51 (number)

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

← 50 51 52 →
Cardinalfifty-one
Ordinal51st
(fifty-first)
Factorization3 × 17
Divisors1, 3, 17, 51
Greek numeralΝΑ´
Roman numeralLI
Binary1100112
Ternary12203
Octal638
Duodecimal4312
Hexadecimal3316

In mathematicsEdit

Fifty-one is a pentagonal number[1] as well as a centered pentagonal number[2] 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 fieldsEdit

51 is:

See alsoEdit

ReferencesEdit

  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, N. J. A. (ed.). "Sequence 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.