51 (number)

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← 50 51 52 →
Cardinal fifty-one
Ordinal 51st
(fifty-first)
Factorization 3 × 17
Divisors 1, 3, 17, 51
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 other fields[edit]

51 is:

  • The atomic number of antimony
  • The code for international direct dial phone calls to Peru
  • The last possible television channel number in the UHF bandplan for American terrestrial television since December 31, 2011, when channels 52—69 were withdrawn

See also[edit]

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 .