9

Last updated

8 9 10
−1 0 1 2 3 4 5 6 7 8 9
Cardinal nine
Ordinal 9th
(ninth)
Numeral system nonary
Factorization 32
Divisors 1,3,9
Greek numeral Θ´
Roman numeral IX, ix
Greek prefix ennea-
Latin prefix nona-
Binary 10012
Ternary 1003
Senary 136
Octal 118
Duodecimal 912
Hexadecimal 916
Amharic
Arabic, Kurdish, Persian, Sindhi, Urdu ٩
Armenian numeral Թ
Bengali
Chinese numeral 九, 玖
Devanāgarī
Greek numeral θ´
Hebrew numeral ט
Tamil numerals
Khmer
Telugu numeral
Thai numeral
Malayalam
Babylonian numeral 𒐝
Egyptian hieroglyph 𓐂
Morse code ____.

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

Contents

Evolution of the Hindu–Arabic digit

Evo9glyph.svg

Circa 300 BC, as part of the Brahmi numerals, 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. [1] How the numbers got to their Gupta form is open to considerable debate. 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 TextFigs196.png .

The form of the number nine (9) could possibly derived from the Arabic letter waw , in which its isolated form (و) resembles the number 9.

Seven-segment 9.svg

The modern digit resembles an inverted 6. To disambiguate the two on objects and labels that can be inverted, they are often underlined. It is sometimes handwritten with two strokes and a straight stem, resembling a raised lower-case letter q, which distinguishes it from the 6. Similarly, in seven-segment display, the number 9 can be constructed either with a hook at the end of its stem or without one. Most LCD calculators use the former, but some VFD models use the latter.

Mathematics

9 is the fourth composite number, and the first odd composite number. 9 is also a refactorable number. [2]

Casting out nines is a quick way of testing the calculations of sums, differences, products, and quotients of integers in decimal, a method known as long ago as the 12th century. [3]

If an odd perfect number exists, it will have at least nine distinct prime factors. [4]

Non-intersecting chords between four points on a circle MotzkinChords4.svg
Non-intersecting chords between four points on a circle

9 is the sum of the cubes of the first two non-zero positive integers which makes it the first cube-sum number greater than one. [5] A number that is 4 or 5 modulo 9 cannot be represented as the sum of three cubes. [6]

Four concentric magic circles with 9 in the center (by Yang Hui), where numbers on each circle and diameter around the center generate a magic sum of 138. Yang Hui magic circle.svg
Four concentric magic circles with 9 in the center (by Yang Hui), where numbers on each circle and diameter around the center generate a magic sum of 138.

There are nine Heegner numbers, or square-free positive integers that yield an imaginary quadratic field whose ring of integers has a unique factorization, or class number of 1. [7]

Geometry

A polygon with nine sides is called a nonagon. [8] A regular nonagon can be constructed with a regular compass, straightedge, and angle trisector. [9]

The lowest number of squares needed for a perfect tiling of a rectangle is 9. [10]

9 is the largest single-digit number in the decimal system.

List of basic calculations

Multiplication 123456789101112131415162025501001000
9 × x9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144 180 225 450 900 9000
Division 123456789101112131415
9 ÷ x94.532.251.81.51.2857141.12510.90.810.750.6923070.64285710.6
x ÷ 90.10.20.30.40.50.60.70.811.11.21.31.41.51.6
Exponentiation 12345678910
9x9817296561590495314414782969430467213874204893486784401
x91 512 1968326214419531251007769640353607134217728387420489 1000000000

Alphabets and codes

Culture and mythology

Indian culture

Nine is a number that appears often in Indian culture and mythology. [11] Some instances are enumerated below.

Chinese culture

Ancient Egypt

European culture

Greek mythology

Mesoamerican mythology

Aztec mythology

Mayan mythology

Australian culture

The Pintupi Nine, a group of 9 Aboriginal Australian women who remained unaware of European colonisation of Australia and lived a traditional desert-dwelling life in Australia's Gibson Desert until 1984.

Anthropology

Idioms

Technique

International maritime signal flag for 9 ICS Niner.svg
International maritime signal flag for 9
Playing cards showing the 9 of all four suits 9 playing cards.jpg
Playing cards showing the 9 of all four suits

Religion and philosophy

Christianity

Islam

There are three verses that refer to nine in the Quran.

We surely gave Moses nine clear signs.1 ˹You, O Prophet, can˺ ask the Children of Israel. When Moses came to them, Pharaoh said to him, “I really think that you, O Moses, are bewitched.”

Surah Al-Isra (The Night Journey/Banī Isrāʾīl):101 [21]

Note 1: The nine signs of Moses are: the staff, the hand (both mentioned in Surah Ta-Ha 20:17-22), famine, shortage of crops, floods, locusts, lice, frogs, and blood (all mentioned in Surah Al-A'raf 7:130-133). These signs came as proofs for Pharaoh and the Egyptians. Otherwise, Moses had some other signs such as water gushing out of the rock after he hit it with his staff, and splitting the sea.

Now put your hand through ˹the opening of˺ your collar, it will come out ˹shining˺ white, unblemished.2 ˹These are two˺ of nine signs for Pharaoh and his people. They have truly been a rebellious people.”

Surah Al-Naml (The Ant):12 [22]

Note 2: Moses, who was dark-skinned, was asked to put his hand under his armpit. When he took it out it was shining white, but not out of a skin condition like melanoma.

And there were in the city nine ˹elite˺ men who spread corruption in the land, never doing what is right.

Surah Al-Naml (The Ant):48 [23]

Other

A nine-pointed star Bahai star.svg
A nine-pointed star

Science

Astronomy

Chemistry

Physiology

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

Psychology

Common terminal digit in psychological pricing.

See also

Related Research Articles

A palindromic number is a number that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis. The term palindromic is derived from palindrome, which refers to a word whose spelling is unchanged when its letters are reversed. The first 30 palindromic numbers are:

12 (twelve) is the natural number following 11 and preceding 13. Twelve is a superior highly composite number, divisible by the numbers from 1 to 4, and 6.

33 (thirty-three) is the natural number following 32 and preceding 34.

69 is the natural number following 68 and preceding 70. An odd number and a composite number, 69 is divisible by 1, 3, 23 and 69.

81 (eighty-one) is the natural number following 80 and preceding 82.

31 (thirty-one) is the natural number following 30 and preceding 32. It is a prime number.

36 (thirty-six) is the natural number following 35 and preceding 37.

64 (sixty-four) is the natural number following 63 and preceding 65.

91 (ninety-one) is the natural number following 90 and preceding 92.

109 is the natural number following 108 and preceding 110.

100 or one hundred is the natural number following 99 and preceding 101.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

<span class="mw-page-title-main">Cube (algebra)</span> Number raised to the third power

In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 23 = 8 or (x + 1)3.

500 is the natural number following 499 and preceding 501.

700 is the natural number following 699 and preceding 701.

It is:

126 is the natural number following 125 and preceding 127.

<span class="mw-page-title-main">1,000,000,000</span> Natural number

1,000,000,000 is the natural number following 999,999,999 and preceding 1,000,000,001. With a number, "billion" can be abbreviated as b, bil or bn.

189 is the natural number following 188 and preceding 190.

888 is the natural number following 887 and preceding 889.

References

  1. Lippman, David (12 July 2021). "6.0.2: The Hindu-Arabic Number System". Mathematics LibreTexts. Retrieved 31 March 2024.
  2. Sloane, N. J. A. (ed.). "SequenceA033950(Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 19 June 2023.
  3. Cajori, Florian (1991, 5e) A History of Mathematics, AMS. ISBN   0-8218-2102-4. p.91
  4. Pace P., Nielsen (2007). "Odd perfect numbers have at least nine distinct prime factors". Mathematics of Computation . 76 (260). Providence, R.I.: American Mathematical Society: 2109–2126. arXiv: math/0602485 . Bibcode:2007MaCom..76.2109N. doi: 10.1090/S0025-5718-07-01990-4 . MR   2336286. S2CID   2767519. Zbl   1142.11086.
  5. Sloane, N. J. A. (ed.). "SequenceA000537(Sum of first n cubes; or n-th triangular number squared.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 19 June 2023.
  6. Davenport, H. (1939), "On Waring's problem for cubes", Acta Mathematica , 71, Somerville, MA: International Press of Boston: 123–143, doi: 10.1007/BF02547752 , MR   0000026, S2CID   120792546, Zbl   0021.10601
  7. Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 93
  8. Robert Dixon, Mathographics. New York: Courier Dover Publications: 24
  9. Gleason, Andrew M. (1988). "Angle trisection, the heptagon, and the triskaidecagon". American Mathematical Monthly . 95 (3). Taylor & Francis, Ltd: 191–194. doi:10.2307/2323624. JSTOR   2323624. MR   0935432. S2CID   119831032.
  10. Sloane, N. J. A. (ed.). "SequenceA219766(Number of nonsquare simple perfect squared rectangles of order n up to symmetry)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  11. DHAMIJA, ANSHUL (16 May 2018). "The Auspiciousness Of Number 9". Forbes India. Retrieved 1 April 2024.
  12. "Vaisheshika | Atomism, Realism, Dualism | Britannica". www.britannica.com. Retrieved 13 April 2024.
  13. "Navratri | Description, Importance, Goddess, & Facts | Britannica". www.britannica.com. 11 April 2024. Retrieved 13 April 2024.
  14. Lochtefeld, James G. (2002). The illustrated encyclopedia of hinduism. New York: the Rosen publ. group. ISBN   978-0-8239-2287-1.
  15. "Lucky Number Nine, Meaning of Number 9 in Chinese Culture". www.travelchinaguide.com. Retrieved 15 January 2021.
  16. Donald Alexander Mackenzie (2005). Myths of China And Japan. Kessinger. ISBN   1-4179-6429-4.
  17. "The Global Egyptian Museum | Nine Bows". www.globalegyptianmuseum.org. Retrieved 16 November 2023.
  18. Mark, Joshua J. "Nine Realms of Norse Cosmology". World History Encyclopedia. Retrieved 16 November 2023.
  19. Galatians 5:22–23
  20. "Meaning of Numbers in the Bible The Number 9". Bible Study. Archived from the original on 17 November 2007.
  21. "Surah Al-Isra - 101". Quran.com. Retrieved 17 August 2023.
  22. "Surah An-Naml - 12". Quran.com. Retrieved 17 August 2023.
  23. "Surah An-Naml - 48". Quran.com. Retrieved 17 August 2023.

Further reading