51 (number)
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Template:Infobox number Template:Wiktionary 51 (fifty-one) is the natural number following 50 and preceding 52.
In mathematics
Fifty-one is
- a pentagonal number<ref>Template:Cite web</ref> as well as a centered pentagonal number<ref>Template:Cite web</ref> and an 18-gonal number<ref>Template:Cite web</ref>
- 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.<ref>Template:Cite web</ref>
- a Perrin number,<ref>Template:Cite web</ref> 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.<ref>Template:Cite web</ref>
- There are 51 different cyclic Gilbreath permutations on 10 elements,<ref>Template:Cite OEIS</ref> and therefore there are 51 different real periodic points of order 10 on the Mandelbrot set.<ref>Template:Citation.</ref>
- 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 Template:Sfrac is constructible, and the number cos Template:Sfrac is expressible in terms of square roots.