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45 (number)
Encyclopedia
45 is the natural number
following 44
and followed by 46
.
, a hexagonal
and 16-gonal number
, a Kaprekar number
, and a Harshad number
.
45 is the sixth positive integer with a prime factorization of the form p2q, with p and q being prime
.
33 is the aliquot sum of 45 and the aliquot sequence
of 45 is (45, 33, 15, 9, 4, 3, 1, 0).
Since the greatest prime factor of 452 + 1 = 2026 is 1013, which is clearly more than 45 twice, 45 is a Størmer number
.
The sum of all the digits is 45 (casually the sum of both digits is 9)(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45).
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 44
44 (number)
44 is the natural number following 43 and preceding 45.- In mathematics :Forty-four is a tribonacci number, a happy number, an octahedral number and a palindromic number....
and followed by 46
46 (number)
46 is the natural number following 45 and preceding 47.- In mathematics :Forty-six is a Wedderburn-Etherington number, an enneagonal number and a centered triangular number. It is the sum of the totient function for the first twelve integers. 46 is the largest even integer that can't be expressed...
.
In mathematics
Forty-five is a triangular numberTriangular number
A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...
, a hexagonal
Hexagonal number
A hexagonal number is a figurate number. The nth hexagonal number will be the number of points in a hexagon with n regularly spaced points on a side.The formula for the nth hexagonal number...
and 16-gonal number
Polygonal number
In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots were thought of as alphas . These are one type of 2-dimensional figurate numbers.- Definition and examples :...
, a Kaprekar number
Kaprekar number
In mathematics, a Kaprekar number for a given base is a non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again. For instance, 45 is a Kaprekar number, because 45² = 2025 and 20+25 = 45. The Kaprekar numbers are...
, and 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...
.
45 is the sixth positive integer with a prime factorization of the form p2q, with p and q being prime
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
.
33 is the aliquot sum of 45 and the aliquot sequence
Aliquot sequence
In mathematics, an aliquot sequence is a recursive sequence in which each term is the sum of the proper divisors of the previous term. The aliquot sequence starting with a positive integer k can be defined formally in terms of the sum-of-divisors function σ1 in the following way:For example, the...
of 45 is (45, 33, 15, 9, 4, 3, 1, 0).
Since the greatest prime factor of 452 + 1 = 2026 is 1013, which is clearly more than 45 twice, 45 is a Størmer number
Størmer number
In mathematics, a Størmer number or arc-cotangent irreducible number, named after Carl Størmer, is a positive integer n for which the greatest prime factor of n2 + 1 meets or exceeds 2n. The first few Størmer numbers are 1, 2, 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 19, 20, etc....
.
The sum of all the digits is 45 (casually the sum of both digits is 9)(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45).
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...
M45Pleiades (star cluster)In astronomy, the Pleiades, or Seven Sisters , is an open star cluster containing middle-aged hot B-type stars located in the constellation of Taurus. It is among the nearest star clusters to Earth and is the cluster most obvious to the naked eye in the night sky...
, a magnitude 1.4 open clusterOpen clusterAn open cluster is a group of up to a few thousand stars that were formed from the same giant molecular cloud and have roughly the same age. More than 1,100 open clusters have been discovered within the Milky Way Galaxy, and many more are thought to exist...
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....
TaurusTaurus (constellation)Taurus is one of the constellations of the zodiac. Its name is a Latin word meaning 'bull', and its astrological symbol is a stylized bull's head:...
, also known as the PleiadesPleiades (star cluster)In astronomy, the Pleiades, or Seven Sisters , is an open star cluster containing middle-aged hot B-type stars located in the constellation of Taurus. It is among the nearest star clusters to Earth and is the cluster most obvious to the naked eye in the night sky... - 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 45NGC 45NGC 45 is a barred spiral galaxy in the constellation of Cetus. It was discovered on 11 November 1835 by the English astronomer John Herschel. In the sky, it is located near the magnitude 6.8 star HD 941.-External links:...
, a magnitude 10.6 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 CetusCetusCetus is a constellation. Its name refers to Cetus, a sea monster in Greek mythology, although it is often called 'the whale' today. Cetus is located in the region of the sky that contains other water-related constellations such as Aquarius, Pisces, and Eridanus.-Ecliptic:Although Cetus is not... - 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 −1436 March 30 and ended on −156 May 7. The duration of Saros series 45 was 1280.1 years, and it contained 72 solar eclipses. - The Saros number of the 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 −1369 August 19 and ended on 182 March. The duration of Saros series 45 was 1550.6 years, and it contained 87 lunar eclipses.
In music
- A type of gramophone recordGramophone recordA gramophone record, commonly known as a phonograph record , vinyl record , or colloquially, a record, is an analog sound storage medium consisting of a flat disc with an inscribed, modulated spiral groove...
classified by its revolution speed of 45 revolutions per minute (rpm)Revolutions per minuteRevolutions per minute is a measure of the frequency of a rotation. It annotates the number of full rotations completed in one minute around a fixed axis... - Included in the title of "45 and Fat", a 1996 song by BabybirdBabybirdBabybird are a British indie band formed in 1995. The band is fronted by Stephen Jones, who has also released records as a solo artist, using his own name.-Career:Jones had begun...
- The title of a 2000 song by The Atomic BitchwaxThe Atomic BitchwaxThe Atomic Bitchwax is a stoner rock band started in 1992 in New Jersey. It started as essentially a "super band" of key members of the notable stoner rock and doom metal bands Godspeed, Monster Magnet, and Core.-History:...
, "Forty-Five" - The title of a 2002 song by Elvis CostelloElvis CostelloElvis Costello , born Declan Patrick MacManus, is an English singer-songwriter. He came to prominence as an early participant in London's pub rock scene in the mid-1970s and later became associated with the punk/New Wave genre. Steeped in word play, the vocabulary of Costello's lyrics is broader...
, "45", both referring to the 45 rpm singles and to the artist's age when he wrote the song, which was released when he was 47 - The title of a 2003 song by ShinedownShinedownShinedown is an American rock band from Jacksonville, Florida, formed in 2001 and founded by members Brent Smith , Brad Stewart , Jasin Todd , and Barry Kerch . A few line-up changes followed, and the band's current line-up consists of Smith and Kerch, the band's only two remaining original...
, "45" see 45 (song)45 (song)"45" is a song by the alternative rock band Shinedown. The song was released on July 13, 2003, on the album Leave a Whisper. Following the album's release, "45" became a popular single. An acoustic cover of "45" was featured on the album's re-release on June 15, 2004.Brent Smith has stated in an... - The title of a 2006 song by noodlesNoodles (band)Noodles is a Japanese alternative rock band currently consisting of Yoko , Ayumi and Ikuno . The band is originally from Yokohama, where they performed their first show....
, "45" - The title of a 2007 song by Ryan Shaw, "Do the 45"
- The title of a 2007 song by The Saturday KnightsThe Saturday KnightsThe Saturday Knights are a Seattle and Tacoma, Washington-based musical group whose music spans many genres, ranging from hip hop to pop music. Their debut full-length CD, Mingle features guest appearances from the Dap-Kings, Chris Ballew, Jack Endino, Holly Deye , Kim Thayil, and Jim Horn & the...
, "45" - The title of a 1982 album by KinoKino (band)Kino was a Soviet rock band headed by Viktor Tsoi. It was one of the most famous Soviet rock groups of the 1980s.-History:The band was formed in the summer of 1981 in Leningrad, USSR Kino was a Soviet rock band headed by Viktor Tsoi. It was one of the most famous Soviet rock groups of the...
, 45 - Repeated continuously in the 1997 song "Brimful of AshaBrimful of Asha"Brimful of Asha" is a 1997 single by the British alternative rock band Cornershop, which originally reached number 60 in the UK Singles Chart in 1997...
" by CornershopCornershopCornershop are a British indie rock band formed in 1991 by Wolverhampton-born Tjinder Singh , his brother Avtar Singh , David Chambers and Ben Ayres , the first three having previously been members of Preston-based band General Havoc, who released one single in 1991...
In other fields
Forty-five may also refer to:- In years of marriage, the sapphireSapphireSapphire is a gemstone variety of the mineral corundum, an aluminium oxide , when it is a color other than red or dark pink; in which case the gem would instead be called a ruby, considered to be a different gemstone. Trace amounts of other elements such as iron, titanium, or chromium can give...
wedding anniversaryWedding anniversary-Official recognition:In the Commonwealth realms, one can receive a message from the monarch for 60th, 65th, and 70th wedding anniversaries, and any wedding anniversary after that...
. - A card game: Forty-five
- I-45 is the designation for a USUnited StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district...
interstate highway in TexasTexasTexas is the second largest U.S. state by both area and population, and the largest state by area in the contiguous United States.The name, based on the Caddo word "Tejas" meaning "friends" or "allies", was applied by the Spanish to the Caddo themselves and to the region of their settlement in...
, connecting the major cities of Dallas and Houston; it is also the shortest "primary" interstate highway (one ending in 0 or 5) - The '45 refers to the 1745 Jacobite RisingJacobite risingThe Jacobite Risings were a series of uprisings, rebellions, and wars in Great Britain and Ireland occurring between 1688 and 1746. The uprisings were aimed at returning James VII of Scotland and II of England, and later his descendants of the House of Stuart, to the throne after he was deposed by...
in Great BritainGreat BritainGreat Britain or Britain is an island situated to the northwest of Continental Europe. It is the ninth largest island in the world, and the largest European island, as well as the largest of the British Isles... - 45 (book)45 (book)45 is a non-fiction book by Bill Drummond, referred to by The Guardian as a "charmingly barking [mad] memoir". It collects various short stories written by Drummond between 1997 and 1998.-Content:* Forty-Five Today* The Winner Takes It All...
, a book of essays by record producer Bill DrummondBill DrummondWilliam Ernest Drummond is a Scottish artist, musician, writer and record producer. He was the co-founder of late 1980s avant-garde pop group The KLF and its 1990s media-manipulating successor, the K Foundation, with which he burned a million pounds in 1994...
, derived both from the speed of a pop single and from his age when he finished writing it - A football match consists of two periods of 45 minutes each.
- Guns or ammunition of .45 caliber. In the United States, "45" is often a reference to one of two specific .45 caliber cartridges— the .45 Colt.45 ColtThe .45 Colt cartridge is a handgun cartridge dating to 1872. It began as a black powder revolver round developed for the Colt Single Action Army revolver, but is offered as a magnum level handgun hunting round in modern usage. This cartridge was adopted by the U.S. Army in 1873 and served as the...
or the .45 ACP.45 ACPThe .45 ACP , also known as the .45 Auto by C.I.P., is a cartridge designed by John Browning in 1904, for use in his prototype Colt semi-automatic .45 pistol and eventually the M1911 pistol adopted by the United States Army in 1911.-Design and history:The U.S...
. - .45 (film).45 (film).45 is an independent 2006 thriller film starring Milla Jovovich, Angus Macfadyen, Aisha Tyler, Stephen Dorff, and Sarah Strange. Gary Lennon, whose last feature was 1995's Drunks, wrote and directed the film...
, a 2006 motion picture. - +45 is the telephone dialing code for DenmarkDenmarkDenmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...
- Forty Five (Doctor Who audio)Forty Five (Doctor Who audio)Forty-five is a Big Finish Productions audio drama based on the long-running British science fiction television series Doctor Who. As the play released at the forty-fifth anniversary of the first episode of Doctor Who, it is made of four one-part stories, by different authors, rather than the...
a Big FinishBig Finish ProductionsBig Finish Productions is a British company that produces books and audio plays based, primarily, on cult British science fiction properties...
2008 audio play made for the forty fifth anniversary of the British science fiction television show Doctor WhoDoctor WhoDoctor Who is a British science fiction television programme produced by the BBC. The programme depicts the adventures of a time-travelling humanoid alien known as the Doctor who explores the universe in a sentient time machine called the TARDIS that flies through time and space, whose exterior...
. - The number of the French department LoiretLoiretLoiret is a department in north-central FranceThe department is named after the river Loiret, a tributary of the Loire. The Loiret is located wholly within the department.- History :...