35 (number)
Encyclopedia
35 is the natural number
following 34
and preceding 36
.
35 is the sum of the first five triangular number
s, making it a tetrahedral number
.
35 is the number of ways that three things can be selected from a set of seven unique things also known
as the "combination
of seven things taken three at a time".
35 is a centered cube number
, a pentagonal number
and a pentatope number
.
35 is a highly cototient number
, since there are more solutions to the equation x - φ(x) = 35 than there are for any other integers below it except 1.
There are 35 free hexomino
es, the polyomino
es made from six squares.
Since the greatest prime factor of 352 + 1 = 1226 is 613, which is obviously more than 35 twice, 35 is a Størmer number
.
35 is a discrete semiprime
(or biprime) (5 × 7); the tenth, and the first with 5 as the lowest non-unitary factor. The aliquot sum of 35 is 13 this being the second composite number
with such an aliquot sum; the first being the cube 27. 35 is the last member of the first triple cluster of semiprimes 33,34,35. 85,86,87 is the second such triple discrete semiprime cluster.
35 is the highest number one can count to on one's fingers using base 6.
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 34
34 (number)
34 is the natural number following 33 and preceding 35.-In mathematics:34 is the ninth distinct semiprime and has four divisors including unity and itself. Its neighbors, 33 and 35, also are distinct semiprimes, having four divisors each, and 34 is the smallest number to be surrounded by numbers...
and preceding 36
36 (number)
36 is the natural number following 35 and preceding 37.- In mathematics :36 is both the square of 6 and a triangular number, making it a square triangular number...
.
In mathematics
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...
s, making it a tetrahedral number
Tetrahedral number
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron...
.
35 is the number of ways that three things can be selected from a set of seven unique things also known
as the "combination
Combination
In mathematics a combination is a way of selecting several things out of a larger group, where order does not matter. In smaller cases it is possible to count the number of combinations...
of seven things taken three at a time".
35 is 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...
, a pentagonal number
Pentagonal number
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical...
and a pentatope number
Pentatope number
A pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row 1 4 6 4 1 either from left to right or from right to left.The first few numbers of this kind are :...
.
35 is a highly cototient number
Highly cototient number
In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above one and has more solutions to the equation...
, since there are more solutions to the equation x - φ(x) = 35 than there are for any other integers below it except 1.
There are 35 free hexomino
Hexomino
A hexomino is a polyomino of order 6, that is, a polygon in the plane made of 6 equal-sized squares connected edge-to-edge. The name of this type of figure is formed with the prefix hex-. When rotations and reflections are not considered to be distinct shapes, there are 35 different free hexominoes...
es, the polyomino
Polyomino
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling with a connected interior....
es made from six squares.
Since the greatest prime factor of 352 + 1 = 1226 is 613, which is obviously more than 35 twice, 35 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....
.
35 is a discrete semiprime
Semiprime
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, ... ....
(or biprime) (5 × 7); the tenth, and the first with 5 as the lowest non-unitary factor. The aliquot sum of 35 is 13 this being the second composite number
Composite number
A composite number is a positive integer which has a positive divisor other than one or itself. In other words a composite number is any positive integer greater than one that is not a prime number....
with such an aliquot sum; the first being the cube 27. 35 is the last member of the first triple cluster of semiprimes 33,34,35. 85,86,87 is the second such triple discrete semiprime cluster.
35 is the highest number one can count to on one's fingers using base 6.
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...
M35, a magnitude 5.5 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....
GeminiGemini (constellation)Gemini is one of the constellations of the zodiac. It was one of the 48 constellations described by the 2nd century astronomer Ptolemy and it remains one of the 88 modern constellations today. Its name is Latin for "twins", and it is associated with the twins Castor and Pollux in Greek mythology...
- 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 35, a galaxyGalaxyA galaxy is a massive, gravitationally bound system that consists of stars and stellar remnants, an interstellar medium of gas and dust, and an important but poorly understood component tentatively dubbed dark matter. The word galaxy is derived from the Greek galaxias , literally "milky", a...
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 -1870 (1871 BC) July 25 and ended on -373 (374 BC374 BCYear 374 BC was a year of the pre-Julian Roman calendar. At the time, it was known as the Second year without Tribunate or Consulship...
) January 9. The duration of Saros series 35 was 1496.5 years, and it contained 84 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 -1550 (1551 BC) May 14 and ended on -252 (253 BC253 BCYear 253 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Caepio and Blaesus...
) July 1. The duration of Saros series 35 was 1298.1 years, and it contained 73 lunar eclipses.
In other fields
35 is also:- 35 mm film35 mm film35 mm film is the film gauge most commonly used for chemical still photography and motion pictures. The name of the gauge refers to the width of the photographic film, which consists of strips 35 millimeters in width...
is the basic film gauge most commonly used for both analog photographyPhotographyPhotography is the art, science and practice of creating durable images by recording light or other electromagnetic radiation, either electronically by means of an image sensor or chemically by means of a light-sensitive material such as photographic film...
and motion pictures - "35 c", a song by JagúarJagúar (band)Jagúar is a funk band formed in 1998 in Reykjavík, Iceland. They went international in 2000, when they performed at the "1000 years since the Vikings found America" celebration in New York. The band gained critical acclaim for their second album, Get the Funk Out, which won the Icelandic Music...
from the album Jagúar - The designation of Interstate 35Interstate 35Interstate 35 is a north–south Interstate Highway in the central United States. I-35 stretches from Laredo, Texas, on the U.S.-Mexico border to Duluth, Minnesota, at Minnesota Highway 61 and 26th Avenue East. Many interstates used to have splits or spurs indicated with suffixed letters , but I-35...
, a freeway that runs from 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...
to MinnesotaMinnesotaMinnesota is a U.S. state located in the Midwestern United States. The twelfth largest state of the U.S., it is the twenty-first most populous, with 5.3 million residents. Minnesota was carved out of the eastern half of the Minnesota Territory and admitted to the Union as the thirty-second state...
and the only freeway to have East–West divisions (in two places, the Twin CitiesTwin citiesTwin cities are a special case of two cities or urban centres which are founded in close geographic proximity and then grow into each other over time...
and the DFW Metroplex) - Convoy of 35Convoy of 35The Convoy of 35 refers to 35 soldiers of the Haganah who were killed while attempting to resupply and or reinforce the Gush Etzion kibbutzim by foot on January 16, 1948, after a number of convoys had been attacked during the early stages of the 1947–1948 Civil War in Mandatory Palestine.- Attack...
Israeli soldiers, who were killed in the war of independence in 1948 - Retired MLB jerseys:
- Randy Jones from the San Diego PadresSan Diego PadresThe San Diego Padres are a Major League Baseball team based in San Diego, California. They play in the National League Western Division. Founded in 1969, the Padres have won the National League Pennant twice, in 1984 and 1998, losing in the World Series both times...
(1997) - Phil NiekroPhil NiekroPhilip Henry Niekro , nicknamed "Knucksie" because of his usage and skill level with the knuckleball, is a former Major League Baseball pitcher. He was inducted into the Baseball Hall of Fame in 1997....
from the Atlanta BravesAtlanta BravesThe Atlanta Braves are a professional baseball club based in Atlanta, Georgia. The Braves are a member of the Eastern Division of Major League Baseball's National League. The Braves have played in Turner Field since 1997....
(1984) - Frank Thomas from the Chicago White SoxChicago White SoxThe Chicago White Sox are a Major League Baseball team located in Chicago, Illinois.The White Sox play in the American League's Central Division. Since , the White Sox have played in U.S. Cellular Field, which was originally called New Comiskey Park and nicknamed The Cell by local fans...
(August 2010)
- Randy Jones from the San Diego Padres
- Licence Plate code of IzmirIzmirIzmir is a large metropolis in the western extremity of Anatolia. The metropolitan area in the entire Izmir Province had a population of 3.35 million as of 2010, making the city third most populous in Turkey...
/TurkeyTurkeyTurkey , known officially as the Republic of Turkey , is a Eurasian country located in Western Asia and in East Thrace in Southeastern Europe...
. - XXXV (album)XXXV (album)XXXV is a 2001 album by Fairport Convention, subtitled "The 35th Anniversary Album".-Track listing:# "Madeleine" - 4:23# "My Love Is in America" - 4:43...
, the thirty-fifth anniversary album by folk rockFolk rockFolk rock is a musical genre combining elements of folk music and rock music. In its earliest and narrowest sense, the term referred to a genre that arose in the United States and the UK around the mid-1960s...
band Fairport ConventionFairport ConventionFairport Convention are an English folk rock and later electric folk band, formed in 1967 who are still recording and touring today. They are widely regarded as the most important single group in the English folk rock movement... - 35 is the title of a book written by Casper Schipper
- The F-35 Lightning IIF-35 Lightning IIThe Lockheed Martin F-35 Lightning II is a family of single-seat, single-engine, fifth generation multirole fighters under development to perform ground attack, reconnaissance, and air defense missions with stealth capability...
Aircraft - The minimum age of candidates for election to the United States Presidency.