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 .
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.
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.
Nine is the fourth composite number, and the first composite number that is odd. Nine is the third square number (3^{2}), and the second non-unitary square prime of the form p^{2}, and, the first that is odd, with all subsequent squares of this form odd as well. Nine has the even aliquot sum of 4, and with a composite number sequence of two (9, 4, 3, 1, 0) within the 3-aliquot tree. It is the first member of the first cluster of two semiprimes (9, 10), preceding (14, 15).^{[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]}
By Mihăilescu's theorem, 9 is the only positive perfect power that is one more than another positive perfect power, since the square of 3 is one more than the cube of 2.^{[4]}^{[5]}
9 is the sum of the cubes of the first two non-zero positive integers $1^{3}+2^{3))$ which makes it the first cube-sum number greater than one.^{[6]}
It is also the sum of the first three nonzero factorials$1!+2!+3!$, and equal to the third exponential factorial, since $9=3^{2^{1)).$^{[7]}
9 is a Motzkin number, for the number of ways of drawing non-intersecting chords between four points on a circle.^{[12]}
The first non-trivial magic square is a $3$ x $3$ magic square made of nine cells, with a magic constant of 15.^{[13]} Meanwhile, a $9$ x $9$ magic square has a magic constant of 369.^{[14]}
9 is related to just 3, 6 and itself. When we do the doubling of all natural numbers we get, 1, 2, 4, 8, 16, 32, 64... Now if we try to get the digital roots of two digit numbers, then, 16= 1+6 =7. 32= 3+2 =5. Such way, only 1, 2, 4, 5, 7, 8 occur. Same thing happens when we start halving the numbers.
Nikola Tesla was a great scientist. Despite his work on free energy etc. he stated, " If the understand the numbers 3, 6, 9, you understand the universe."
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.^{[24]}
In base-$N$, the divisors of $N-1$ have this property.
There are other interesting patterns involving multiples of nine:
9 × 12345679 = 111111111
18 × 12345679 = 222222222
81 × 12345679 = 999999999
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.
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.
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...)
Another consequence of 9 being 10 − 1 is that it is a Kaprekar number, preceding the ninth and tenth triangle numbers, 45 and 55 (where all 9, 99, 999, 9999, ... are Keprekar numbers).^{[25]}
Six recurring nines appear in the decimal places 762 through 767 of π. (See six nines in pi).
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 117 scales – 81 yang (masculine, heavenly) and 36 yin (feminine, earthly). All three numbers are multiples of 9 (9 × 13 = 117, 9 × 9 = 81, 9 × 4 = 36)^{[31]} as well as having the same digital root of 9.
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.
The name of the area called Kowloon in Hong Kong literally means: nine dragons.
The nine-dotted line (Chinese: 南海九段线; pinyin: nánhǎi jiǔduàn xiàn; lit. 'Nine-segment line of the South China Sea') delimits certain island claims by China in the South China Sea.
The nine-rank system was a civil service nomination system used during certain Chinese dynasties.
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.
The word "K-9" pronounces the same as canine and is used in many US police departments to denote the police dog unit. Despite not sounding like the translation of the word canine in other languages, many police and military units around the world use the same designation.
Someone dressed "to the nines" is dressed up as much as they can be.
In North American urban culture, "nine" is a slang word for a 9mmpistol or homicide, the latter from the Illinois Criminal Code for homicide.
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^{[34]} and a 1988 fiction book by Anthea Fraser;^{[35]} the name derives from "a very curious old semi-pagan, semi-Christian" song.^{[36]}
In the series A Song of Ice and Fire, there are nine regions of Westeros (the Crownlands, the North, the Riverlands, the Westerlands, the Reach, the Stormlands, the Vale of Arryn, the Iron Islands and Dorne). Additionally, there is a group of nine city-states in western Essos known collectively as the Free Cities (Braavos, Lorath, Lys, Myr, Norvos, Pentos, Qohor, Tyrosh and Volantis).
In The Wheel of Time series, Daughter of the Nine Moons is the title given to the heir to the throne of Seanchan, and the Court of the Nine Moons serves as the throne room of the Seanchan rulers themselves. Additionally, the nation of Illian is partially governed by a body known as the Council of Nine, and the flag of Illian displays nine golden bees on it. Furthermore, in the Age of Legends, the Nine Rods of Dominion were nine regional governors who administered individual areas of the world under the ruling world government.
Divine Nine – The National Pan-Hellenic Council (NPHC) is a collaborative organization of nine historically African American, international Greek-lettered fraternities and sororities.
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.”
— SurahAl-Isra (The Night Journey/Banī Isrāʾīl):101^{[39]}
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.”
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.
Nine, as the highest single-digit number (in base ten), symbolizes completeness in the Baháʼí Faith. In addition, the word Baháʼ in the Abjad notation has a value of 9, and a 9-pointed star is used to symbolize the religion.
The number 9 is revered in Hinduism and considered a complete, perfected and divine number because it represents the end of a cycle in the decimal system, which originated from the Indian subcontinent as early as 3000 BC.
In Buddhism, Gautama Buddha was believed to have nine virtues, which he was (1) Accomplished, (2) Perfectly Enlightened, (3) Endowed with knowledge and Conduct or Practice, (4) Well-gone or Well-spoken, (5) the Knower of worlds, (6) the Guide Unsurpassed of men to be tamed, (7) the Teacher of gods and men, (8) Enlightened, and (9) Blessed.
Important Buddhist rituals usually involve nine monks.
The first nine days of the Hebrew month of Av are collectively known as "The Nine Days" (Tisha HaYamim), and are a period of semi-mourning leading up to Tisha B'Av, the ninth day of Av on which both Temples in Jerusalem were destroyed.
Nine is a significant number in Norse Mythology. Odin hung himself on an ash tree for nine days to learn the runes.
The Fourth Way Enneagram is one system of knowledge which shows the correspondence between the 9 integers and the circle.
ISO 9 is the ISO's standard for the transliteration of Cyrillic characters into Latin characters
In the Rich Text Format specification, 9 is the language code for the English language. All codes for regional variants of English are congruent to 9 mod 256.
The9 Limited (owner of the9.com) is a company in the video-game industry, including former ties to the extremely popular MMORPGWorld of Warcraft.
"Revolution 9", a sound collage which appears on The Beatles' eponymous 1968 album The Beatles (aka The White Album), prominently features a loop of a man's voice repeating the phrase "Number nine".^{[43]}
There are 9 semitones in a Major 6th interval in music.^{[44]}
^Coxeter, H. S. M. (1956), "Regular honeycombs in hyperbolic space", Proceedings of the International Congress of Mathematicians, vol. III, Amsterdam: North-Holland Publishing Co., pp. 167–169, MR0087114
^Martin Gardner, A Gardner's Workout: Training the Mind and Entertaining the Spirit. New York: A. K. Peters (2001): 155
^Glover, Diane (9 October 2019). "#9 Dream: John Lennon and numerology". www.beatlesstory.com. Beatles Story. Retrieved 6 November 2022. Perhaps the most significant use of the number 9 in John's music was the White Album's 'Revolution 9', an experimental sound collage influenced by the avant-garde style of Yoko Ono and composers such as Edgard Varèse and Karlheinz Stockhausen. It featured a series of tape loops including one with a recurring 'Number Nine' announcement. John said of 'Revolution 9': 'It's an unconscious picture of what I actually think will happen when it happens; just like a drawing of a revolution. One thing was an engineer's testing voice saying, 'This is EMI test series number nine.' I just cut up whatever he said and I'd number nine it. Nine turned out to be my birthday and my lucky number and everything. I didn't realise it: it was just so funny the voice saying, 'number nine'; it was like a joke, bringing number nine into it all the time, that's all it was.'