51 (number)

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← 50 51 52 →
Cardinal fifty-one
Ordinal 51st
(fifty-first)
Factorization 3 × 17
Divisors 1, 3, 17, 51
Greek numeral ΝΑ´
Roman numeral LI
Binary 1100112
Ternary 12203
Quaternary 3034
Quinary 2015
Senary 1236
Octal 638
Duodecimal 4312
Hexadecimal 3316
Vigesimal 2B20
Base 36 1F36

51 (fifty-one) is the natural number 51 following 50 and preceding 52.

In mathematics[edit]

Fifty-one is a pentagonal number[1] as well as a centered pentagonal number[2] (one of the few numbers to be both) and an 18-gonal number[3] and a Perrin number.[4] It is also the 6th Motzkin number, telling the number of ways to draw non-intersecting chords between any six points on a circle's boundary, no matter where the points may be located on the boundary.[5]

Since the greatest prime factor of 512 + 1 = 2602 is 1301, which is substantially more than 51 twice, 51 is a Størmer number.[6] There are 51 different cyclic Gilbreath permutations on 10 elements,[7] and therefore there are 51 different real periodic points of order 10 on the Mandelbrot set.[8]

Since 51 is the product of the distinct Fermat primes 3 and 17, a regular polygon with 51 sides is constructible with compass and straightedge, the angle π/51 is constructible, and the number cos π/51 is expressible in terms of square roots.

In history[edit]

Alexander Hamilton wrote 51 of the 85 federalist papers.

In other fields[edit]

51 is:

See also[edit]

  • AD 51, a year in the Julian calendar
  • List of highways numbered 51
  • The model number of the P-51 Mustang World War II fighter aircraft
  • Area 51, a parcel of U.S. military-controlled land in southern Nevada, apparently containing a secret aircraft testing facility
  • Photo 51, an X-ray image of key importance in elucidating the structure of DNA in the 1950s
  • Fifty-One Tales, part of the title of a collection of stories by Lord Dunsany
  • "51st State", any future US state, usually referring to Washington D.C. or Puerto Rico. Occasionally used in commentary to refer to non-US entities (such as Alberta) adopting US-like policies or seeking to become part of the US.
  • 51 (film), a 2011 American horror film
  • "Fifty-One", an episode of Breaking Bad
  • Pastis 51, often just called "51", is a brand of pastis owned by Pernod Ricard.
  • Greg Murphy used "#51" for most of the seasons he raced in V8 Supercars

References[edit]

  1. ^ "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  2. ^ "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  3. ^ "Sloane's A051870 : 18-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  4. ^ "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  5. ^ "Sloane's A001006 : Motzkin numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  6. ^ "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30. 
  7. ^ "Sloane's A000048". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 
  8. ^ Diaconis, Persi; Graham, Ron (2012), "Chapter 5: From the Gilbreath Principle to the Mandelbrot Set", Magical Mathematics: the mathematical ideas that animate great magic tricks, Princeton University Press, pp. 61–83 .