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 ...

following 134 and preceding 136.

In mathematics

135 is the number of partitions of 14, and the number of rooted trees with 15 nodes and height at most 2. 135 is 5- smooth, since its prime factorization is

3^3 \times 5

, and a Harshad number in decimal. 135 is not, however, square-free. Using its own digits, 135 in base-10 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, wh ...

. Also: *the Euler totient 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 language, 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 polygon, simple pentagon is ...

. *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 coll ...

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 symm ...

. 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 recipr ...

of all eight divisors of 135. The aliquot sum of 135 is

105 105 may refer to: *105 (number), the number *AD 105, a year in the 2nd century AD *105 BC, a year in the 2nd century BC * 105 (telephone number) * 105 (MBTA bus) * 105 (Northumberland) Construction Regiment, Royal Engineers, an English military unit ...

, 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 i ...

, 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 between

1,000 1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000. A group of one thousand thi ...

and

2,000 2000 (two thousand) is a natural number following 1999 and preceding 2001. It is: :*the highest number expressible using only two unmodified characters in Roman numerals (MM) :*an Achilles number :*smallest four digit eban number Selected ...

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 ex ...

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 ...

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

asteroid An asteroid is a minor planet of the Solar System#Inner solar system, 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 o ...

which orbits among the Nysa 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 cas ...

, the cartridge version of 35mm photographic film, used widely in still photography. * The

Canon FD 135 mm lens Several different models of Canon FD 135 mm lenses were produced by Canon Inc. for the Canon FD lens mount. Two were produced in the original "Old FD" style with a silver locking ring for the breech lock mount at the base, while three models ...

. * In

astrology Astrology is a range of 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 objects. Di ...

, 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 measur ...

called a sesquiquadrate. The aspect was first used by Johannes Kepler. * Sonnet 135 by

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 natio ...

. *

Municipal District of Peace No. 135 The Municipal District of Peace No. 135 is a municipal district (MD) in northwestern Alberta, Canada. Located in Census Division No. 19, its municipal office is located outside but adjacent to the Village of Berwyn. Geography Communities ...

, 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

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." Indi ...

in Alberta, Canada is home to the Enoch Cree Nation. * The EZ 135 Drive 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 magn ...

introduced by SyQuest Technology in 1995. * OC-135B Open Skies 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