Difference between revisions of "9 (number)" - New World Encyclopedia

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:''This article is about the number nine.''
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<!-- New version: {{Number|number=9
 
<!-- New version: {{Number|number=9
 
| <div style="align:center;font-size:1000%;font-family:times;padding: 0.5em 0">9</div>
 
| <div style="align:center;font-size:1000%;font-family:times;padding: 0.5em 0">9</div>
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|-
 
|-
 
| [[numerical prefix|prefix]]es
 
| [[numerical prefix|prefix]]es
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| [[Wiktionary:ennea-|ennea-]] (from [[Greek language|Greek]])  
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| ennea- (from [[Greek language|Greek]])  
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[[Wiktionary:nona-|nona-]] (from [[Latin]])
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nona- (from [[Latin]])
 
|-
 
|-
 
| [[Binary numeral system|Binary]]
 
| [[Binary numeral system|Binary]]
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|}
 
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'''9''' ('''nine''') is a [[number]], [[numeral]], and [[glyph]] that represents the number. It is the [[natural number]]<ref>A natural number is any number that is a positive integer, such as 1, 2, 3, 4, and so forth. Often, the number 0 is also called a natural number.</ref> that follows [[8 (number)|8]] and precedes [[10 (number)|10]]. It is an [[integer]] and a [[cardinal number]], that is, a number that is used for counting.<ref>A cardinal number indicates the quantity of things, but not the order in which they occur. By contrast, ordinal numbers are first, second, third, and so on, indicating their positions in a series.</ref> In addition, it is classified as a [[real number]],<ref>A real number is a number that can be given by a finite or infinite decimal representation. The term "real number" was coined to distinguish it from an "imaginary number." The set of real numbers includes rational and irrational numbers, which can be positive, negative, or zero.</ref> distinguishing it from [[imaginary number]]s.
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'''9''' '''(nine)''' is a [[number]], [[numeral]], and [[glyph]] that represents the number. It is the [[natural number]]<ref>A natural number is any number that is a positive integer, such as 1, 2, 3, 4, and so forth. Often, the number 0 is also called a natural number.</ref> that follows [[8 (number)|8]] and precedes [[10 (number)|10]]. It is an [[integer]] and a [[cardinal number]], that is, a number that is used for counting.<ref>A cardinal number indicates the quantity of things, but not the order in which they occur. By contrast, ordinal numbers are first, second, third, and so on, indicating their positions in a series.</ref> In addition, it is classified as a [[real number]],<ref>A real number is a number that can be given by a finite or infinite decimal representation. The term "real number" was coined to distinguish it from an "imaginary number." The set of real numbers includes rational and irrational numbers, which can be positive, negative, or zero.</ref> distinguishing it from [[imaginary number]]s. Nine is the highest single-digit number in the [[decimal]] system. A group of nine is called an ''ennead''.
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{{toc}}
 
== Evolution of the glyph ==
 
== Evolution of the glyph ==
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According to Georges Ifrah,<ref>Georges Ifrah, ''The Universal History of Numbers: From Prehistory to the Invention of the Computer'' (New York: Wiley, 2000, ISBN 0471393401).</ref> the origin of the 9 integers can be traced to the ancient Indian civilization. These numbers were adopted by subsequent civilizations in conjunction with the [[0 (number)|0]].
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According to Georges Ifrah,<ref>Georges Ifrah. 1985. ''From One to Zero: A Universal History of Numbers.'' New York: Viking. ISBN 0670373958.</ref> the origin of the 9 integers can be traced to the ancient Indian civilization. These numbers were adopted by subsequent civilizations in conjunction with the [[0 (number)|0]].
 
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[[Image:Evo9glyph.svg|360px]]
 
  
 
At first, 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''. Over time, 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.
 
At first, 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''. Over time, 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.
  
 +
[[Image:Evo9glyph.svg|400px|left]]
 
While the shape of the 9 character has an [[ascender]] in most modern [[typeface]]s, in typefaces with [[text figures]] the character usually has a [[descender]], for example, in [[Image:TextFigs196.png]].
 
While the shape of the 9 character has an [[ascender]] in most modern [[typeface]]s, in typefaces with [[text figures]] the character usually has a [[descender]], for example, in [[Image:TextFigs196.png]].
  
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This numeral resembles an inverted ''6''. To disambiguate the two on objects and documents that could be inverted, the 9 has often been underlined (as is done for the 6). Another distinction from the 6 is that it is often handwritten with a straight stem.
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This numeral resembles an inverted ''6.'' To disambiguate the two on objects and documents that could be inverted, the 9 has often been underlined (as is done for the 6). Another distinction from the 6 is that 9 is often handwritten with a straight stem.
  
 
==In mathematics==
 
==In mathematics==
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Since <math>9 = 3^{2^1}</math>, 9 is an [[exponential factorial]].
 
Since <math>9 = 3^{2^1}</math>, 9 is an [[exponential factorial]].
  
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8 and 9 form a [[Ruth-Aaron pair]] under the second definition that counts repeated prime factors as often as they occur.
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Eight and 9 form a [[Ruth-Aaron pair]] under the second definition that counts repeated prime factors as often as they occur.
  
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A [[polygon]] with nine sides is called an [[enneagon]] (technically) or nonagon (in common usage).<ref>Robert Dixon, ''Mathographics''. New York: Courier Dover Publications: 24</ref> A group of nine of anything is called an ennead.
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A [[polygon]] with nine sides is called an [[enneagon]] (technically) or nonagon (in common usage).<ref>Robert Dixon, ''Mathographics'' (New York: Dover Publications, 1991, ISBN 0486266397).</ref> A group of nine of anything is called an ''ennead''.
  
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In [[decimal|base 10]] a number is evenly divisible by nine [[if and only if]] its [[digital root]] is 9.<ref>[[Martin Gardner]], ''A Gardner's Workout: Training the Mind and Entertaining the Spirit''. New York: A. K. Peters (2001): 155</ref> 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:
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In [[decimal|base 10]], a number is evenly divisible by nine [[if and only if]] its [[digital root]] is 9.<ref>Martin Gardner, ''A Gardner's Workout: Training the Mind and Entertaining the Spirit'' (Natick, MA: A.K Peters, 2001, ISBN 1568811209).</ref> 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)
 
* 2 × 9 = 18 (1 + 8 = 9)
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* 35967930-03356799 = 32611131; 3+2+6+1+1+1+3+1 = 18, 1+8 = 9.
 
* 35967930-03356799 = 32611131; 3+2+6+1+1+1+3+1 = 18, 1+8 = 9.
  
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[[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.<ref>Cajori, Florian (1991, 5e) ''A History of Mathematics'', AMS. ISBN 0-8218-2102-4. p.91</ref>
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[[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 twelfth century.<ref>Florian Cajori, ''A History of Mathematics,'' 5th edition (Providence, RI: AMS Chelsea, 1999, ISBN 0821821024), 91.</ref>
  
 
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).
 
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).
  
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Six recurring nines appear in the decimal places 762 through 767 of [[pi]]. This is known as the [[Feynman point]] (see also [http://mathworld.wolfram.com/FeynmanPoint.html MathWorld]).
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Six recurring nines appear in the decimal places 762 through 767 of [[pi]]. This is known as the [[Feynman point]].<ref>[https://mathworld.wolfram.com/FeynmanPoint.html Feynman Point] ''Wolfram Math World''. Retrieved December 16, 2022.</ref>
  
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If an odd [[perfect number]] is of the form 36''k'' + 9, it has at least nine distinct prime factors.<ref>Eyob Delele Yirdaw, "[http://arxiv.org/abs/0804.0152v1 Proving Touchard's Theorem from Euler's Form]" ArXiv preprint.</ref>
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If an odd [[perfect number]] is of the form 36''k'' + 9, it has at least nine distinct prime factors.<ref>Eyob Delele Yirdaw, [https://arxiv.org/abs/0804.0152v1 Proving Touchard's Theorem from Euler's Form] ''ArXiv''. Retrieved October 7, 2022.</ref>
  
 
Nine is the binary complement of number [[6 (number)|six]]:
 
Nine is the binary complement of number [[6 (number)|six]]:
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===List of basic calculations===
 
===List of basic calculations===
  
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;Multiplication
 
{|class="wikitable" style="text-align: center; background: white"
 
{|class="wikitable" style="text-align: center; background: white"
 
|-
 
|-
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!9
 
!9
 
!10
 
!10
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!width="5px"|
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|-
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|<math>9 \times x</math>
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|'''9'''
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|[[18 (number)|18]]
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|[[27 (number)|27]]
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|[[36 (number)|36]]
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|[[45 (number)|45]]
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|[[54 (number)|54]]
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|[[63 (number)|63]]
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|[[72 (number)|72]]
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|[[81 (number)|81]]
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|[[90 (number)|90]]
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|}
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{|class="wikitable" style="text-align: center; background: white"
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|-
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!width="105px"|[[Multiplication]]
 
!11
 
!11
 
!12
 
!12
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!19
 
!19
 
!20
 
!20
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!1000
 
 
|-
 
|-
 
|<math>9 \times x</math>
 
|<math>9 \times x</math>
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|'''9'''
 
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|[[18 (number)|18]]
 
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|[[27 (number)|27]]
 
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|[[36 (number)|36]]
 
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|[[45 (number)|45]]
 
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|[[54 (number)|54]]
 
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|[[63 (number)|63]]
 
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|[[72 (number)|72]]
 
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|[[81 (number)|81]]
 
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|[[90 (number)|90]]
 
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!
 
 
|[[99 (number)|99]]
 
|[[99 (number)|99]]
 
|[[108 (number)|108]]
 
|[[108 (number)|108]]
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|[[171 (number)|171]]
 
|[[171 (number)|171]]
 
|[[180 (number)|180]]
 
|[[180 (number)|180]]
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!
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|}
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{|class="wikitable" style="text-align: center; background: white"
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|-
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!width="105px"|[[Multiplication]]
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!21
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!22
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!23
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!24
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!25
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!width="5px"|
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!50
 +
!100
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!1000
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|-
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|<math>9 \times x</math>
 
|[[189 (number)|189]]
 
|[[189 (number)|189]]
 
|[[198 (number)|198]]
 
|[[198 (number)|198]]
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|}
 
|}
  
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;Division
 
{|class="wikitable" style="text-align: center; background: white"
 
{|class="wikitable" style="text-align: center; background: white"
 
|-
 
|-
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!9
 
!9
 
!10
 
!10
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!width="5px"|
 
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!11
 
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!12
 
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!13
 
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!14
 
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!15
 
 
|-
 
|-
 
|<math>9 \div x</math>
 
|<math>9 \div x</math>
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|1
 
|1
 
|[[0 (number)|0]].9
 
|[[0 (number)|0]].9
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!
 
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|<math>0.\overline{81}</math>
 
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|0.[[75 (number)|75]]
 
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|<math>0.\overline{692307}</math>
 
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|<math>0.6\overline{428571}</math>
 
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|0.6
 
 
|-
 
|-
 
|<math>x \div 9</math>
 
|<math>x \div 9</math>
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|1
 
|1
 
|<math>1.\overline{1}</math>
 
|<math>1.\overline{1}</math>
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!
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|}
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{|class="wikitable" style="text-align: center; background: white"
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|-
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!width="105px"|[[Division (mathematics)|Division]]
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!11
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!12
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!13
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!14
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|-
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|<math>9 \div x</math>
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|<math>0.\overline{81}</math>
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|0.[[75 (number)|75]]
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|<math>0.\overline{692307}</math>
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|<math>0.6\overline{428571}</math>
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|0.6
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|-
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|<math>x \div 9</math>
 
|<math>1.\overline{2}</math>
 
|<math>1.\overline{2}</math>
 
|<math>1.\overline{3}</math>
 
|<math>1.\overline{3}</math>
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|}
 
|}
  
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;Exponentiation
 
{|class="wikitable" style="text-align: center; background: white"
 
{|class="wikitable" style="text-align: center; background: white"
 
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|-
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!9
 
!9
 
!10
 
!10
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!width="5px"|
 
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!11
 
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!12
 
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|<math>9 ^ x\,</math>
 
|<math>9 ^ x\,</math>
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|387420489
 
|387420489
 
|3486784401
 
|3486784401
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!
 
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|31381059609
 
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|282429536481
 
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|2541865828329
 
 
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|<math>x ^ 9\,</math>
 
|<math>x ^ 9\,</math>
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|387420489
 
|387420489
 
|[[1000000000 (number)|1000000000]]
 
|[[1000000000 (number)|1000000000]]
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!
 
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|2357947691
 
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|5159780352
 
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|10604499373
 
 
|}
 
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{|class="wikitable" style="text-align: center; background: white"
 
{|class="wikitable" style="text-align: center; background: white"
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!rowspan="2" width="105px"|[[Radix]]
 
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!1
 
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!5
 
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!10
 
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!15
 
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!20
 
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!25
 
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!30
 
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<!--
 
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!35
 
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!width="105px"|[[Exponentiation]]
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|-
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|rowspan="2"|<math>x_{9} \ </math>
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|<math>9 ^ x\,</math>
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|1
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|31381059609
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|282429536481
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|<math>11_{9} \ </math>
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|2541865828329
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|<math>16_{9} \ </math>
 
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|<math>22_{9} \ </math>
 
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|<math>27_{9} \ </math>
 
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|<math>33_{9} \ </math>
 
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<!--
 
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|<math>32_{11} \ </math>
 
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—>
 
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|<math>44_{9} \ </math>
 
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<!--
 
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|<math>41_{11} \ </math>
 
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—>
 
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|<math>55_{9} \ </math>
 
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|<math>66_{9} \ </math>
 
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|<math>77_{9} \ </math>
 
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|<math>88_{9} \ </math>
 
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|<math>110_{9} \ </math>
 
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|<math>121_{9} \ </math>
 
 
|-
 
|-
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|<math>132_{9} \ </math>
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|<math>x ^ 9\,</math>
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|<math>143_{9} \ </math>
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|2357947691
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|<math>154_{9} \ </math>
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|5159780352
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|<math>165_{9} \ </math>
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|10604499373
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|<math>176_{9} \ </math>
 
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<!--
 
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|<math>136_{11} \ </math>
 
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|<math>145_{11} \ </math>
 
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|<math>154_{11} \ </math>
 
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|<math>163_{11} \ </math>
 
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—>
 
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|<math>242_{9} \ </math>
 
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|<math>307_{9} \ </math>
 
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|<math>615_{9} \ </math>
 
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|<math>1331_{9} \ </math>
 
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|<math>14641_{9} \ </math>
 
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|<math>162151_{9} \ </math>
 
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|<math>1783661_{9} \ </math>
 
 
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=== Chemistry ===
 
=== Chemistry ===
 
* Nine is the [[atomic number]] of [[fluorine]].
 
* Nine is the [[atomic number]] of [[fluorine]].
 +
* An [[alkane]] [[hydrocarbon]] with a chain of nine [[carbon]] atoms is called ''nonane''.
 +
 +
=== Biology ===
 +
* A human [[pregnancy]] normally lasts nine months.
  
 
===Astronomy===
 
===Astronomy===
−
 
 
*Before 2006 (when [[Pluto]] was officially designated a dwarf planet), the [[Solar System]] was said to have nine [[planet]]s.
 
*Before 2006 (when [[Pluto]] was officially designated a dwarf planet), the [[Solar System]] was said to have nine [[planet]]s.
−
*The [[Saros]] number<ref>[http://eclipse.gsfc.nasa.gov/SEsaros/SEsaros0-180.html Solar Eclipses of Saros 0 to 180.] NASA Eclipse Web Site. Retrieved August 20, 2008.</ref> 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.
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*The [[Saros]] number of the [[solar eclipse]] series that began on February 6, 2568 B.C.E. and ended on April 4, 1252 B.C.E.. The duration of Saros series 9 was 1316.20 years, and it contained 74 solar eclipses.<ref>NASA, [https://eclipse.gsfc.nasa.gov/SEsaros/SEsaros009.html Saros Series 9] Saros Series Catalog of Solar Eclipses. Retrieved October 7, 2022.</ref>
−
*The Saros number<ref>[http://sunearth.gsfc.nasa.gov/eclipse/LEsaros/LEsaros1-175.html Lunar Eclipses of Saros Series 1 to 175.] NASA Eclipse Web Site. Retrieved August 20, 2008.</ref> 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.
+
*The Saros number of the [[lunar eclipse]] series that began on June 26, 2501 B.C.E. and ended on September 5, 1167 B.C.E.. The duration of Saros series 9 was 1334.23 years, and it contained 75 lunar eclipses.<ref>NASA, [https://eclipse.gsfc.nasa.gov/LEsaros/LEsaros009.html Saros Series 9] Catalog of Lunar Eclipse Saros Series. Retrieved October 7, 2022.</ref>
  
 
===Probability===
 
===Probability===
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In [[probability]], the '''nine''' is a [[logarithmic measure]] of probability of an event, defined as the negative of the base-[[10 (number)|10]] [[logarithm]] of the probability of the event's [[Probability axioms|complement]].
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* In [[probability]] calculations, the '''nine''' is a [[logarithmic measure]] of probability of an event, defined as the negative of the base-[[10 (number)|10]] [[logarithm]] of the probability of the event's [[Probability axioms|complement]]. For example, an event that is 99 percent likely to occur has an unlikelihood of 1 percent or 0.01, which amounts to −log<sub>10</sub>&nbsp;0.01&nbsp;=&nbsp;2 nines of probability.
−
For example, an event that is 99% likely to occur has an unlikelihood of 1% or 0.01, which amounts to −log<sub>10</sub>&nbsp;0.01&nbsp;=&nbsp;2 nines of probability.
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* [[0 (number)|Zero]] probability gives zero nines (−log<sub>10</sub>&nbsp;1&nbsp;=&nbsp;0).
−
[[0 (number)|Zero]] probability gives zero nines (−log<sub>10</sub>&nbsp;1&nbsp;=&nbsp;0).
+
* The purity of chemicals, the effectivity of processes, the [[availability]] of systems, and so on, can similarly be expressed in nines. For example, "five nines" (99.999 percent) availability implies a total [[downtime]] of no more than five minutes per year.
−
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]].
 
  
−
==Physiology==
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==In technology==
−
A human [[pregnancy]] normally lasts nine months.
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[[Image:Seven-segment 9 alt.svg|50px|right]]
 +
[[Image:Seven-segment 9.svg|50px|right]]
 +
* [[ISO 9]] is the standard of the [[International Organization for Standardization]] for the transliteration of [[Cyrillic]] characters into [[Latin]] characters.
 +
* In the [[Rich Text Format]] specification, 9 is the language code for the [[English language]].
 +
* In [[computer]] [[system administration]], [[uptime]] (a [[Measurement|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 percent reliability, which translates to a total downtime of no longer than five minutes per year.
  
 
==In religion==
 
==In religion==
−
*Important Buddhist rituals usually involve nine monks.
 
−
*The first nine days of the [[Hebrew calendar|Hebrew month]] of [[Av (month)|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 [[Temple in Jerusalem|Temples in Jerusalem]] were destroyed.
 
−
*Nine, as the highest single-digit number (in [[decimal|base ten]]), symbolizes completeness in the [[Bahá'í Faith]]. In addition, the word Bahá' in the [[Abjad numerals|Abjad notation]] has a value of 9, and a 9-pointed star is used to [[Bahá'í symbols|symbolize]] the religion.
 
−
*Nine is a significant number in [[Norse Mythology]]. [[Odin]] hung himself on an ash tree for nine days to learn the runes.
 
−
*[[Jesus]] healed ten [[lepers]]; nine did not even thank him.
 
−
*[[Anton LaVey]] applied the number to [[Satan]].
 
  
−
==As lucky or unlucky number, Chinese culture==
+
=== Judaism ===
−
Nine (九 [[pinyin]] jiǔ) is considered a good [[Numbers in Chinese culture|number in Chinese culture]] because it sounds the same as the word "longlasting" ([[久]] pinyin jiǔ){{Fact|date=April 2008}}. The Japanese consider 9 to be unlucky, however, because it sounds similar to the Japanese word for "pain" or "distress" ([[苦]] [[Kunrei-shiki|kunrei]] ku){{Fact|date=April 2008}}. The fear of the number nine is [[enneaphobia]].
+
* The first nine days of the [[Hebrew calendar|Hebrew month]] of [[Av (month)|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 [[Temple in Jerusalem|Temples in Jerusalem]] were destroyed.
  
−
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&times;13 scales, 9&times;9 being [[yin and yang|yang]] (masculine, or bad influence) and 9&times;4 being yin (feminine, or good influence).<ref>{{cite book | title = Myths of China And Japan | author = Donald Alexander Mackenzie | url = http://books.google.com/books?id=vzbeLy4TBa4C&pg=PA46&ots=J6kKXff4wC&dq=chinese+dragon+scales+yin+36&ei=Jte_Ru-eApimoALp9_yPDQ&sig=r3ONvB8j3UsHjqSl8rDpH5MggKM | publisher = Kessinger | year = 2005 | isbn = 1417964294 }}</ref>
+
=== Christianity ===
−
The dragon often symbolizes the [[Emperor of China|Emperor]], and the number nine can be found in many ornaments in the [[Forbidden City]].
+
* [[Jesus]] healed ten [[lepers]], nine of whom did not even thank him.
−
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&times;9 plates.
+
* In the [[Catholic Church]], a '''novena''' is a [[devotion]] consisting of [[prayer]]s said (most typically) on nine successive days, asking to obtain special graces.
 +
* In the Catholic faith, there are 9 choirs of holy angels.
  
−
==In music==
+
=== Bahá'í ===
−
*There is a rapper named [[Tech N9ne]] whose name stands for "Tech Nine" because 9 is the number of completion
+
* Nine, as the highest single-digit number (in [[decimal|base ten]]), symbolizes completeness in the [[Bahá'í Faith]].
 +
* The word Bahá' in the [[Abjad numerals|Abjad notation]] has a value of 9.
 +
* A 9-pointed star is used to [[Bahá'í symbols|symbolize]] the Bahá'í religion.
  
−
*In [[music theory]] a [[ninth]] is the ninth [[note]] of a [[scale (music)|musical scale]] or the [[interval (music)|interval]] between the first note and the ninth. A [[extended chord|ninth chord]] is a chord with a ninth.
+
=== Buddhism ===
 +
*Important Buddhist rituals usually involve nine monks.
  
−
*In [[Western classical music|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 [[Symphony No. 10 (Beethoven)|Tenth Symphony]] unfinished, is regarded by the superstition as the first victim of the curse.
+
==As lucky or unlucky number, Chinese culture==
 +
Nine (九 [[pinyin]] jiǔ) is considered a good [[Numbers in Chinese culture|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-shiki|kunrei]] ku). Fear of the number nine is called [[enneaphobia]].
  
−
*Bands with the number nine in their name include [[Nine]], [[Stroke 9]], [[Nine Days]], [[Nine Inch Nails]] and [[Alice Nine]].
+
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&times;13 scales, 9&times;9 being [[yin and yang|yang]] (masculine, or bad influence) and 9&times;4 being yin (feminine, or good influence).<ref>Donald Alexander Mackenzie, ''Myths of China and Japan'' (Whitefish, MT: Kessinger, ISBN 1417964294).</ref>
  
−
*[[The Beatles]] released a song called "[[Revolution 9]]" which appears on ''[[The Beatles (album)|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 "[[Number Nine Dream|#9 Dream]]."
+
The dragon often symbolizes the [[Emperor of China|Emperor]], and the number nine can be found in many ornaments in the [[Forbidden City]].
  
−
*Composer [[Maury Yeston]] adapted [[Federico Fellini]]'s [[8½]] for [[Broadway theatre|Broadway]] as the [[Musical theater|musical]] [[Nine (musical)|Nine]], which won several [[Tony Awards]] in 1982, and was successfully revived in 2003 starring [[Antonio Banderas]].
+
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&times;9 plates.
−
 
 
−
*''9'' is also the name of various albums, including ''[[9 (Mercyful Fate album)|9]]'' by [[Mercyful Fate]], released in 1999, and ''[[9 (Public Image Limited album)|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.
 
−
 
 
−
*Dublin pop-punk band [[Nine IX Lives]] formed in 2005 and use 'IX' in their logo.
 
  
 +
==In music==
 +
*In [[music theory]], a [[ninth]] is the ninth [[note]] of a [[scale (music)|musical scale]] or the [[interval (music)|interval]] between the first note and the ninth. A [[extended chord|ninth chord]] is a chord with a ninth.
 +
*In [[Western 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 [[Symphony No. 10 (Beethoven)|Tenth Symphony]] unfinished, is regarded by the superstition as the first victim of the curse.
 
*A group of nine voices or instruments is called a nonet.
 
*A group of nine voices or instruments is called a nonet.
  
 
==In sports==
 
==In sports==
−
 
 
*[[Nine ball]] is the standard professional pocket [[billiards]] variant played in the United States.
 
*[[Nine ball]] is the standard professional pocket [[billiards]] variant played in the United States.
−
* In association [[soccer|football]] (soccer) the centre-forward/striker traditionally (since at least the fifties) wears the number 9 shirt. The number has been worn by a great number of famous centre-forwards and strikers including, [[Ronaldo]], [[Wayne Rooney]], [[Ruud van Nistelrooy]], [[Luca Toni]], [[Mia Hamm]], [[Ally McCoist]], [[Alan Shearer]], [[Hernán Crespo]], [[Fernando Torres]] and [[Samuel Eto'o]].
+
* In association [[soccer|football]] (soccer), the center-forward/striker traditionally (since at least the fifties) wears the number 9 shirt.
−
* 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.
 
* 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 [[Rugby union|rugby union]], nine is the number generally worn by the [[scrum half]].
−
* In [[ice hockey]] the number 9 is one of the most prestigious sweater numbers, having been worn by legends like [[Maurice Richard]], [[Bobby Hull]], [[Gordie Howe]], and [[Mike Modano]]. It was also worn, doubled as 99, by the great [[Wayne Gretzky]].
+
*In [[Rugby league|rugby league]], nine is the number generally worn by the [[Rugby league positions#Hooker|hooker]].
−
*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.
 
−
*The number worn by [[Roy Hobbs]] in the movie [[The Natural]].
 
−
*In [[Rugby union|rugby union]], the number generally worn by the [[scrum half]].
 
−
*In [[Rugby league|rugby league]], the number generally worn by the [[Rugby league positions#Hooker|hooker]].
 
−
*The number worn by [[Rashard Lewis]] of the [[Orlando Magic]].
 
−
*The number worn by both [[Michael Jordan]] and [[Dwyane Wade]] in the [[United States at the Olympics|U.S. Olympics Team]].
 
−
*Number worn by [[Lisa Leslie]] currently on the [[Los Angeles Sparks]].
 
−
 
 
−
==In technology==
 
−
[[Image:Seven-segment 9 alt.svg|25px|right]]
 
−
[[Image:Seven-segment 9.svg|25px|right]]
 
−
* [[ISO 9]] is the [[International Organization for Standardization|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 [[Measurement|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 traced back to the Rig Veda of ancient India, can also be seen to speak of the 9, via theosophical addition (3 + 6 + 0 = 9).<ref>[http://www.quantumyoga.org/theosophical%20addition.html Theosophical Addition.] Retrieved July 29, 2008.</ref>
 
  
 
==In other fields==
 
==In other fields==
−
[[Image:ICS Niner.svg|right|thumb|100px|[[International maritime signal flag]] for 9]]
+
[[Image:ICS Niner.svg|right|thumb|350px|[[International maritime signal flag]] for 9]]
−
[[Image:9 playing cards.jpg|thumb|250px|[[Playing card]]s showing the 9 of all four suits]]
+
[[Image:9 playing cards.jpg|thumb|400px|[[Playing card]]s showing the 9 of all four suits]]
−
*In the catholic faith there are 9 choirs of holy angels.
+
* The [[Enneagram]] is one system of knowledge which shows the correspondence between the 9 integers and the circle.  
−
*Nine is the highest single-digit number in the decimal system.  
 
 
*In the [[NATO phonetic alphabet]], the digit 9 is called "[[Novenine]]."
 
*In the [[NATO phonetic alphabet]], the digit 9 is called "[[Novenine]]."
−
*[[Nine Network|Channel 9]], an [[Australia]]n [[free-to-air]] [[television]] station
 
 
*Nine judges sit on the [[United States Supreme Court]].
 
*Nine judges sit on the [[United States Supreme Court]].
 
*The word "K-9" pronounces the same as ''canine'' and is used in many [[United States|U.S.]] police departments to denote the unit working with [[police dog]].
 
*The word "K-9" pronounces the same as ''canine'' and is used in many [[United States|U.S.]] police departments to denote the unit working with [[police dog]].
−
*The ordinal adjective is ''ninth''.
 
 
*There are nine circles of Hell in Dante's "Divine Comedy."
 
*There are nine circles of Hell in Dante's "Divine Comedy."
 
*[[Stanine]]s are measured on a scale of 1 to 9.
 
*[[Stanine]]s are measured on a scale of 1 to 9.
−
*The name of the area called ''[[Kowloon]]'' in [[Hong Kong]] literally means: ''nine [[Chinese dragon|dragons]]''.
+
*Nine is a significant number in [[Norse Mythology]]. [[Odin]] hung himself on an ash tree for nine days to learn the runes.
 +
*The name of the area called ''[[Kowloon]]'' in [[Hong Kong]] literally means: ''Nine [[Chinese dragon|dragons]]''.
 
*Someone dressed "to the nines" is dressed up as much as they can be.
 
*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.
+
*There is a saying that a [[cat]] has nine lives.
−
*[[Nine rank system]]
+
*The [[Nine Worthies]] were nine historical, scriptural, mythological or semi-legendary figures who, in [[the Middle Ages]], were believed to personify the ideals of [[chivalry]].
−
*''[[The Nine Chapters on the Mathematical Art]]''
+
*[[Nine Unknown Men]] were, in occult legend, custodians of the sciences of the world since ancient times.
−
*[[Nine Worthies]]
+
* Many mathematical magic tricks have a connection to the number nine, that because every multiplication of nine adds up to nine, any number minus the sum of all digits becomes a multiplication of nine, and any three digit number minus the same number in reverse becomes a multiplication of nine.
−
* [[9: The Last Resort]] was a 1995 computer game.
 
−
* ''9'' is the name of Shane Acker's [[9_(film)|short film]], and its [[9_(2008_film)|2008 adaption]].
 
−
* [[Seven of Nine]], [[fictional character]] from the ''[[Star Trek]]'' universe
 
−
* ''[[Magic: The Gathering]]'' 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 (TV series)|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 Nines]]'' is a film written and directed by [[John August]], starring [[Ryan Reynolds]], [[Hope Davis]] and [[Melissa McCarthy]]. It premiered at the 2007 [[Sundance Film Festival]], and is now out on [[DVD]].
 
−
* 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.
 
−
* In Middle Earth, there are nine rings of power given to men, and consequently, nine ringwraiths.
 
−
* "A [[cat-o'-nine-tails]] suggests perfect punishment and atonement."—[[Robert Ripley]].
 
−
* [[Wally Cleaver]]'s locker number was #9.
 
−
* 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<ref>{{cite book | title = Women's Poetry of the 1930s: A Critical Anthology | author = Jane Dowson | year = 1996 | publisher = Routledge | isbn = 0415130956 | url = http://books.google.com/books?id=fVTQPI3ZIHcC&pg=RA1-PA103&dq=nine-bright-shiners+ridler&as_brr=3&ei=wb8KR7fiOo—ogKi2f3SCA&ie=ISO-8859-1&sig=Q_mL_ekiNw9q_SQZCpdxyUTGB9g#PRA1-PA103,M1 }}</ref> and a 1988 fiction book by Anthea Fraser;<ref>{{cite book | title = The Nine Bright Shiners | author = Anthea Fraser | publisher = Doubleday | year = 1988 | isbn = 0385243235 | url =  }}</ref> the name derives from "a very curious old semi-pagan, semi-Christian" song.<ref>{{cite book | title = Recollections of an Eton Colleger, 1898-1902 | author = Charles Herbert Malden | publisher = Spottiswoode | year = 1905 | url = http://books.google.com/books?id=EKB9T4pPcfkC&pg=PA182&dq=nine-bright-shiners&ei=n7wKR7-YH56KpwKI_4nTCA#PPA180,M1 }}</ref>
 
−
* "Nine" is a song title on the [[Neurosis (band)|Neurosis]] album ''[[Given to the Rising]]''.
 
−
* Many mathematical magic tricks have a connection to the number nine, that because every multiplication of nine adds up to nine, any number minus the sum of all digits becomes a multiplication of nine, and any three digit number minus the same number in reverse becomes a multiplication of nine
 
−
*Nine was the client number of [[Eliot Spitzer]] at [[Eliot Spitzer prostitution scandal|The Emperor's Club]].
 
−
* The character Cirno from the [[Touhou Project|Touhou series]] is often called "nine," "⑨," "circle-nine," or "nineball," because in the game manual for "Phantasmagoria of Flower View," she was labeled {{Nihongo|''(9) Idiot''|⑨ バカ|⑨　baka}}.<ref>Cirno - TouhouWiki http://www.pooshlmer.com/touhouwiki/index.php/Cirno#Fun_Facts</ref>
 
−
*A group of nine is called an ''ennead''.
 
  
 
== See also ==
 
== See also ==
−
 
+
* [[Arithmetic]]
 +
* [[Integer]]
 
* [[Number]]
 
* [[Number]]
  
Line 576: Line 469:
  
 
==References==
 
==References==
 +
* Cajori, Florian. ''A History of Mathematics'', 5th edition. Providence, RI: AMS Chelsea, 1999. ISBN 0821821024
 +
* Dixon, Robert. ''Mathographics''. New York: Dover Publications, 1991. ISBN 0486266397
 +
* Flegg, Graham. ''Numbers: Their History and Meaning.'' Mineola, NY: Dover Publications, 2002. ISBN 0486421651
 +
* Gardner, Martin. ''A Gardner's Workout: Training the Mind and Entertaining the Spirit''. Natick, MA: A.K Peters, 2001. ISBN 1568811209
 +
* Higgins, Peter M. ''Number Story: From Counting to Cryptography.'' London: Copernicus, 2008. ISBN 978-1848000001
 +
* Ifrah, Georges. ''The Universal History of Numbers: From Prehistory to the Invention of the Computer.'' Translated by David Bellos et al. New York: Wiley, 2000. ISBN 0471393401
 +
* Mackenzie, Donald Alexander. ''Myths of China and Japan''. Whitefish, MT: Kessinger. ISBN 1417964294
 +
* McLeish, John. ''The Story of Numbers: How Mathematics Has Shaped Civilization.'' New York: Fawcett Columbine, 1994. ISBN 0449909387
 +
* Menninger, Karl. ''Number Words and Number Symbols: A Cultural History of Numbers.'' New York: Dover Publications, 1992. ISBN 0486270963
 +
* Wells, D. G. ''The Penguin Dictionary of Curious and Interesting Numbers.'' London: Penguin Books, 1998. ISBN 0140261494
  
−
* Flegg, Graham. 2002. ''Numbers: Their History and Meaning.'' Mineola, NY: Dover Publications. ISBN 0486421651.
+
== External links ==
−
 
+
All links retrieved June 13, 2023.
−
* Higgins, Peter M. 2008. ''Number Story: From Counting to Cryptography.'' London: Copernicus. ISBN 978-1848000001.
+
* [https://ezinearticles.com/?The-Power-of-the-Number-Nine---Is-It-Just-Magic-Or-Is-It-Real&id=322023 The Power of the Number Nine - Is It Just Magic or Is It Real?] By Ann LaRoche, ''Ezine articles''.
−
 
+
* [https://www.ridingthebeast.com/numbers/nu9.php Properties of the number 9]
−
* Ifrah, Georges. 2000. ''The Universal History of Numbers: From Prehistory to the Invention of the Computer.'' Translated by David Bellos et al. New York: Wiley. ISBN 0471393401.
 
−
 
 
−
* McLeish, John. 1994. ''The Story of Numbers: How Mathematics Has Shaped Civilization.'' New York: Fawcett Columbine. ISBN 0449909387.
 
−
 
 
−
* Menninger, Karl. 1992. ''Number Words and Number Symbols: A Cultural History of Numbers.'' New York: Dover Publications. ISBN 0486270963.
 
  
−
* Wells, D. G. 1998. ''The Penguin Dictionary of Curious and Interesting Numbers.'' Rev. ed. London, UK: Penguin Books. ISBN 0140261494.
 
  
 
[[Category:Physical sciences]]
 
[[Category:Physical sciences]]

Latest revision as of 06:48, 13 June 2023

9

0 1 2 3 4 5 6 7 8 9 >>

List of numbers — Integers

0 10 20 30 40 50 60 70 80 90 >>

Cardinal 9
nine
Ordinal 9th
ninth
Numeral system novenary
Factorization
Divisors 1, 3, 9
Amharic ፱
Roman numeral IX
Roman numeral (Unicode) Ⅸ, ⅸ
prefixes ennea- (from Greek)

nona- (from Latin)

Binary 1001
Octal 11
Duodecimal 9
Hexadecimal 9
Arabic-Indic numeral ٩
Armenian numeral Թ
Bengali ৯
Chinese/Japanese numeral 九
玖 (formal writing)
Devanāgarī ९
Greek numeral θ´
Hebrew numeral ט (Tet)
Tamil numeral ௯
Khmer ៩
Thai numeral ๙

9 (nine) is a number, numeral, and glyph that represents the number. It is the natural number[1] that follows 8 and precedes 10. It is an integer and a cardinal number, that is, a number that is used for counting.[2] In addition, it is classified as a real number,[3] distinguishing it from imaginary numbers. Nine is the highest single-digit number in the decimal system. A group of nine is called an ennead.

Evolution of the glyph

According to Georges Ifrah,[4] the origin of the 9 integers can be traced to the ancient Indian civilization. These numbers were adopted by subsequent civilizations in conjunction with the 0.

At first, 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. Over time, 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.

Evo9glyph.svg

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, for example, in TextFigs196.png.

This numeral resembles an inverted 6. To disambiguate the two on objects and documents that could be inverted, the 9 has often been underlined (as is done for the 6). Another distinction from the 6 is that 9 is often handwritten with a straight stem.

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 (32). It has a unique aliquot sum 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 second composite member of the 3-aliquot tree.

There are nine Heegner numbers.

Since , 9 is an exponential factorial.

Eight 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).[5] 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.[6] 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, known as long ago as the twelfth century.[7]

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.[8]

If an odd perfect number is of the form 36k + 9, it has at least nine distinct prime factors.[9]

Nine is the binary complement of number six: 

9 = 1001
6 = 0110

In numeral systems

Base Numeral system
2 binary 1001
3 ternary 100
4 quaternary 21
5 quinary 14
6 senary 13
7 septenary 12
8 octal 11
9 novenary 10
over 9 (decimal, hexadecimal) 9

List of basic calculations

Multiplication
Multiplication 1 2 3 4 5 6 7 8 9 10
9 18 27 36 45 54 63 72 81 90
Multiplication 11 12 13 14 15 16 17 18 19 20
99 108 117 126 135 144 153 162 171 180
Multiplication 21 22 23 24 25 50 100 1000
189 198 207 216 225 450 900 9000
Division
Division 1 2 3 4 5 6 7 8 9 10
9 4.5 3 2.25 1.6 1.5 1.125 1 0.9
1
Division 11 12 13 14 15
0.75 0.6
Exponentiation
Exponentiation 1 2 3 4 5 6 7 8 9 10
9 81 729 6561 59049 531441 4782969 43046721 387420489 3486784401
1 512 19683 262144 1953125 10077696 40353607 134217728 387420489 1000000000
Exponentiation 11 12 13
31381059609 282429536481 2541865828329
2357947691 5159780352 10604499373

In science

Chemistry

Biology

  • A human pregnancy normally lasts nine months.

Astronomy

  • Before 2006 (when Pluto was officially designated a dwarf planet), the Solar System was said to have nine planets.
  • The Saros number of the solar eclipse series that began on February 6, 2568 B.C.E. and ended on April 4, 1252 B.C.E. The duration of Saros series 9 was 1316.20 years, and it contained 74 solar eclipses.[10]
  • The Saros number of the lunar eclipse series that began on June 26, 2501 B.C.E. and ended on September 5, 1167 B.C.E. The duration of Saros series 9 was 1334.23 years, and it contained 75 lunar eclipses.[11]

Probability

  • In probability calculations, 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 percent likely to occur has an unlikelihood of 1 percent or 0.01, which amounts to −log10 0.01 = 2 nines of probability.
  • Zero probability gives zero nines (−log10 1 = 0).
  • The purity of chemicals, the effectivity of processes, the availability of systems, and so on, can similarly be expressed in nines. For example, "five nines" (99.999 percent) availability implies a total downtime of no more than five minutes per year.

In technology

Seven-segment 9 alt.svg
Seven-segment 9.svg
  • ISO 9 is the standard of the International Organization for Standardization for the transliteration of Cyrillic characters into Latin characters.
  • In the Rich Text Format specification, 9 is the language code for the English language.
  • 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 percent reliability, which translates to a total downtime of no longer than five minutes per year.

In religion

Judaism

  • 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.

Christianity

  • Jesus healed ten lepers, nine of whom did not even thank him.
  • In the Catholic Church, a novena is a devotion consisting of prayers said (most typically) on nine successive days, asking to obtain special graces.
  • In the Catholic faith, there are 9 choirs of holy angels.

Bahá'í

  • Nine, as the highest single-digit number (in base ten), symbolizes completeness in the Bahá'í Faith.
  • The word Bahá' in the Abjad notation has a value of 9.
  • A 9-pointed star is used to symbolize the Bahá'í religion.

Buddhism

  • Important Buddhist rituals usually involve nine monks.

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). Fear of the number nine is called enneaphobia.

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).[12]

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 Western 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.
  • A group of nine voices or instruments is called a nonet.

In sports

  • Nine ball is the standard professional pocket billiards variant played in the United States.
  • In association football (soccer), the center-forward/striker traditionally (since at least the fifties) wears the number 9 shirt.
  • In baseball, nine represents the right fielder's position.
  • In rugby union, nine is the number generally worn by the scrum half.
  • In rugby league, nine is the number generally worn by the hooker.

In other fields

International maritime signal flag for 9
Playing cards showing the 9 of all four suits
  • The Enneagram is one system of knowledge which shows the correspondence between the 9 integers and the circle.
  • In the NATO phonetic alphabet, the digit 9 is called "Novenine."
  • 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.
  • There are nine circles of Hell in Dante's "Divine Comedy."
  • Stanines are measured on a scale of 1 to 9.
  • Nine is a significant number in Norse Mythology. Odin hung himself on an ash tree for nine days to learn the runes.
  • 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.
  • There is a saying that a cat has nine lives.
  • The Nine Worthies were nine historical, scriptural, mythological or semi-legendary figures who, in the Middle Ages, were believed to personify the ideals of chivalry.
  • Nine Unknown Men were, in occult legend, custodians of the sciences of the world since ancient times.
  • Many mathematical magic tricks have a connection to the number nine, that because every multiplication of nine adds up to nine, any number minus the sum of all digits becomes a multiplication of nine, and any three digit number minus the same number in reverse becomes a multiplication of nine.

See also

Notes

  1. ↑ A natural number is any number that is a positive integer, such as 1, 2, 3, 4, and so forth. Often, the number 0 is also called a natural number.
  2. ↑ A cardinal number indicates the quantity of things, but not the order in which they occur. By contrast, ordinal numbers are first, second, third, and so on, indicating their positions in a series.
  3. ↑ A real number is a number that can be given by a finite or infinite decimal representation. The term "real number" was coined to distinguish it from an "imaginary number." The set of real numbers includes rational and irrational numbers, which can be positive, negative, or zero.
  4. ↑ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer (New York: Wiley, 2000, ISBN 0471393401).
  5. ↑ Robert Dixon, Mathographics (New York: Dover Publications, 1991, ISBN 0486266397).
  6. ↑ Martin Gardner, A Gardner's Workout: Training the Mind and Entertaining the Spirit (Natick, MA: A.K Peters, 2001, ISBN 1568811209).
  7. ↑ Florian Cajori, A History of Mathematics, 5th edition (Providence, RI: AMS Chelsea, 1999, ISBN 0821821024), 91.
  8. ↑ Feynman Point Wolfram Math World. Retrieved December 16, 2022.
  9. ↑ Eyob Delele Yirdaw, Proving Touchard's Theorem from Euler's Form ArXiv. Retrieved October 7, 2022.
  10. ↑ NASA, Saros Series 9 Saros Series Catalog of Solar Eclipses. Retrieved October 7, 2022.
  11. ↑ NASA, Saros Series 9 Catalog of Lunar Eclipse Saros Series. Retrieved October 7, 2022.
  12. ↑ Donald Alexander Mackenzie, Myths of China and Japan (Whitefish, MT: Kessinger, ISBN 1417964294).

References
ISBN links support NWE through referral fees

  • Cajori, Florian. A History of Mathematics, 5th edition. Providence, RI: AMS Chelsea, 1999. ISBN 0821821024
  • Dixon, Robert. Mathographics. New York: Dover Publications, 1991. ISBN 0486266397
  • Flegg, Graham. Numbers: Their History and Meaning. Mineola, NY: Dover Publications, 2002. ISBN 0486421651
  • Gardner, Martin. A Gardner's Workout: Training the Mind and Entertaining the Spirit. Natick, MA: A.K Peters, 2001. ISBN 1568811209
  • Higgins, Peter M. Number Story: From Counting to Cryptography. London: Copernicus, 2008. ISBN 978-1848000001
  • Ifrah, Georges. The Universal History of Numbers: From Prehistory to the Invention of the Computer. Translated by David Bellos et al. New York: Wiley, 2000. ISBN 0471393401
  • Mackenzie, Donald Alexander. Myths of China and Japan. Whitefish, MT: Kessinger. ISBN 1417964294
  • McLeish, John. The Story of Numbers: How Mathematics Has Shaped Civilization. New York: Fawcett Columbine, 1994. ISBN 0449909387
  • Menninger, Karl. Number Words and Number Symbols: A Cultural History of Numbers. New York: Dover Publications, 1992. ISBN 0486270963
  • Wells, D. G. The Penguin Dictionary of Curious and Interesting Numbers. London: Penguin Books, 1998. ISBN 0140261494

External links

All links retrieved June 13, 2023.

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