91 (number)
Encyclopedia
91 is the natural number
following 90
and preceding 92
.
and the second of the form (7.q). The aliquot sum of 91 is 21 within the aliquot sequence (91,21,11,1,0) 91 being the fourth composite number in the 11-aliquot tree.
Ninety-one is a triangular number
and a hexagonal number
, one of the few such numbers to also be a centered hexagonal number
, and it is also a centered nonagonal number
and a centered cube number
. It is a square pyramidal number
, being the sum of the squares of the first six integer
s.
It is the smallest positive integer expressible as a sum of two cubes in two different ways if negative roots are allowed (alternatively the sum of two cubes and the difference of two cubes): 91 = 63+(-5)3 = 43+33. (See 1729
for more details).
It is also the smallest positive integer expressible as a sum of six distinct squares: 91 = 12+22+32+42+52+62. The only other ways to write 91 as a sum of distinct squares are: 91 = 12+42+52+72 and 91 = 12+32+92.
It is also the smallest pseudoprime
satisfying the congruence 3n = 3 mod n.
91 is a repdigit
in base 9 (111).
91 is after number 90 and before number 92.
In astronomy
,
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 90
90 (number)
90 is the natural number preceded by 89 and followed by 91.- In mathematics :*Because 90 is the sum of its unitary divisors , it is a unitary perfect number, and because it is equal to the sum of a subset of its divisors, it is a semiperfect number. 90 is a pronic number. But it is also a...
and preceding 92
92 (number)
92 is the natural number following 91 and preceding 93.- In mathematics:Ninety-two is a pentagonal number.There are 92 Johnson solids...
.
In mathematics
Ninety-one is the twenty-seventh distinct semiprimeSemiprime
In mathematics, a semiprime is a natural number that is the product of two prime numbers. The first few semiprimes are 4, 6, 9, 10, 14, 15, 21, 22, 25, 26, ... ....
and the second of the form (7.q). The aliquot sum of 91 is 21 within the aliquot sequence (91,21,11,1,0) 91 being the fourth composite number in the 11-aliquot tree.
Ninety-one is a triangular number
Triangular 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...
and a hexagonal number
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...
, one of the few such numbers to also be a centered hexagonal number
Centered hexagonal number
A centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice....
, and it is also a centered nonagonal number
Centered nonagonal number
A centered nonagonal number is a centered figurate number that represents a nonagon with a dot in the center and all other dots surrounding the center dot in successive nonagonal layers...
and a centered cube number
Centered cube number
A centered cube number is a centered figurate number that represents a cube. The centered cube number for n is given byn^3 + ^3.The first few centered cube numbers are...
. It is a square pyramidal number
Square pyramidal number
In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square base...
, being the sum of the squares of the first six integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
s.
It is the smallest positive integer expressible as a sum of two cubes in two different ways if negative roots are allowed (alternatively the sum of two cubes and the difference of two cubes): 91 = 63+(-5)3 = 43+33. (See 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...
for more details).
It is also the smallest positive integer expressible as a sum of six distinct squares: 91 = 12+22+32+42+52+62. The only other ways to write 91 as a sum of distinct squares are: 91 = 12+42+52+72 and 91 = 12+32+92.
It is also the smallest pseudoprime
Pseudoprime
In number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem.- Definition :...
satisfying the congruence 3n = 3 mod n.
91 is a repdigit
Repdigit
In recreational mathematics, a repdigit is a natural number composed of repeated instances of the same digit, most often in the decimal numeral system....
in base 9 (111).
91 is after number 90 and before number 92.
In science
- 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 protactiniumProtactiniumProtactinium is a chemical element with the symbol Pa and atomic number 91. It is a dense, silvery-gray metal which readily reacts with oxygen, water vapor and inorganic acids. It forms various chemical compounds where protactinium is usually present in the oxidation state +5, but can also assume...
, an actinide. - McCarthy 91 functionMcCarthy 91 functionThe McCarthy 91 function is a recursive function, defined by computer scientist John McCarthy as a test case for formal verification within computer science.The McCarthy 91 function is defined as...
, a recursive function in discrete mathematicsDiscrete mathematicsDiscrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not...
In astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
,
- 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...
M91Messier 91Messier 91 is a barred spiral galaxy located in the Coma Berenices constellation and is part of the Virgo Cluster of galaxies. M91 is about 63 million light-years away from the earth. It was the last of a group of eight nebulae discovered by Charles Messier in 1781...
, a magnitude 11.5 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....
Coma BerenicesComa BerenicesComa Berenices is a traditional asterism that has since been defined as one of the 88 modern constellations. It is located near Leo, to which it formerly belonged, and accommodates the North Galactic Pole...
- 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 91, a single starStarA star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
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 August 6, 159 BC and ended on 1175 October. The duration of Saros series 91 was 1334.2 years, and it contained 75 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 161 May and ended on 1459 July. The duration of Saros series 91 was 1298.1 years, and it contained 73 lunar eclipses.
In other fields
Ninety-one is also:- The year AD 9191Year 91 was a common year starting on Saturday of the Julian calendar. At the time, it was known as the Year of the Consulship of Glabrio and Traianus...
, 91 BC91 BCYear 91 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Philippus and Caesar...
, or 1991. - The designation of AmericanUnited StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district...
Interstate 91Interstate 91Interstate 91 is an Interstate Highway in the New England region of the United States. It provides the primary north–south thoroughfare in the western part of New England...
, a freeway that runs from ConnecticutConnecticutConnecticut is a state in the New England region of the northeastern United States. It is bordered by Rhode Island to the east, Massachusetts to the north, and the state of New York to the west and the south .Connecticut is named for the Connecticut River, the major U.S. river that approximately...
to VermontVermontVermont is a state in the New England region of the northeastern United States of America. The state ranks 43rd in land area, , and 45th in total area. Its population according to the 2010 census, 630,337, is the second smallest in the country, larger only than Wyoming. It is the only New England... - The designation of U.S. Route 91, a north-south highway that runs from UtahUtahUtah is a state in the Western United States. It was the 45th state to join the Union, on January 4, 1896. Approximately 80% of Utah's 2,763,885 people live along the Wasatch Front, centering on Salt Lake City. This leaves vast expanses of the state nearly uninhabited, making the population the...
to IdahoIdahoIdaho is a state in the Rocky Mountain area of the United States. The state's largest city and capital is Boise. Residents are called "Idahoans". Idaho was admitted to the Union on July 3, 1890, as the 43rd state.... - The code for international direct dial phone calls to 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...
- In cents of a U.S. dollarUnited States dollarThe United States dollar , also referred to as the American dollar, is the official currency of the United States of America. It is divided into 100 smaller units called cents or pennies....
, the amount of money one has if one has one each of the coins of denominations less than a dollarDollarThe dollar is the name of the official currency of many countries, including Australia, Belize, Canada, Ecuador, El Salvador, Hong Kong, New Zealand, Singapore, Taiwan, and the United States.-Etymology:...
(pennyPennyA penny is a coin or a type of currency used in several English-speaking countries. It is often the smallest denomination within a currency system.-Etymology:...
, nickelNickelNickel is a chemical element with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel belongs to the transition metals and is hard and ductile...
, dimeDime (United States coin)The dime is a coin 10 cents, one tenth of a United States dollar, labeled formally as "one dime". The denomination was first authorized by the Coinage Act of 1792. The dime is the smallest in diameter and is the thinnest of all U.S...
, quarterQuarter (United States coin)A quarter dollar, commonly shortened to quarter, is a coin worth ¼ of a United States dollar, or 25 cents. The quarter has been produced since 1796. The choice of 25¢ as a denomination, as opposed to 20¢ which is more common in other parts of the world, originated with the practice of dividing...
and half dollarHalf dollarHalf dollar may refer to a half-unit of several currencies that are named "dollar". Normally, $1 is divided into 100 cents, so a half dollar is equal to 50 cents...
) - The ISBN Group Identifier for books published in SwedenSwedenSweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....
. - Psalm 91Psalm 91Psalm 91 , referred to by its Latin title Qui habitat , is known as the Psalm of Protection. As a religious song, this Psalm is commonly invoked in times of hardship...
is known as the Psalm of Protection. It is also the title of a book by Peggy Joyce Ruth - 91 is a solitaireSolitaireSolitaire is any tabletop game which one can play by oneself or with other people. The solitaire card game Klondike is often known as simply Solitaire....
card game where the object is to move cards, so the top cards total 91. - STS-91STS-91STS-91 was the final Space Shuttle mission to the Mir space station. It was flown by Space Shuttle Discovery, and launched from Kennedy Space Center, Florida, on 2 June 1998.-Crew:-Mission parameters:*Mass:...
Space Shuttle DiscoverySpace Shuttle DiscoverySpace Shuttle Discovery is one of the retired orbiters of the Space Shuttle program of NASA, the space agency of the United States, and was operational from its maiden flight, STS-41-D on August 30, 1984, until its final landing during STS-133 on March 9, 2011...
mission to the International Space StationInternational Space StationThe International Space Station is a habitable, artificial satellite in low Earth orbit. The ISS follows the Salyut, Almaz, Cosmos, Skylab, and Mir space stations, as the 11th space station launched, not including the Genesis I and II prototypes...
, June 2, 1998 - SwedishSwedenSweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....
comic strip 91:an91:an (comic strip)91:an is a popular Swedish comic strip, first created in 1932 with the title En beväringsmans upplevelser och äventyr. This name soon changed to 91:an Karlsson, by Rudolf Petersson... - The 91st Space Wing91st Space WingThe 91st Missile Wing is a United States Air Force unit assigned to the Air Force Global Strike Command Twentieth Air Force. It is stationed at Minot Air Force Base, North Dakota as a tenant unit....
(91 SW) is a Minuteman (missile) III unit of the United States Air ForceUnited States Air ForceThe United States Air Force is the aerial warfare service branch of the United States Armed Forces and one of the American uniformed services. Initially part of the United States Army, the USAF was formed as a separate branch of the military on September 18, 1947 under the National Security Act of...
, based at Minot Air Force BaseMinot Air Force BaseMinot Air Force Base is a U.S. Air Force installation in Ward County, North Dakota, north of the city of Minot. In the 2010 census, the base was counted as a CDP with a total population of 5,521....
, North DakotaNorth DakotaNorth Dakota is a state located in the Midwestern region of the United States of America, along the Canadian border. The state is bordered by Canada to the north, Minnesota to the east, South Dakota to the south and Montana to the west. North Dakota is the 19th-largest state by area in the U.S.... - The number of the French department EssonneEssonneEssonne is a French department in the region of Île-de-France. It is named after the Essonne River.It was formed on 1 January 1968 when Seine-et-Oise was split into smaller departments.- History :...