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81 (number)
Encyclopedia
81 is the natural number
following 80
and preceding 82
.
of 9 and the fourth power of 3. Like all powers of three, 81 is a perfect totient number
. It is a heptagonal number and a centered octagonal number
. It is also a tribonacci number, and an open meandric number. 81 is the ninth member of the Mian-Chowla sequence.
In base 10, it is a Harshad number
, and one of three non-trivial numbers (the other two are 1458
and 1729
) which, when its digits are added together, produces a sum which, when multiplied by its reversed self, yields the original number:
(although this case is somewhat degenerate, as the sum has only a single digit).
The inverse of 81 is 0.012345679 recurring, missing only the digit "8" from the complete set of digits. This is an example of the general rule that, in base b,
omitting only the digit b−2.
81 was the number worn by James Amato of the Flying Hellfish flag football team
In China, 81 always reminds people People's Liberation Army
as it was founded on August 1.
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...
following 80
80 (number)
80 is the natural number following 79 and preceding 81.- In mathematics :The sum of Euler's totient function φ over the first sixteen integers is 80....
and preceding 82
82 (number)
82 is the natural number following 81 and preceding 83.-In mathematics:Eighty-two is the twenty-third biprime and the twelfth of the form...
.
In mathematics
Eighty-one is the squareSquare number
In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself...
of 9 and the fourth power of 3. Like all powers of three, 81 is a perfect totient number
Perfect totient number
In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number n, apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers;...
. It is a heptagonal number and a centered octagonal number
Centered octagonal number
A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers...
. It is also a tribonacci number, and an open meandric number. 81 is the ninth member of the Mian-Chowla sequence.
In base 10, it is a Harshad number
Harshad number
A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit + , meaning joy-giver. The Niven...
, and one of three non-trivial numbers (the other two are 1458
1458 (number)
1458 is the integer after 1457 and before 1459.The maximum determinant of an 11 by 11 matrix of zeroes and ones is 1458.1458 is one of three numbers which, when its base 10 digits are added together, produces a sum which, when multiplied by its reversed self, yields the original number:The only...
and 1729
1729 (number)
1729 is the natural number following 1728 and preceding 1730.1729 is known as the Hardy–Ramanujan number after a famous anecdote of the British mathematician G. H. Hardy regarding a hospital visit to the Indian mathematician Srinivasa Ramanujan...
) which, when its digits are added together, produces a sum which, when multiplied by its reversed self, yields the original number:
- 8 + 1 = 9
- 9 × 9 = 81
(although this case is somewhat degenerate, as the sum has only a single digit).
The inverse of 81 is 0.012345679 recurring, missing only the digit "8" from the complete set of digits. This is an example of the general rule that, in base b,
omitting only the digit b−2.
In astronomy
- Messier objectMessier objectThe Messier objects are a set of astronomical objects first listed by French astronomer Charles Messier in 1771. The original motivation of the catalogue was that Messier was a comet hunter, and was frustrated by objects which resembled but were not comets...
M81Messier 81Messier 81 is a spiral galaxy about 12 million light-years away in the constellation Ursa Major. Due to its proximity to Earth, large size and active galactic nucleus Messier 81 (also known as NGC 3031 or Bode's Galaxy) is a spiral galaxy about 12 million light-years away in the constellation Ursa...
, a magnitude 8.5 spiral galaxySpiral galaxyA spiral galaxy is a certain kind of galaxy originally described by Edwin Hubble in his 1936 work The Realm of the Nebulae and, as such, forms part of the Hubble sequence. Spiral galaxies consist of a flat, rotating disk containing stars, gas and dust, and a central concentration of stars known as...
in the constellationConstellationIn modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....
Ursa MajorUrsa MajorUrsa Major , also known as the Great Bear, is a constellation visible throughout the year in most of the northern hemisphere. It can best be seen in April...
, also known as Bode's Galaxy, and the first of what is known as the M81 GroupM81 GroupThe M81 Group is a group of galaxies in the constellation Ursa Major that includes the well-known galaxies Messier 81 and Messier 82, as well as several other galaxies with high apparent brightnesses. The approximate center of the group is located at a distance of 3.6 Mpc, making it one of the...
of galaxies - The New General CatalogueNew General CatalogueThe New General Catalogue of Nebulae and Clusters of Stars is a well-known catalogue of deep sky objects in astronomy. It contains 7,840 objects, known as the NGC objects...
object NGC 81, a spiral galaxySpiral galaxyA spiral galaxy is a certain kind of galaxy originally described by Edwin Hubble in his 1936 work The Realm of the Nebulae and, as such, forms part of the Hubble sequence. Spiral galaxies consist of a flat, rotating disk containing stars, gas and dust, and a central concentration of stars known as...
in the constellation AndromedaAndromeda (constellation)Andromeda is a constellation in the northern sky. It is named after Andromeda, the princess in the Greek legend of Perseus who was chained to a rock to be eaten by the sea monster Cetus... - The Saros number of the solar eclipseSolar eclipseAs seen from the Earth, a solar eclipse occurs when the Moon passes between the Sun and the Earth, and the Moon fully or partially blocks the Sun as viewed from a location on Earth. This can happen only during a new moon, when the Sun and the Moon are in conjunction as seen from Earth. At least...
series which began on -322 May 12 and ended on 958 June. The duration of Saros series 81 was 1280.1 years, and it contained 72 solar eclipses. Further, the number of lunar eclipseLunar eclipseA lunar eclipse occurs when the Moon passes behind the Earth so that the Earth blocks the Sun's rays from striking the Moon. This can occur only when the Sun, Earth, and Moon are aligned exactly, or very closely so, with the Earth in the middle. Hence, a lunar eclipse can only occur the night of a...
series which began on -20 February 19 and ended on 1296 April. The duration of Saros series 81 was 1316.2 years, and it contained 74 lunar eclipses.
In other fields
Eighty-one is also:- The number of squares on a shogiShogi, also known as Japanese chess, is a two-player board game in the same family as Western chess, chaturanga, and Chinese Xiangqi, and is the most popular of a family of chess variants native to Japan...
playing board - The year AD 81, 81 BC81 BCYear 81 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Decula and Dolabella...
, or 1981. - The atomic numberAtomic numberIn chemistry and physics, the atomic number is the number of protons found in the nucleus of an atom and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol Z. The atomic number uniquely identifies a chemical element...
of thalliumThalliumThallium is a chemical element with the symbol Tl and atomic number 81. This soft gray poor metal resembles tin but discolors when exposed to air. The two chemists William Crookes and Claude-Auguste Lamy discovered thallium independently in 1861 by the newly developed method of flame spectroscopy... - The symbolic number of the Hells AngelsHells AngelsThe Hells Angels Motorcycle Club is a worldwide one-percenter motorcycle gang and organized crime syndicate whose members typically ride Harley-Davidson motorcycles. In the United States and Canada, the Hells Angels are incorporated as the Hells Angels Motorcycle Corporation. Their primary motto...
Motorcycle Club. 'H' and 'A' are the 8th and 1st letter of the alphabet, respectively. - The title of a short film by Stephen Burke: 81
- The model number of Sinclair ZX81Sinclair ZX81The ZX81 was a home computer produced by Sinclair Research and manufactured in Scotland by Timex Corporation. It was launched in the United Kingdom in March 1981 as the successor to Sinclair's ZX80 and was designed to be a low-cost introduction to home computing for the general public...
- The number of the department in France called Tarn
- The designation of Interstate 81Interstate 81Interstate 81 is an Interstate Highway in the eastern part of the United States. Its southern terminus is at Interstate 40 in Dandridge, Tennessee; its northern terminus is on Wellesley Island at the Canadian border, where the Thousand Islands Bridge connects it to Highway 401, the main freeway...
, a freeway that runs from TennesseeTennesseeTennessee is a U.S. state located in the Southeastern United States. It has a population of 6,346,105, making it the nation's 17th-largest state by population, and covers , making it the 36th-largest by total land area...
to New YorkNew YorkNew York is a state in the Northeastern region of the United States. It is the nation's third most populous state. New York is bordered by New Jersey and Pennsylvania to the south, and by Connecticut, Massachusetts and Vermont to the east...
. - The code for international direct dial phone calls to JapanJapanJapan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
- One of two ISBN Group Identifiers for books published in IndiaIndiaIndia , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
- Number of stanzas or chapters in the Tao te ChingTao Te ChingThe Tao Te Ching, Dao De Jing, or Daodejing , also simply referred to as the Laozi, whose authorship has been attributed to Laozi, is a Chinese classic text...
(in the most common arrangements). - Number of provinces in TurkeyTurkeyTurkey , known officially as the Republic of Turkey , is a Eurasian country located in Western Asia and in East Thrace in Southeastern Europe...
. 81st one is DüzceDüzceDüzce is the capital city of Düzce Province in Turkey. The mayor is İsmail Bayram . The population is 125,240 which is an increase from 61.878 in 1990.- Overview :...
. - Number of prayers said in the Rosary in each night.
- The 81 is a 1965 song by Candy and the Kisses.
- Artemis 81 is a 1981 BBCBBCThe British Broadcasting Corporation is a British public service broadcaster. Its headquarters is at Broadcasting House in the City of Westminster, London. It is the largest broadcaster in the world, with about 23,000 staff...
TV sci-fi drama. - 'The Eighty-One Brothers' is a Japanese fable
81 was the number worn by James Amato of the Flying Hellfish flag football team
In Culture
The Arabic characters for the numerals 8 and 1 are visible in the left palm of the human hand.In China, 81 always reminds people People's Liberation Army
People's Liberation Army
The People's Liberation Army is the unified military organization of all land, sea, strategic missile and air forces of the People's Republic of China. The PLA was established on August 1, 1927 — celebrated annually as "PLA Day" — as the military arm of the Communist Party of China...
as it was founded on August 1.