51 (number)
(Redirected from Fifty-one)
| ||||
|---|---|---|---|---|
| Cardinal | fifty-one | |||
| Ordinal | 51st (fifty-first) | |||
| Factorization | 3 × 17 | |||
| Divisors | 1, 3, 17, 51 | |||
| Greek numeral | ΝΑ´ | |||
| Roman numeral | LI, li | |||
| Binary | 1100112 | |||
| Ternary | 12203 | |||
| Senary | 1236 | |||
| Octal | 638 | |||
| Duodecimal | 4312 | |||
| Hexadecimal | 3316 | |||
Look up fifty-one in Wiktionary, the free dictionary.
51 (fifty-one) is the natural number following 50 and preceding 52.
In mathematics
[edit]Fifty-one is
- a pentagonal number[1] as well as a centered pentagonal number[2] and an 18-gonal number[3]
- 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.[4]
- a Perrin number,[5] coming after 22, 29, 39 in the sequence (and the sum of the first two)
- a Størmer number, since the greatest prime factor of 512 + 1 = 2602 is 1301, which is substantially more than 51 twice.[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.
References
[edit]- ^ "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- ^ "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- ^ "Sloane's A051870 : 18-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- ^ "Sloane's A001006 : Motzkin numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- ^ "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- ^ "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- ^ Sloane, N. J. A. (ed.). "Sequence A000048". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.