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9 (number)

Cardinal 9
nine
Ordinal 9th
ninth
Numeral system novenary
Factorization <math> 3^2 </math>
Divisors 1, 3, 9
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
Chinese numeral 九
玖 (formal writing)
Eastern Arabic-Indic (Persian and Urdu) numeral ۹
Greek numeral θ´
Hebrew numeral ט (Tet)
Indian (Hindi/Devanagari) numeral ९
Japanese numeral 九
玖 (formal writing)
Tamil numeral ௯
Thai numeral ๙
9 (number):Wiktionary-logo-en
Look up nine in
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For other senses of this word, see 9 (disambiguation).

9 (nine) is the natural number following 8 and preceding 10.


Contents

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.

Since <math>9 = 3^{2^1}</math>, 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:

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.

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).

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 −log10 0.01 = 2 nines of probability.Zero probability gives zero nines (−log10 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.

Six recurring nines appear in the decimal places 762 through 767 of pi. This is known as the Feynman point (see also MathWorld).

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

One billion is a number that contains nine zeros.

List of basic calculations

Multiplication12345678910111213141516171819202122232425501001000
<math>9 \times x</math>9182736455463728190991081171261351441531621711801891982072162254509009000
Division123456789101112131415
<math>9 \div x</math>94.532.251.61.5<math>1.\overline{2}8571\overline{4}</math>1.12510.9<math>0.\overline{8}\overline{1}</math>0.75<math>0.\overline{6}9230\overline{7}</math><math>0.6\overline{4}2857\overline{1}</math>0.6
<math>x \div 9</math><math>0.\overline{1}</math><math>0.\overline{2}</math><math>0.\overline{3}</math><math>0.\overline{4}</math><math>0.\overline{5}</math><math>0.\overline{6}</math><math>0.\overline{7}</math><math>0.\overline{8}</math>1<math>1.\overline{1}</math><math>1.\overline{2}</math><math>1.\overline{3}</math><math>1.\overline{4}</math><math>1.\overline{5}</math><math>1.\overline{6}</math>
Exponentiation123456789101112
<math>9 ^ x\,</math>981729656159049531441478296943046721387420489348678440131381059609282429536481
<math>x ^ 9\,</math>15121968326214419531251007769640353607134217728387420489100000000023579476915159780352
Radix151015202530405060708090100
1101201301401502002505001000100001000001000000
<math>x_{9} \ </math>15<math>11_{9} \ </math><math>16_{9} \ </math><math>22_{9} \ </math><math>27_{9} \ </math><math>33_{9} \ </math><math>44_{9} \ </math><math>55_{9} \ </math><math>66_{9} \ </math><math>77_{9} \ </math><math>88_{9} \ </math><math>110_{9} \ </math><math>121_{9} \ </math>
<math>132_{9} \ </math><math>143_{9} \ </math><math>154_{9} \ </math><math>165_{9} \ </math><math>176_{9} \ </math><math>242_{9} \ </math><math>307_{9} \ </math><math>615_{9} \ </math><math>1331_{9} \ </math><math>14641_{9} \ </math><math>162151_{9} \ </math><math>1783661_{9} \ </math>

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]

9 (number):Image:Evo9glyph.png

In the beginning, various Indians wrote 9 similar to the modern closing question mark, but dotless. 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 to 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, and 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.

In fonts with text figures, 9 usually has a descender, for example, 9 (number):Image:TextFigs196.png.

See also: Hindu-Arabic numeral system.

In science

Astronomy

In literature

In religion

In mythology

Germanic

Norse mythology and Germanic mythology recognized nine realms of existence. Eight of the realms were embodiments of opposites: fire and ice, heaven and hell, creation and destruction, and light and darkness. These realms all converged on the center realm, where humans lived out their lives.

Egyptian

In Egyptian mythology, there are nine major gods and goddesses (see also Ennead).The ancient Egyptians believed that a person had to earn the right to enter the afterlife. Before an individual could pass into the next realm, nine great gods known collectively as the Ennead had to judge his worthiness.

Greek

In Greek mythology, nine goddesses called the Muses were responsible for inspiring the art of musicians, artists, and writers.

Mayan

In Maya mythology, nine levels existed in the underworld. Metnal, the ninth level, was a place of eternal darkness, cold, and suffering.

Celtic

One of the most famous legends in Celtic mythology tells the story of nine magical hazel trees at the center of the Otherworld. They hang over the Well of Wisdom and drop their nuts into it, importing wisdom and inspiration to all who drink from the water or eat the salmon of the river.

In astrology, the ninth sign of the Zodiac is Sagittarius, identified by the Greeks as a centaur. Centaurs are magical creatures known for their skills as archers, philosophers, and predictors of the future.

As lucky or unlucky number

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.

In Thai, the word for nine, 'gao', is the same as the verb for 'to develop or progress'.

In music

In sports

In technology

9 (number):9DN2
9 (number):9DN

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]

In other fields

9 (number):International maritime signal flag for 9
Enlarge
International maritime signal flag for 9

References

  1. From One to Zero (1985), Georges Ifra, Viking, ISBN 0-670-37395-8.

See also

Historical years

9 A.D., 9 B.C., 1909, 2009, etc.

Categories


Integers

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