135 (one hundred ndthirty-five) is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal n ...

following

134 134 may refer to: * 134 (number) * AD 134 * 134 BC * 134 (MBTA bus) *134 (New Jersey bus) 134 may refer to: *134 (number) * AD 134 *134 BC *134 (MBTA bus) The Massachusetts Bay Transportation Authority bus division operates bus routes in the B ...

and preceding 136.

In mathematics

135 is the number of

partitions Partition may refer to: Computing Hardware * Disk partitioning, the division of a hard disk drive * Memory partition, a subdivision of a computer's memory, usually for use by a single job Software * Partition (database), the division of a ...

of 14, and the number of rooted trees with 15 nodes and height at most 2. 135 is 5-

smooth Smooth may refer to: Mathematics * Smooth function, a function that is infinitely differentiable; used in calculus and topology * Smooth manifold, a differentiable manifold for which all the transition maps are smooth functions * Smooth algebrai ...

, since its prime factorization is

3^3 \times 5

, and a

Harshad number In mathematics, 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 in base are also known as -harshad (or -Niven) numbers. Harshad numbers ...

decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...

. 135 is not, however,

square-free {{no footnotes, date=December 2015 In mathematics, a square-free element is an element ''r'' of a unique factorization domain ''R'' that is not divisible by a non-trivial square. This means that every ''s'' such that s^2\mid r is a unit of ''R''. A ...

. Using its own digits, 135 in

base-10 The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...

can be expressed in operations as the sum of consecutive powers of its digits, and as a sum-product number: :

135 = 1^1 + 3^2 + 5^3

135 = (1 + 3 + 5)(1 \times 3 \times 5)

135 is the number of degrees in the

internal angle In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or ) if ...

of a regular eight-sided

octagon In geometry, an octagon (from the Greek ὀκτάγωνον ''oktágōnon'', "eight angles") is an eight-sided polygon or 8-gon. A '' regular octagon'' has Schläfli symbol and can also be constructed as a quasiregular truncated square, t, whi ...

. Also: *the

Euler totient In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In o ...

of 135 is 72: the degrees of an

central angle A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. Central angles are subtended by an arc between those two points, and the arc le ...

in a regular

pentagon In geometry, a pentagon (from the Greek πέντε ''pente'' meaning ''five'' and γωνία ''gonia'' meaning ''angle'') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simpl ...

. *the

arithmetic mean In mathematics and statistics, the arithmetic mean ( ) or arithmetic average, or just the ''mean'' or the ''average'' (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The colle ...

of the divisors of 135 is 30: the degrees in a central angle of a regular

dodecagon In geometry, a dodecagon or 12-gon is any twelve-sided polygon. Regular dodecagon A regular dodecagon is a figure with sides of the same length and internal angles of the same size. It has twelve lines of reflective symmetry and rotational sym ...

. While the central angle of a regular octagon is 135 ÷ 3 = 45 degrees, 4.5 is the

harmonic mean In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired. The harmonic mean can be expressed as the recipro ...

of all eight divisors of 135. The

aliquot sum In number theory, the aliquot sum ''s''(''n'') of a positive integer ''n'' is the sum of all proper divisors of ''n'', that is, all divisors of ''n'' other than ''n'' itself. That is, :s(n)=\sum\nolimits_d. It can be used to characterize the prim ...

of 135 is 105, which is the 14th

triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...

, or equivalently the sum of the first fourteen non-zero positive

integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...

s. There are a total of 135

primes A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

between 1,000 and 2,000.

135 = 11 n^2 + 11 n + 3

for

n = 3

is a

polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An exa ...

that plays an essential role in Apéry's proof that

\zeta(3)

is irrational.

In other fields

* The year AD 135 or 135 BC. * 135 AH is a year in the

Islamic calendar The Hijri calendar ( ar, ٱلتَّقْوِيم ٱلْهِجْرِيّ, translit=al-taqwīm al-hijrī), also known in English as the Muslim calendar and Islamic calendar, is a lunar calendar consisting of 12 lunar months in a year of 354 or ...

that corresponds to 752–753 CE. * 135 Hertha is a large

main belt The asteroid belt is a torus-shaped region in the Solar System, located roughly between the orbits of the planets Jupiter and Mars. It contains a great many solid, irregularly shaped bodies, of many sizes, but much smaller than planets, called ...

asteroid An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. ...

which orbits among the

Nysa Nysa may refer to: Greek Mythology * Nysa (mythology) or Nyseion, the mountainous region or mount (various traditional locations), where nymphs raised the young god Dionysus * Nysiads, nymphs of Mount Nysa who cared for and taught the infant ...

asteroid family. *

135 film 135 film, more popularly referred to as 35 mm film or 35 mm, is a format of photographic film used for still photography. It is a film with a film gauge of loaded into a standardized type of magazine – also referred to as a casse ...

, the cartridge version of 35mm photographic film, used widely in still photography. * The Canon FD 135 mm lens. * In

astrology Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of Celestial o ...

, when two planets are 135 degrees apart, they are in an

astrological aspect In astrology, an aspect is an angle that planets make to each other in the Horoscope; as well as to the Ascendant, Midheaven, Descendant, Lower Midheaven, and other points of astrological interest. As viewed from Earth, aspects are measured ...

called a sesquiquadrate. The aspect was first used by

Johannes Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...

. *

Sonnet 135 In Shakespeare's Sonnet 135, the speaker appeals to his mistress after having been rejected by her. Synopsis In the first quatrain of the sonnet, the speaker pledges himself to the mistress, while he humbly refers to himself as "I that vex th ...

William Shakespeare William Shakespeare ( 26 April 1564 – 23 April 1616) was an English playwright, poet and actor. He is widely regarded as the greatest writer in the English language and the world's pre-eminent dramatist. He is often called England's nation ...

. *

Municipal District of Peace No. 135 The Municipal District of Peace No. 135 is a List of municipal districts in Alberta, municipal district (MD) in northwestern Alberta, Canada. Located in Division No. 19, Alberta, Census Division No. 19, its List of municipal districts in Albert ...

, a

municipal district A municipal district is an administrative entity comprising a clearly-defined territory and its population. It can refer to a city, a town, a village, a small grouping of them, or a rural area. Brazil In Brazil, municipal districts are, in genera ...

in northwest

Alberta Alberta ( ) is one of the thirteen provinces and territories of Canada. It is part of Western Canada and is one of the three prairie provinces. Alberta is bordered by British Columbia to the west, Saskatchewan to the east, the Northwest Ter ...

, Canada. *

Enoch Cree Nation 135 Enoch Cree Nation 135, ( cr, ᒪᐢᑫᑯᓯᐦᐠ, translit=maskêkosihk ) previously known as Stony Plain No. 135, is an Indian reserve of the Enoch Cree Nation #440 in Alberta. It is adjacent to the City of Edmonton to the east and Parkland ...

Indian reserve In Canada, an Indian reserve (french: réserve indienne) is specified by the '' Indian Act'' as a "tract of land, the legal title to which is vested in Her Majesty, that has been set apart by Her Majesty for the use and benefit of a band." Ind ...

in Alberta, Canada is home to the

Enoch Cree Nation The Enoch Cree Nation #440 ( cr, script=Cans, ᒪᐢᑫᑯᓯᐦᐠ, ) is a First Nations band government in Alberta, Canada. Members of the Nation are of Cree ancestry and speak the Plains Cree dialect of the Cree language group. The band i ...

. * The

EZ 135 Drive The EZ 135 Drive is a 3.5" removable platter hard disk drive. It was introduced by SyQuest Technology in 1995. It had a maximum capacity of 135 MB per disk. A successor drive, known as the SyQuest EZFlyer, was released in 1996. It was backwa ...

removable

hard disk drive A hard disk drive (HDD), hard disk, hard drive, or fixed disk is an electro-mechanical data storage device that stores and retrieves digital data using magnetic storage with one or more rigid rapidly rotating platters coated with magnet ...

introduced by

SyQuest Technology SyQuest Technology, Inc. () was an early entrant into the hard disk drive market for personal computers. The company was founded on January 27, 1982 by Syed Iftikar who had been a founder of Seagate, along with Ben Alaimo, Bill Krajewski, Anil N ...

in 1995. *

OC-135B Open Skies The OC-135B Open Skies is a United States Air Force observation aircraft that supports the Treaty on Open Skies. The aircraft, a modified WC-135B, flies unarmed observation flights over participating parties of the treaty. Three OC-135B aircr ...

United States Air Force observation aircraft flies unarmed observation flights over nations of the

Treaty on Open Skies The Treaty on Open Skies establishes a program of unarmed aerial surveillance flights over the entire territory of its participants. The treaty is designed to enhance mutual understanding and confidence by giving all participants, regardless ...

References

{{DEFAULTSORT:135 (Number) Integers

In mathematics

In other fields

See also

References