digit 9 similar in shape to the modern closingquestion markwithout the bottom dot. The Kshatrapa, Andhra and Gupta started curving the bottom vertical line coming up with a3-look-alike.How the numbers got to their Gupta form is open to considerable debate. The Nagari continued the bottom stroke to make a circle and enclose the 3-look-alike, in much the same way that the sign @ encircles a lowercasea.As time went on, the enclosing circle became bigger and its line continued beyond the circle downwards, as the 3-look-alike became smaller. Soon, all that was left of the 3-look-alike was a squiggle. The Arabs simply connected that squiggle to the downward stroke at the middle and subsequent European change was purely cosmetic.

While the shape of the glyph for the digit 9 has anascenderin most moderntypefaces,in typefaces withtext figuresthe character usually has adescender,as, for example, in.

The form of the number nine (9) could possibly derived from the Arabic letterwaw,in which its isolated form (و) resembles the number 9.

The modern digit resembles an inverted6.To disambiguate the two on objects and labels that can be inverted, they are often underlined. It is sometimes handwritten with two strokes and a straight stem, resembling a raised lower-case letterq,which distinguishes it from the 6. Similarly, inseven-segment display,the number 9 can be constructed either with a hook at the end of its stem or without one. MostLCDcalculators use the former, but someVFDmodels use the latter.

Mathematics

9 is the fourthcomposite number,and the first odd composite number. 9 is also arefactorable number.

Casting out ninesis a quick way of testing the calculations of sums, differences, products, andquotientsofintegersindecimal,a method known as long ago as the 12th century.

If anoddperfect numberexists, it will have at least nine distinctprime factors.

Non-intersectingchordsbetween four points on a circle

9 is the sum of thecubesof the first two non-zero positive integers$1^{3}+2^{3}$which makes it the first cube-sum number greater thanone.A number that is 4 or 5modulo9 cannot be represented as thesum of three cubes.

Four concentricmagic circleswith9in the center (byYang Hui), where numbers on each circle anddiameteraround the center generate amagic sumof138.

There are nineHeegner numbers,orsquare-free positive integers$n$that yield an imaginaryquadratic field$\mathbb {Q} \left[{\sqrt {-n}}\right]$whosering of integershas aunique factorization,orclass numberof 1.

Geometry

Apolygonwith nine sides is called anonagon.A regular nonagon can beconstructedwith a regularcompass,straightedge,andangle trisector.

The lowest number ofsquaresneeded for aperfect tilingof arectangleis 9.

9 is the largest single-digit number in thedecimal system.

List of basic calculations

Multiplication	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	20	25	50	100	1000
9 ×x	9	18	27	36	45	54	63	72	81	90	99	108	117	126	135	144	180	225	450	900	9000

Division	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
9 ÷x	9	4.5	3	2.25	1.8	1.5	1.285714	1.125	1	0.9	0.81	0.75	0.692307	0.6428571	0.6
x÷ 9	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	1	1.1	1.2	1.3	1.4	1.5	1.6

Exponentiation	1	2	3	4	5	6	7	8	9	10
9x	9	81	729	6561	59049	531441	4782969	43046721	387420489	3486784401
x9	1	512	19683	262144	1953125	10077696	40353607	134217728	387420489	1000000000

Alphabets and codes

• In theNATO phonetic alphabet,the digit 9 is called "Niner".
• Five-digitproducePLU codesthat begin with 9 indicateorganic foods.

Culture and mythology

Indian culture

Nine is a number that appears often inIndian cultureand mythology.Some instances are enumerated below.

• Nineinfluencersare attested inIndian astrology.
• In theVaisheshikabranch ofHindu philosophy,there are nine universal substances or elements:Earth,Water,Air,Fire,Ether,Time,Space,Soul,andMind.
• Navaratriis a nine-day festival dedicated to thenineforms ofDurga.
• Navaratna,meaning "nine jewels" may also refer toNavaratnas– accomplished courtiers,Navratan– a kind of dish, or a form ofarchitecture.
• InIndian aesthetics,there are nine kinds ofRasa.

Chinese culture

• Nine (Cửu;pinyin:jiǔ) is considered a goodnumber in Chinese culturebecause it sounds the same as the word "long-lasting" (Cửu;pinyin:jiǔ).
• Nine is strongly associated with theChinese dragon,a symbol of magic and power. There are nine forms of the dragon, it is described in terms of nine attributes, and it has nine children. It has 117 scales – 81yang(masculine, heavenly) and 36yin(feminine, earthly). All three numbers are multiples of 9 (9 × 13 = 117,9 × 9 = 81,9 × 4 = 36)as well as having the samedigital rootof 9.
• The dragon often symbolizes theEmperor,and the number nine can be found in many ornaments in theForbidden City.
• The circular altar platform (Earthly Mount) of theTemple of Heavenhas one circular marble plate in the center, surrounded by a ring of nine plates, then by a ring of 18 plates, and so on, for a total of nine rings, with the outermost having81 = 9 × 9 plates.
• The name of the area calledKowloonin Hong Kong literally means:ninedragons.
• Thenine-dotted line(Chinese:Nam hải cửu đoạn tuyến;pinyin:nánhǎi jiǔduàn xiàn;lit.'Nine-segment line of the South China Sea') delimits certain islandclaims by Chinain the South China Sea.
• Thenine-rank systemwas a civil service nomination system used during certain Chinese dynasties.
• 9 Points of theHeart(Heal) / Heart Master (Immortality) Channels inTraditional Chinese Medicine.

Ancient Egypt

• Thenine bowsis a term used in Ancient Egypt to represent the traditional enemies of Egypt.
• TheEnneadis a group of nine Egyptian deities, who, in some versions of theOsiris myth,judged whetherHorusorSetshould inherit Egypt.

European culture

• InNorse mythology,the universe is divided intonine worldswhich are all connected by theworld treeYggdrasil.
• InNorse mythologyas well, the number nine is associated withOdin,as that is how many days he hung from theworld treeYggdrasilbefore attaining knowledge of therunes.

Greek mythology

• The nineMusesin Greek mythology areCalliope(epic poetry),Clio(history),Erato(erotic poetry),Euterpe(lyric poetry),Melpomene(tragedy),Polyhymnia(song),Terpsichore(dance),Thalia(comedy), andUrania(astronomy).
• It takes nine days (for an anvil) to fall from heaven to earth, and nine more to fall from earth toTartarus.
• Letolabored for nine days and nine nights forApollo,according to theHomeric Hymnto Delian Apollo.

Mesoamerican mythology

• TheLords of the Night,is a group of nine deities who each ruled over every ninth night forming a calendrical cycle.

Aztec mythology

• Mictlanthe underworld in Aztec mythology, consists of nine levels.

Mayan mythology

• The Mayan underworldXibalbaconsists of nine levels.
• El Castillo,the Mayan step-pyramid inChichén Itzá,consists of nine steps. It is said that this was done to represent the nine levels ofXibalba.

Australian culture

ThePintupi Nine,a group of 9Aboriginal Australianwomen who remained unaware of European colonisation of Australia and lived a traditional desert-dwelling life in Australia's Gibson Desert until 1984.

Anthropology

Idioms

• "to go the whole nine yards-"
• "Acat-o'-nine-tailssuggests perfect punishment and atonement. "–Robert Ripley.
• "A cat has nine lives"
• "to be on cloud nine"
• "A stitch in time saves nine"
• "found true 9 out of 10 times"
• "possession is nine tenths of the law"
• The word "K-9" pronounces the same ascanineand is used in many US police departments to denote thepolice dogunit. Despite not sounding like the translation of the wordcaninein other languages, many police and military units around the world use the same designation.
• Someone dressed "to the nines" is dressed up as much as they can be.
• In North Americanurban culture,"nine" is a slang word for a9mmpistolorhomicide,the latter from the Illinois Criminal Code for homicide.

Technique

International maritime signal flagfor 9

Playing cardsshowing the 9 of all four suits

• Stanines,a method of scaling test scores, range from 1 to 9.
• There are 9square feetin asquare yard.

Religion and philosophy

Christianity

• In Christianity there are nineFruit of the Holy Spiritwhich followers are expected to have:love,joy,peace,patience,kindness,goodness,faithfulness,gentleness,andself-control.
• The Bible recorded that Christ died at the 9th hour of the day (3 pm).

Islam

There are threeversesthat refer to nine in theQuran.

We surely gave Moses nine clear signs.¹˹You, O Prophet, can˺ ask the Children of Israel. When Moses came to them, Pharaoh said to him, “I really think that you, O Moses, are bewitched.”

— SurahAl-Isra(The Night Journey/Banī Isrāʾīl):101

Note 1: The nine signs ofMosesare: the staff, the hand (both mentioned in SurahTa-Ha20:17-22), famine, shortage of crops, floods, locusts, lice, frogs, and blood (all mentioned in SurahAl-A'raf7:130-133). These signs came as proofs forPharaohand theEgyptians.Otherwise, Moses had some other signs such as water gushing out of the rock after he hit it with his staff, and splitting the sea.

Now put your hand through ˹the opening of˺ your collar, it will come out ˹shining˺ white, unblemished.²˹These are two˺ of nine signs for Pharaoh and his people. They have truly been a rebellious people.”

— SurahAl-Naml(The Ant):12

Note 2: Moses, who was dark-skinned, was asked to put his hand under his armpit. When he took it out it was shining white, but not out of a skin condition like melanoma.

And there were in the city nine ˹elite˺ men who spread corruption in the land, never doing what is right.

— Surah Al-Naml (The Ant):48

• Ramadan,the month of fasting and prayer, is the ninth month of theIslamic calendar.

Other

A nine-pointed star

• Nine, as the largest single-digit number (inbase ten), symbolizes completeness in theBaháʼí Faith.In addition, the word Baháʼ in theAbjad notationhas a value of 9, and a 9-pointed star is used tosymbolize the religion.
• The number 9 is revered in Hinduism and considered a complete, perfected and divine number because it represents the end of a cycle in thedecimalsystem, which originated from the Indian subcontinent as early as3000 BC.
• In Buddhism,Gautama Buddhawas believed to have nine virtues, which he was (1) Accomplished, (2) Perfectly Enlightened, (3) Endowed with knowledge and Conduct or Practice, (4) Well-gone or Well-spoken, (5) the Knower of worlds, (6) the Guide Unsurpassed of men to be tamed, (7) the Teacher of gods and men, (8) Enlightened, and (9) Blessed.
• Important Buddhist rituals usually involve nine monks.
• The first nine days of theHebrew monthofAvare collectively known as "The Nine Days" (Tisha HaYamim), and are a period of semi-mourning leading up toTisha B'Av,the ninth day of Av on which bothTemples in Jerusalemwere destroyed.
• Nine is a significant number inNorse Mythology.Odinhung himself on an ash tree for nine days to learn the runes.
• TheFourth Way Enneagramis one system of knowledge which shows the correspondence between the 9 integers and the circle.
• Tian's Trigram Number, of Feng Shui, inTaoism.

Science

Astronomy

• Before 2006 (when Pluto wasofficially designated as a non-planet), there were nineplanetsin theSolar System.
• Messier objectM9is a magnitude 9.0globular clusterin the constellationOphiuchus.
• TheNew General CatalogueobjectNGC 9,aspiral galaxyin theconstellationPegasus.

Chemistry

• The purity of chemicals (seeNine (purity)).
• Nine is theatomic numberoffluorine.

Physiology

A humanpregnancynormally lasts nine months, the basis ofNaegele's rule.

Psychology

Common terminal digit inpsychological pricing.

See also

• 9 (disambiguation)
• 0.999...
• Cloud Nine
• List of highways numbered 9

Further reading

• Cecil Balmond, "Number 9, the search for the sigma code" 1998, Prestel 2008,ISBN3-7913-1933-7,ISBN978-3-7913-1933-9