| |
|
| 9 | |
|---|---|
| Cardinal | Nine |
| Ordinal | Ninth |
| Numeral system | novenary |
| Factorization | 3*3 |
| Roman numeral | IX |
| Binary | 1001 |
| Hexadecimal | 09 |
Mathematics
Nine is a composite number, its proper divisors being 1 and 3.
In base-10 a number is evenly divisible by nine if and only if the iterative sum of its digits reduces to 9. This is equivalent to saying a number is divisible by 9 if and only if its decimal digit total is divisible by 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.
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, 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.
Six recurring nines appear in the decimal places 762 through 767 of pi. This is known as the Feynman point (see also MathWorld).
| 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 | |
Music
Bands with the number nine in their name include Stroke 9, Nine Days and Nine Inch Nails. There is also a song called "Love Potion #9".
Both Ludwig van Beethoven and Anton Bruckner wrote nine symphonies. After Beethoven died leaving his Tenth Symphony unfinished, composers were superstitious about writing Ninth Symphonies for the rest of the nineteenth century. Gustav Mahler tried to "cheat death" by writing his Ninth Symphony but calling it Das Lied von der Erde instead. Afterwards he wrote a work called Ninth Symphony, but thinking of it as his Tenth. He died with his Tenth (or Eleventh in his mind) unfinished. Perhaps Antonín Dvořák was also superstitious about the number nine, because he wrote no symphonies after his New World Symphony, which is nowadays considered his Ninth, but which he thought was his Eighth because he considered the score of his early C minor Symphony lost forever. He lived for seven more years. In the twentieth century, a handful of composers, such as Dmitri Shostokovich, have written a Ninth Symphony and lived to write more.
Other fields
Nine is the number of musicians in a nonet. Nine babies born into a single birth are called nonuplets, although not one baby born into a set of nonuplets has ever survived infancy. A polygon with nine sides is an enneagon or nonagon. A group of nine of anything is called an ennead.
Nine is: