9


← 8 9 10 →
-1 0 1 2 3 4 5 6 7 8 9
Cardinalnine
Ordinal9th
(ninth)
Numeral systemnonary
Factorization32
Divisors1, 3, 9
Greek numeralΘ´
Roman numeralIX, ix
Greek prefixennea-
Latin prefixnona-
Binary10012
Ternary1003
Octal118
Duodecimal912
Hexadecimal916
Amharic
Arabic, Kurdish, Persian, Sindhi, Urdu٩
Armenian numeralԹ
Bengali
Chinese numeral九, 玖
Devanāgarī
Greek numeralθ´
Hebrew numeralט
Tamil numerals
Khmer
Telugu numeral
Thai numeral

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

Contents

Mathematics


9 is a composite number, its proper divisors being 1 and 3. It is 3 times 3 and hence the third square number. Nine is a Motzkin number.[1] 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 (p2) and the first that is odd. All subsequent squares of this form are odd.

Since 9 = 321, 9 is an exponential factorial.[2]

A polygon with nine sides is called a nonagon or enneagon.[3] 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.[4] 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:

There are other interesting patterns involving multiples of nine:

This works for all the multiples of 9. n = 3 is the only other n > 1 such that a number is divisible by n if and only if its digital root is divisible by n. 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:

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.[5]

Six recurring nines appear in the decimal places 762 through 767 of π, 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. 274/999 = 0.274274274274...)

There are nine Heegner numbers.[6]

List of basic calculations


Multiplication 1 2 3 4 5 6 7 8 9 10 20 25 50 100 1000
9 × x 9 18 27 36 45 54 63 72 81 90 180 225 450 900 9000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
9 ÷ x 9 4.5 3 2.25 1.8 1.5 1.285714 1.125 1 0.9 0.81 0.75 0.692307 0.6428571 0.6
x ÷ 9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1 1.1 1.2 1.3 1.4 1.5 1.6
Exponentiation 1 2 3 4 5 6 7 8 9 10
9x 9 81 729 6561 59049 531441 4782969 43046721 387420489 3486784401
x9 1 512 19683 262144 1953125 10077696 40353607 134217728 387420489 1000000000
Radix 1 5 10 15 20 25 30 40 50 60 70 80 90 100
110 120 130 140 150 200 250 500 1000 10000 100000 1000000
x9 1 5 119 169 229 279 339 449 559 669 779 889 1109 1219
1329 1439 1549 1659 1769 2429 3079 6159 13319 146419 1621519 17836619

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 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 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 typefaces, 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


Commerce


Culture and mythology


Indian culture

Nine is a number that appears often in Indian culture and mythology. Some instances are enumerated below.

Chinese culture

Ancient Egypt

European culture

Greek mythology

Mesoamerican mythology

Aztec mythology

Mayan mythology

Anthropology


Idioms

Society

Technique

Literature


Organizations


Places and thoroughfares


Religion and philosophy


Science


Astronomy

Chemistry

Physiology

A human pregnancy normally lasts nine months, the basis of Naegele's rule.

Sports


Technology


Music


See also


References


  1. ^ "Sloane's A001006 : Motzkin numbers" . The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  2. ^ "Sloane's A049384 : a(0)=1, a(n+1) = (n+1)^a(n)" . The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
  3. ^ Robert Dixon, Mathographics. New York: Courier Dover Publications: 24
  4. ^ Martin Gardner, A Gardner's Workout: Training the Mind and Entertaining the Spirit. New York: A. K. Peters (2001): 155
  5. ^ Cajori, Florian (1991, 5e) A History of Mathematics, AMS. ISBN 0-8218-2102-4. p.91
  6. ^ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 93
  7. ^ "Lucky Number Nine, Meaning of Number 9 in Chinese Culture" . www.travelchinaguide.com. Retrieved 2021-01-15.
  8. ^ Donald Alexander Mackenzie (2005). Myths of China And Japan . Kessinger. ISBN 1-4179-6429-4.
  9. ^ Jane Dowson (1996). Women's Poetry of the 1930s: A Critical Anthology . Routledge. ISBN 0-415-13095-6.
  10. ^ Anthea Fraser (1988). The Nine Bright Shiners . Doubleday. ISBN 0-385-24323-5.
  11. ^ Charles Herbert Malden (1905). Recollections of an Eton Colleger, 1898-1902 . Spottiswoode. p. 182 . nine-bright-shiners.
  12. ^ "Web site for NINE: A Journal of Baseball History & Culture" . Archived from the original on 2009-11-04. Retrieved 20 February 2013.

Further reading









Categories: Integers | 9 (number) | Superstitions about numbers




Information as of: 07.06.2021 03:40:43 CEST

Source: Wikipedia (Authors [History])    License : CC-BY-SA-3.0

Changes: All pictures and most design elements which are related to those, were removed. Some Icons were replaced by FontAwesome-Icons. Some templates were removed (like “article needs expansion) or assigned (like “hatnotes”). CSS classes were either removed or harmonized.
Wikipedia specific links which do not lead to an article or category (like “Redlinks”, “links to the edit page”, “links to portals”) were removed. Every external link has an additional FontAwesome-Icon. Beside some small changes of design, media-container, maps, navigation-boxes, spoken versions and Geo-microformats were removed.

Please note: Because the given content is automatically taken from Wikipedia at the given point of time, a manual verification was and is not possible. Therefore LinkFang.org does not guarantee the accuracy and actuality of the acquired content. If there is an Information which is wrong at the moment or has an inaccurate display please feel free to contact us: email.
See also: Legal Notice & Privacy policy.