9 (nine) is the natural number
following and preceding .
9 is a composite number
, its proper divisor
s being and . It is 3 times 3 and hence the third square number
. Nine is a Motzkin number
. It is the first composite lucky number
, along with the first composite odd number and only single-digit composite odd number.
9 is the only positive perfect power
that is one more than another positive perfect power, by Mihăilescu's Theorem
9 is the highest single-digit number in the decimal system
. It is the second non-unitary square prime
of the form (''p''2
) and the first that is odd. All subsequent squares of this form are odd.
Since , 9 is an exponential factorial
with nine sides is called a nonagon
or enneagon. A group of nine of anything is called an ennead.
In base 10
, a positive number is divisible by 9 if and only if
its digital root
is 9. That is, if any natural number
is multiplied by 9, and the digits of the answer are repeatedly added until it is just one digit, the sum will be nine:
*2 × 9 = 18 (1 + 8 = 9)
*3 × 9 = 27 (2 + 7 = 9)
*9 × 9 = 81 (8 + 1 = 9)
*121 × 9 = 1089 (1 + 0 + 8 + 9 = 18; 1 + 8 = 9)
*234 × 9 = 2106 (2 + 1 + 0 + 6 = 9)
*578329 × 9 = 5204961 (5 + 2 + 0 + 4 + 9 + 6 + 1 = 27; 2 + 7 = 9)
*482729235601 × 9 = 4344563120409 (4 + 3 + 4 + 4 + 5 + 6 + 3 + 1 + 2 + 0 + 4 + 0 + 9 = 45; 4 + 5 = 9)
There are other interesting patterns involving multiples of nine:
*12345679 × 9 = 111111111
*12345679 × 18 = 222222222
*12345679 × 81 = 999999999
This works for all the multiples of 9. is the only other such that a number is divisible by ''n'' if and only if its digital root is divisible by ''n''. In base-''N''
, the divisor
s of have this property. Another consequence of 9 being , is that it is also a Kaprekar number
The difference between a base-10 positive integer and the sum of its digits is a whole multiple of nine. Examples:
*The sum of the digits of 41 is 5, and 41 − 5 = 36. The digital root of 36 is 3 + 6 = 9, which, as explained above, demonstrates that it is divisible by nine.
*The sum of the digits of 35967930 is 3 + 5 + 9 + 6 + 7 + 9 + 3 + 0 = 42, and 35967930 − 42 = 35967888. The digital root of 35967888 is 3 + 5 + 9 + 6 + 7 + 8 + 8 + 8 = 54, 5 + 4 = 9.
Casting out nines
is a quick way of testing the calculations of sums, differences, products, and quotients of integers known as long ago as the 12th century.
Six recurring nines appear in the decimal places 762 through 767 of
, see Six nines in pi
If dividing a number by the amount of 9s corresponding to its number of digits, the number is turned into a repeating decimal
. (e.g. )
There are nine Heegner number
List of basic calculations
Evolution of the Arabic digit
In the beginning
, various Indians wrote a digit 9 similar in shape to the modern closing question mark
without the bottom dot. The Kshatrapa, Andhra and Gupta started curving the bottom vertical line coming up with a -look-alike. 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 lowercase ''a''. 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 an ascender
in most modern typeface
s, in typefaces with text figures
the character usually has a descender
, as, for example, in .
The modern digit resembles an inverted ''6''. To disambiguate the two on objects and documents that can be inverted, they are often underlined. Another distinction from the 6 is that it is sometimes handwritten with two strokes and a straight stem, resembling a raised lower-case letter q.
Alphabets and codes
*In the NATO phonetic alphabet
, the digit 9 is called "Niner".
*Five-digit produce PLU codes
that begin with 9 are organic
*Common terminal digit in psychological pricing
Culture and mythology
Nine is a number that appears often in Indian culture
and mythology. Some instances are enumerated below.
are attested in Indian astrology
*In the Vaisheshika
branch of Hindu philosophy
, there are nine universal substances or elements: Earth
, and Mind
is a nine-day festival dedicated to the nine
forms of Durga
, meaning "nine jewels" may also refer to Navaratnas
– accomplished courtiers, Navratan
– a kind of dish, or a form of architecture
*In Indian aesthetics
, there are nine kinds of Rasa
*Nine ( pinyin
jiǔ) is considered a good number in Chinese culture
because it sounds the same as the word "long-lasting" ( pinyin
*Nine is strongly associated with the Chinese 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 – 81 yang
(masculine, heavenly) and 36 yin
(feminine, earthly). All three numbers are multiples of 9 (, , ) as well as having the same digital root
*The dragon often symbolizes the Emperor
, and the number nine can be found in many ornaments in the Forbidden City
*The circular altar platform (''Earthly Mount'') of the Temple of Heaven
has 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 having
*The name of the area called ''Kowloon
'' in Hong Kong literally means: ''nine dragons
*The nine-dotted line
() delimits certain island claims by China
in the South China Sea.
*The nine-rank system
was a civil service nomination system used during certain Chinese dynasties.
*9 Points of the Heart
) / Heart Master (Immortality
) Channels in Traditional Chinese Medicine
*The nine bows
is a term used in Ancient Egypt to represent the traditional enemies of Egypt.
is a group of nine Egyptian deities, who, in some versions of the Osiris myth
, judged whether Horus
should inherit Egypt.
*The Nine Worthies
are nine historical, or semi-legendary figures who, in the Middle Ages, were believed to personify the ideals of chivalry.
*In Norse mythology
, the universe is divided into nine worlds
which are all connected by the world tree Yggdrasil
*In Norse mythology
as well, the number nine is associated with Odin
, as that is how many days he hung from the world tree Yggdrasil
before attaining knowledge of the runes
*The nine Muse
s in Greek mythology are Calliope
(epic poetry), Clio
(erotic poetry), Euterpe
(lyric poetry), Melpomene
(comedy), and Urania
*It takes nine days (for an anvil) to fall from heaven to earth, and nine more to fall from earth to Tartarus
labored for nine days and nine nights for Apollo
, according to the Homeric Hymn to Delian Apollo
* The Lords of the Night
, is a group of nine deities who each ruled over every ninth night forming a calendrical cycle
the underworld in Aztec mythology, consists of nine levels.
* The Mayan underworld Xibalba
consists of nine levels.
* El Castillo
the Mayan step-pyramid in Chichén Itzá
, consists of nine steps. It is said that this was done to represent the nine levels of Xibalba
*"to go the whole nine yards-"
suggests 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 as ''canine'' and is used in many US police departments to denote the police dog
unit. Despite not sounding like the translation of the word ''canine'' in 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 American urban culture
, "nine" is a slang word for a 9mm pistol
, the latter from the Illinois Criminal Code for homicide.
*''The 9 on Yahoo!
'', hosted by Maria Sansone
, was a daily video compilation show, or vlog, on Yahoo! featuring the nine top "web finds" of the day.
*Nine justices sit on the United States Supreme Court
s showing the 9 of all four suits]]
s, a method of scaling test scores, range from 1 to 9.
*There are 9 square feet
in a square yard
*There are nine circles of Hell
in Dante's ''Divine Comedy
*The Nine Bright Shiners
, characters in Garth Nix's Old Kingdom trilogy
. ''The Nine Bright Shiners'' was a 1930s book of poems by Anne Ridler and a 1988 fiction book by Anthea Fraser; the name derives from "a very curious old semi-pagan, semi-Christian" song.
*''The Nine Tailors
'' is a 1934 mystery novel
by British writer Dorothy L. Sayers
, her ninth featuring sleuth Lord Peter Wimsey
*Nine Unknown Men
are, in occult legend, the custodians of the sciences of the world since ancient times.
*In J. R. R. Tolkien
, there are nine rings of power given to men, and consequently, nine ringwraiths
. Additionally, The Fellowship of the Ring
consists of nine companions.
*In ''Lorien Legacies
'' there are nine Garde sent to Earth.
*Number Nine is a character in ''Lorien Legacies
*In the series ''A Song of Ice and Fire
'', there are nine regions of Westeros (the Crownlands, the North, the Riverlands, the Westerlands, the Reach, the Stormlands, the Vale of Arryn, the Iron Islands and Dorne). Additionally, there is a group of nine city-states in western Essos known collectively as the Free Cities (Braavos, Lorath, Lys, Myr, Norvos, Pentos, Qohor, Tyrosh and Volantis).
*In ''The Wheel of Time
'' series, Daughter of the Nine Moons is the title given to the heir to the throne of Seanchan, and the Court of the Nine Moons serves as the throne room of the Seanchan rulers themselves. Additionally, the nation of Illian is partially governed by a body known as the Council of Nine, and the flag of Illian displays nine golden bees on it. Furthermore, in the Age of Legends, the Nine Rods of Dominion were nine regional governors who administered individual areas of the world under the ruling world government.
*Divine Nine – The National Pan-Hellenic Council
(NPHC) is a collaborative organization of nine historically African American, international Greek-lettered fraternities and sororities.
Places and thoroughfares
*List of highways numbered 9
is a major avenue in Manhattan.
has 9 provinces
Religion and philosophy
*Nine, as the highest single-digit number (in base ten
), symbolizes completeness in the Baháʼí Faith
. In addition, the word Baháʼ in the Abjad notation
has a value of 9, and a 9-pointed star is used to symbolize 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 the decimal
system, which originated from the Indian subcontinent as early as 3000 BC
*In Buddhism, Gautama Buddha
was 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 the Hebrew month
are collectively known as "The Nine Days" (''Tisha HaYamim''), and are a period of semi-mourning leading up to Tisha B'Av
, the ninth day of Av on which both Temples in Jerusalem
*Nine is a significant number in Norse Mythology
hung himself on an ash tree for nine days to learn the runes.
*The Fourth Way Enneagram
is one system of knowledge which shows the correspondence between the 9 integers and the circle.
*In the Christian angelic hierarchy
there are 9 choirs of angels.
, the month of fasting and prayer, is the ninth month of the Islamic calendar
*Tian's Trigram Number, of Feng Shui, in Taoism
*In Christianity there are nine Fruit of the Holy Spirit
which followers are expected to have: love
, and self-control
*Before 2006 (when Pluto was officially designated as a non-planet
), there were nine planet
s in the solar system
*Messier object M9
is a magnitude 9.0 globular cluster
in the constellation Ophiuchus
*The New General Catalogue
, a spiral galaxy
in the constellation Pegasus
*The purity of chemicals (see Nine (purity)
*Nine is the atomic number
A human pregnancy
normally lasts nine months, the basis of Naegele's rule
thumb|right|200px|Billiards: A rack
_with_the_no._9_ball_at_the_center.html" style="text-decoration: none;"class="mw-redirect" title="Rack (billiards)">rack with the no. 9 ball at the center">Rack (billiards)">rack with the no. 9 ball at the center
is the standard professional pocket billiards
variant played in the United States.
*In association football
(soccer), the centre-forward/striker traditionally (since at least the fifties) wears the number 9 shirt.
**There are nine players on the field including the pitcher.
**There are nine innings in a standard game.
**9 represents the right fielder
**''NINE: A Journal of Baseball History and Culture'', published by the University of Nebraska Press
*In rugby league
, the jersey number assigned to the hooker
in most competitions. (An exception is the Super League
, which uses static squad numbering.)
*In rugby union
, the number worn by the starting scrum-half
is the ISO
's standard for the transliteration of Cyrillic
characters into Latin
*In the Rich Text Format
specification, 9 is the language code for the English language
. All codes for regional variants of English are congruent to 9 mod 256.
*The seven-segment display
allows the number 9 to be constructed two ways, either with a hook at the end of its stem or without one. Most LCD
calculators use the former, but some VFD
models use the latter.
Limited (owner othe9.com
is a company in the video-game industry, including former ties to the extremely popular MMORPG World of Warcraft
", a sound collage which appears on The Beatles' eponymous 1968 album ''The Beatles'' (aka ''The White Album'')
, prominently features a loop of a man's voice repeating the phrase "Number nine".
*There are 9 semitones in a Major 6th
interval in music.
*There was a superstition
among some notable classical music composers that they would die after completing their ninth symphony. Some composers who died after composing their ninth symphony include Ludwig van Beethoven
, Anton Bruckner
, Antonin Dvorak
and Gustav Mahler
*List of highways numbered 9
*Cecil Balmond, "Number 9, the search for the sigma code" 1998, Prestel 2008, ,
Category:Superstitions about numbers