nine
nine | |
---|---|
9 | |
presentation | |
Roman | IX |
dual | 1001 |
Octal | 11 |
Duodecimal | 9 |
Hexadecimal | 9 |
Morse code | - - - - · |
Arabic | ٩ |
Chinese | 九 |
Mathematical properties | |
sign | positive |
parity | odd |
Factorization | |
Divider | 1, 3, 9 |
The nine (9) is the natural number between eight and ten . It is odd , a square number and the highest single-digit number in the decimal system .
Linguistic
The numeral nine could perhaps belong to the Indo-European root for new . According to this, one would have counted with four fingers of one hand and started counting "new" at nine (see eight ).
The Latin word for nine, novem with the ordinal number nonus (the ninth) found its way into foreign words such as none (interval), nonet (ensemble) and November (originally the ninth month). The Latin numerals for 19, 29 to 89 are - as with octo (8) - not formed with novem , but circumscribed, e.g. B. un-de-viginti for 19, literally: 1 of 20 (subtracted).
The Greek word for nine, ἐννέα (ennea) can also be found in some foreign words, including the enneagram , an esoteric symbol.
mathematics
Nine is the smallest odd composite number and the smallest odd composite number that is not a Fermat pseudoprime . It is the smallest natural number n , for which every nonnegative integer can be represented as a sum of at most n positive cubic numbers (see: Waring's problem ), and the smallest positive natural number n , for which n squares of different positive edge lengths exist in pairs, which can be put together to form a rectangle .
The nine is the number that (in the decimal number system) after multiplication with any whole number (except 0) always appears as a single-digit checksum , as well as the number that adds to any other (except 0 and -9) as a single-digit The checksum gives the same result as the original number itself - it behaves almost neutrally. It only has this behavior in common with zero . The proof for the behavior in addition can be made with the help of the observation that the sum of a single-digit number (not equal to 0) and 9 always results in a number consisting of the digits 1 and the starting number reduced by 1 (example: 6 + 9 = 15). The behavior when multiplied by 9 results from the fact that a number multiplied by 9 can always be represented as 9 + 9 + 9 +… + 9, since the cross sum of nine is 9, the cross sum of 9 + 9 is then the same 9 and so on. (Proof with complete induction ). However, other numbers behave in the same way in the corresponding number systems, e.g. eight in a nine-number system).
The nine is also a Størmer number .
accounting
In accounting, the fact that a difference found is either nine or a multiple thereof ( checksum = nine) suggests that the number could be rotated .
The test of nine is a method of detecting incorrect addition, subtraction or multiplication. There's also the term nines for the remainder of a number that it leaves when divided by 9.
An example of the accounting check is shown below: 83 → 38, difference 45, checksum 4 + 5 = 9.
Nature and science
The fish-like lampreys got their historical name because their seven gill openings together with the nostril and the actual eyes give the impression of nine eyes.
The red- backed bird got its German name because it impales its prey on thorns or spikes for storage, which led to the popular belief that it kills nine animals before consuming one.
The solar system had nine planets from 1930 to 2006, each with mythological and astrological significance, whereby Uranus , Neptune and Pluto were unknown in antiquity. Pluto was stripped of its planet status in 2006.
Mythology and religion
The Nine is regarded as the number of perfection, as they three times in many cultures as a "divine" respected figure Three contains. When counting the system of ten, 9 is the highest, i.e. completed one- digit number.
- In Egyptian mythology there is the Ennead of Heliopolis , the ninth of the creator deities according to the cosmogony of the priests in the Egyptian city of Heliopolis .
- The symbol of the Baha'i is a nine-pointed star and stands for the unity of humanity and the unity of religions . The architecture of the Baha'i house of worship, the House of Worship , is a nine-sided dome structure with nine entrances. The special meaning of the number nine can be explained with the Abdschad (number system) value of the Arabic word Baha (German: glory ), which is also nine.
- In Chinese numerical symbols , the nine stands for the dragon .
- In Greek mythology there are nine muses and the nine-headed hydra .
- In the Catholic Church there is a nine-day prayer sequence, the novena , for high celebrations and other important occasions , for example the “funeral novena” after the death of a Pope.
- For the Celts , the whole universe was in nine . Three times three ( the divine number ) gave them an absolute character. This includes the five , which recorded time and space, as well as the four as the number of cardinal points.
- In Norse mythology , the number nine also plays an important role. So Odin's self-sacrifice lasted nine days and nine nights; Heimdall is born to nine mothers.
- The nine choirs of angels go back to a division of the heavenly beings of Christian mythology into nine orders going back to the early Middle Ages .
- Also in Satanism the Nine appears more often, for example, in the naming of the Order of Nine Angles (Engl., Order of nine angle ') or in Anton LaVey , the nine in "The Satanic Rituals" as a figure of Satan and the ego called . He picked up the number for The Nine Satanic Statements , The Nine Satanic Sins and the decision-making body called the Council of Nine of the Church of Satan he founded . The Temple of The Black Light describes on its website a ritual in which one sacrifices nine drops of blood from the left thumb , and the contour of Lilith's shape as an enneagram.
- In the Gospel of John, Christ says : “I am the Alpha and the Omega.” In the Greek numerical order this corresponds to the number 108 (i.e. 9 (1 + 8)), the Greek word for dove (for the birth of Christ and for the Holy Spirit ) is 'peristera' stands for 801 as the inversion of the number 108, the attribute of the human soul, which emerges from the " triune God " and has to reintegrate into it.
- Avicenna : “Know that any number is nothing more than 9 or a multiple thereof, plus anything beyond that. Whoever knows what goes beyond that and the multiplier of nine knows the nature and the number in every relationship. ” Kabbalistic is 9 is the realization of every balance, the perfection. It is the sign of every circle. (360 degrees, cross sum = 9), it is the sphere of the universe, the macrocosm .
History and society
- In the customs of the Ore Mountains there is the nine things , a traditional Christmas Eve meal.
- The Neunerlei Gewürz is a traditional mixture of spices during Advent.
- A Sudoku usually consists of nine by nine boxes in which the numbers 1 to 9 have to be entered nine times.
- The expression all nine comes from the nine number of pins in bowling !
- Cats are popularly said to have nine lives .
- The number “9” on the back is the number of the center forward in football.
- In German one uses the exclamation "Oh, you Green Neune ".
- In the Texas penitentiary system, death row prisoners' numbers start with "999".
Culture, literature, music and intellectual life
- Film # 9 is an American animated film directed by Shane Acker.
- Plotin's nine-volume work is called Ennead in Greek .
- In the book The Lord of the Rings , the ring community with nine companions stands opposite the nine ring spirits ( Nazgûl ).
- Morgane and her eight sisters were enough to represent the entire Otherworld on Avalon Island .
- The "hazel bush of wisdom" bears nine hazelnuts .
- In the 14th century the Topos of the Nine Good Heroes was created , which brought together three pagan-ancient, Old and New Testament heroes to form a list of the ideal knights who were iconographically represented for the ideal government and who were represented in many municipal buildings. The Nine Good Heroines developed analogously .
- Ludwig van Beethoven , Anton Bruckner , Antonín Dvořák , Gustav Mahler , Louis Spohr and Ralph Vaughan Williams each completed nine (printed) symphonies . Some composers, especially Gustav Mahler, developed a superstitious fear of the curse of the Ninth Symphony from this .
- In the Divine Comedy by Dante Alighieri is the hell out of nine circles.
- For the polar explorer Ernest Shackleton , the number was of particular importance, as it repeatedly marked important stages in his life. On April 9, 1904, he married his wife Emily, and on January 9, 1909, Shackleton reached its highest southern latitude at 88 ° 23'S during the Nimrod expedition . On July 9, 1913, he was the best man at the wedding of his friend Philip Brocklehurst . A silver version of the number was on Shackleton's cabin door on the expedition ship on the Quest expedition . The nine-armed star became his personal emblem, which is also immortalized on his gravestone. Finally Emily Shackleton died on June 9, 1936 after several months of serious illness.
See also
- Nine Badges of Honor - Chinese Emperor's rewards for outstanding officials
- Neuneck - a geometric figure
- Nine - disambiguation page
- Neuner - disambiguation page
literature
- Cecil Balmond : Number 9, the Search for the Sigma Code. 1998, Prestel Verlag 2008 (in English), ISBN 3-7913-1933-7 , ISBN 978-3-7913-1933-9
Web links
Individual evidence
- ↑ Paul Naudon: Les Loges de Saint Jean et la Philosophie esoterique de la Connaissance > “Throughout antiquity, 9 was regarded as a perfect number because, at the end of the series of simple numbers, it completes this.”
- ↑ ^{a } ^{b } ^{c} Reinhard Federmann: The royal art. A history of alchemy. Vienna: Neff 1964.
- ^ Anton Szandor LaVey: The Nine Satanic Statements .
- ^ Anton Szandor LaVey: The Nine Satanic Sins .
- ↑ Oneiric Union with the Angels of the Black Moon ( Memento of 16 December 2009 at the Internet Archive ).
- ^ The Nightmarish Vision of Ama Lilith ( Memento June 28, 2009 in the Internet Archive ).
- ↑ Texas Department of Criminal Justice: Texas Department of Criminal Justice. In: www.tdcj.state.tx.us. Retrieved March 13, 2016 .