135 (number)

From HandWiki
Short description: Natural number
← 134 135 136 →
Cardinalone hundred thirty-five
Ordinal135th
(one hundred thirty-fifth)
Factorization33 × 5
Divisors1, 3, 5, 9, 15, 27, 45, 135
Greek numeralΡΛΕ´
Roman numeralCXXXV
Binary100001112
Ternary120003
Quaternary20134
Quinary10205
Senary3436
Octal2078
DuodecimalB312
Hexadecimal8716
Vigesimal6F20
Base 363R36

135 (one hundred [and] thirty-five) is the natural number following 134 and preceding 136.

In mathematics

This number in base 10 can be expressed in operations using its own digits in at least two different ways. One is as a sum-product number,

[math]\displaystyle{ 135 = (1 + 3 + 5)(1 \times 3 \times 5) }[/math]

(1 and 144 share this property)[1] and the other is as the sum of consecutive powers of its digits:[2]

[math]\displaystyle{ 135 = 1^1 + 3^2 + 5^3 }[/math]

(175, 518, and 598 also have this property).

There are a total of 135 primes between 1,000 and 2,000.

[math]\displaystyle{ 135 = 11 n^2 + 11 n + 3 }[/math] for [math]\displaystyle{ n = 3 }[/math]. This polynomial plays an essential role in Apéry's proof that [math]\displaystyle{ \zeta(3) }[/math] is irrational.

In the military

In transportation

  • London Buses route 135 is a Transport for London contracted bus route in London
  • 135th Street station on the IND Eighth Avenue Line of the New York City Subway on St. Nicholas Avenue in Manhattan
  • 135th Street station on the IRT Lenox Avenue Line of the New York City Subway on Lenox Avenue in Manhattan

In other fields

  • The year AD 135 or 135 BC
  • 135 AH is a year in the Islamic calendar that corresponds to 752–753 CE
  • 135 Hertha is a large main belt asteroid which orbits among the Nysa asteroid family
  • 135 film, the cartridge version of 35mm photographic film, used widely in still photography
  • The Canon FD 135 mm lens
  • In astrology, when two planets are 135 degrees apart, they are in an astrological aspect called a sesquiquadrate. The aspect was first used by Johannes Kepler
  • Sonnet 135 by William Shakespeare
  • Municipal District of Peace No. 135, a municipal district in northwest Alberta, Canada
  • Enoch Cree Nation 135 Indian reserve in Alberta, Canada is home to the Enoch Cree Nation
  • The EZ 135 Drive removable hard disk drive introduced by SyQuest Technology in 1995

See also

  • List of highways numbered 135
  • United Nations Security Council Resolution 135
  • United States Supreme Court cases, Volume 135

References