'9' ('nine') is the
natural number following
8 and preceding
10.
In mathematics
Nine is a
composite number, its proper
divisors being
1 and
3. It is 3 times 3 and hence the third
square number. 9 is a
Motzkin number. It is the first composite
lucky number.
9 is the second non-unitary square prime (3^2). It has a unique
aliquot sum σ(n)
4 which is itself a square prime. 9 is the only square prime with an aliquot sum of the same form. The
aliquot sequence of 9 has 5 members (9,4,3,1,0) this number being the 2nd
composite member of the 3-aliquot tree.
There are nine
Heegner numbers.
Since
, 9 is an
exponential factorial.
8 and 9 form a
Ruth-Aaron pair under the second definition that counts repeated prime factors as often as they occur.
A
polygon with nine sides is called an
enneagon (technically) or nonagon (in common usage). A group of nine of anything is called an ennead.
In
base 10 a number is evenly divisible by nine
if and only if its
digital root is 9. That is, if you multiply nine by any whole number (except zero), and repeatedly add the digits of the answer until it's just one digit, you will end up with 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))
★ (Exception) 0 x 9 = 0 (0 is not equal to 9)(though it can be considered -1 in the tens place and 10 in the ones place(10-1=9))
The only other number with this property is
three. In
base N, the
divisors of N − 1 have this property. Another consequence of 9 being 10 − 1, 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 evenly 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.
Subtracting two base-10 positive integers that are transpositions of each other yields a number that is a whole multiple of nine. Some examples:
★ 41-14 = 27. The digital root of 27 is 2+7 = 9.
★ 36957930-35967930 = 990000, which is obviously a multiple of nine.
This works regardless of the number of digits that are transposed. For example, the largest transposition of 35967930 is 99765330 (all digits in descending order) and its smallest transposition is 03356799 (all digits in ascending order); subtracting pairs of these numbers produces:
★ 99765330-35967930 = 63797400; 6+3+7+9+7+4+0+0 = 36, 3+6 = 9.
★ 99765330-03356799 = 96408531; 9+6+4+0+8+5+3+1 = 36.
★ 35967930-03356799 = 32611131; 3+2+6+1+1+1+3+1 = 18, 1+8 = 9.
Casting out nines is a quick way of testing the calculations of sums, differences, products, and quotients of integers.
Every prime in a
Cunningham chain of the first kind with a length of 4 or greater is congruent to 9 mod 10 (the only exception being the chain 2, 5, 11, 23, 47).
Six recurring nines appear in the decimal places 762 through 767 of
pi. This is known as the
Feynman point (see also
MathWorld).
If an odd
perfect number is of the form 36k+9, it has at least nine distinct prime factors.
Nine is the binary complement of number
six:
9 = 1001
6 = 0110
In numeral systems
One billion is a number that contains nine zeros.
List of basic calculations
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Evolution of the glyph
According to Georges Ifra, the origin of the 9 integers can be attributed to the ancient Indian civilization, and was adopted by subsequent civilizations in conjunction with the
0.
[1]
Evo9glyph.png
In the beginning, various Indians wrote 9 similar to the modern closing question mark without the bottom dot. The Kshtrapa, Andhra and Gupta started curving the bottom vertical line coming up with a
3-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 @ character 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 9 character has an
ascender in most modern
typefaces, in typefaces with
text figures the character usually has a
descender, as, for example, in
TextFigs196.png
.
See also:
Hindu-Arabic numeral system.
In science
★ Nine is the
atomic number of
fluorine.
Astronomy
★ Before 2006 (when Pluto was officially designated as a non-planet), there were nine
planets in the
solar system.
★
Messier object M9 is a magnitude 9.0
globular cluster in the constellation
Ophiuchus.
★ The
New General Catalogue object NGC 9, a
spiral galaxy in the
constellation Pegasus
★ The
Saros number of the
solar eclipse series which began on
-2568 February 6 and ended on
-1252 April 4. The duration of Saros series 9 was 1316.2 years, and it contained 74 solar eclipses.
★ The Saros
number of the
lunar eclipse series which began on
-2501 June 26 and ended on
-1149 September 16. The duration of Saros series 9 was 1352.2 years, and it contained 76 lunar eclipses.
Probability
In
probability, the 'nine' is a
logarithmic measure of probability of an event, defined as the negative of the base-
10 logarithm of the probability of the event's
complement.
For example, an event that is 99% likely to occur has an unlikelihood of 1% or 0.01, which amounts to −log
10 0.01 = 2 nines of probability.
Zero probability gives zero nines (−log
10 1 = 0).
The purity of chemicals (see
Nine (purity)), the effectivity of processes, the
availability of systems etc. can similarly be expressed in nines. For example, "five nines" (99.999%) availability implies a total
downtime of no more than five minutes per year. This measure can be confusing, a fact which is discussed in the
myth of the nines.
In religion
★ Important Buddhist rituals usually involve nine monks.
★ The first nine days of the
Hebrew month of
Av 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 were destroyed.
★ Nine, as the highest single-digit number (in
base ten), symbolizes completeness in the
Bahá'í Faith. In addition, the word Bahá' in the
Abjad notation has a value of 9, and a 9-pointed star (
Enneagram) is used to
symbolize the religion.
As lucky or unlucky number, Chinese culture
Nine (九
pinyin jiǔ) is considered a good
number in Chinese culture because it sounds the same as the word "longlasting" (久
pinyin jiǔ). The Japanese consider 9 to be unlucky, however, because it sounds similar to the Japanese word for "pain" or "distress" (苦
kunrei ku).
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 9×13 scales, 9×9 being
yang (masculine, or bad influence) and 9×4 being
yin (feminine, or good influence).
[2]
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 81=9×9 plates.
In music
★ In
music theory a
ninth is the ninth
note of a
musical scale or the
interval between the first note and the ninth. A
ninth chord is a chord with a ninth.
★ In
classical music the
curse of the ninth refers to the superstition that a composer who writes a ninth
symphony will die soon. Beethoven, who left his
Tenth Symphony unfinished, is regarded by the superstition as the first victim of the curse.
★ Bands with the number nine in their name include
Nine,
Stroke 9,
Nine Days, and
Nine Inch Nails.
★
The Beatles released a song called "
Revolution 9" which appears on ''
The White Album'' (more properly known as ''
The Beatles)''; its principal vocal feature is a voice repeating, ''"Number nine...number nine...number nine..."''
John Lennon, the primary composer of "Revolution 9", also released a solo recording entitled "
#9 Dream". The Beatles also released a song called "One After 909" in 1970, although it was recorded in 1969, and Lennon and McCartney had worked on it since the very early days. Lennon is known to have felt a connection with the number 9. Both he and his son,
Sean were born on October 9
th. Also, John died on the 9
th (UK Time). Ironically, of all the Beatles' singles that made the U.S. Top 10 in ''Billboard'', all peak positions were covered except #9.
★ The first single of
Leeds-based band
¡Forward, Russia! was called ''Nine'' and was released in April 2005. The title did not carry any symbolism, but followed the then "tradition" of the band for naming their songs in the order in which they were written.
★ Composer
Maury Yeston adapted
Federico Fellini's
8½ for
Broadway as the
musical Nine, which won several
Tony Awards in 1982, and was successfully revived in 2003 starring
Antonio Banderas.
★
Roger Miller had a hit with the song "Engine Engine Number Nine."
★ ''9'' is also the name of various albums, including ''
9'' by
Mercyful Fate, released in
1999, and ''
9'' by
Public Image Limited.
Fairport Convention also released an album with the number for a title. Irish singer/songwriter
Damien Rice released an album called 9 in November 2006.
★ In
urban culture, 'nine' is a
slang word for a
9mm pistol or
homicide, the latter from the Illinois Criminal Code for homicide.
★ Rock band
Linkin Park released a song in their album
Meteora called "Figure.09"
★ In hip-hop, the rapper
Nine, who got his big break in late 1993 as a featured guest on First Funkmaster Flex and the Ghetto Celebs, released 2 albums (''Nine Livez'' in 1995 and Cloud Nine'' in 1996) and is now making a comeback.
[1]
In sports
★
Nine ball is the standard professional pocket
billiards variant played in the United States.
★ In
football the centre-forward/striker commonly wears the number 9 shirt. The number was made most famous by
Ronaldo and has also been used by other famous strikers such as
Hernan Crespo and
Samuel Eto'o.
★ The car number of the 1988
NASCAR Nextel Cup championship-winning team, when
Bill Elliott won the title. He used this number again from
2001 to
2003.
Kasey Kahne has driven the 9 car since
2004.
★ In
baseball, nine represents the
right fielder's position.
★ The retired uniform numbers of former baseball players
Ted Williams and
Roger Maris.
Reggie Jackson also wore 9 with the
Oakland A's for nine years and is now retired.
★ In
ice hockey the number 9 is one of the most prestigious sweater numbers, having been worn by legends like
Maurice Richard,
Bobby Hull, and
Gordie Howe. It was also worn, doubled as 99, by the great
Wayne Gretzky.
★ In
association football players that wear the number 9 are key players in the offense and likely to score many goals.
★ Famed
football(soccer) player
Ronaldo (Brazilian men's national team) wears #9.
★ The
San Francisco 49ers are sometimes referred to as the "niners".
★ The most notable NFL quarterbacks to ever wear the number 9 are
Drew Brees of the
New Orleans Saints,
Carson Palmer of the
Cincinnati Bengals,
Tony Romo of the
Dallas Cowboys and
Steve McNair of the
Baltimore Ravens.
★ The number worn by current
NBA player
Tony Parker of the
San Antonio Spurs, MVP of the 2007
NBA Finals.
In technology
★
ISO 9 is the
ISO's standard for the transliteration of
Cyrillic characters into
Latin characters
★ 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.
★ In
computer system administration,
uptime, a
measure of the
time a
computer system has been up and running, is sometimes measured in "nines"—that is, the number of "9" digits in the percentage of time the computer is normally running. For example, "five nines" means 99.999% reliability, which translates to a total downtime of no longer than five minutes per year.
Nine and the circle
The
Enneagram is one system of knowledge which shows the correspondence between the 9 integers and the circle. The 360 degrees of the circle, which can be trace back to the Rig Veda of ancient India, can also be seen to speak of the 9, via theosophical addition (3 + 6 + 0 = 9)
[2]. [2]
In other fields
★ Nine is the highest single-digit number in the decimal system.
★ In the
NATO phonetic alphabet, the digit 9 is called "
niner".
★
Channel 9, an
Australian free-to-air television station
★ Nine judges sit on the
United States Supreme Court.
★ The word "K-9" pronounces the same as ''canine'' and is used in many
U.S. police departments to denote the unit working with
police dog.
★ The ordinal adjective is ''ninth''.
★
Stanines are measured on a scale of 1 to 9.
★ The name of the area called ''
Kowloon'' in
Hong Kong literally means: ''nine
dragons''.
★ Someone dressed "to the nines" is dressed up as much as they can be.
★
Nine Lives Cat Food got its name from the legend that a
cat has nine lives.
★
Nine rank system
★ ''
The Nine Chapters on the Mathematical Art''
★
Nine Worthies
★ was a
1995 computer game.
★
Seven of Nine,
fictional character from the ''
Star Trek'' universe
★ '' has a set of nine rare cards, widely regarded as overpowered, known as the
Power Nine.
★
Nine West is a popular brand for clothing.
★ The number of hostages in the TV show ''
The Nine''
★
Ninth Avenue is a major avenue in Manhattan.
★
Nine Unknown Men are, in occult legend, the custodians of the sciences of the world since ancient times.
★ The 9, a show on the Internet, hosted by
Maria Sansone.
The 9
★ ''
The Nines'' is a film written and directed by
John August, starring
Ryan Reynolds,
Hope Davis and
Melissa McCarthy. It is scheduled to premiere at the 2007
Sundance Film Festival.
★ In the game of Craps, 9 is known as the center field because it is in the middle of the seven numbers on the field bet.
★ "A
cat-o'-nine-tails suggests perfect punishment and atonement." --
Robert Ripley.
★
Wally Cleaver's locker number was #9.
References
1. From One to Zero: A Universal History of Numbers, Georges Ifrah, , , Viking, 1985,
2. Myths of China And Japan, Donald Alexander Mackenzie, , , Kessinger, 2005,
See also
★
Enneagram
Historical years
'9 A.D.',
9 B.C.,
1909,
2009, etc.
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