51 (number)

Template:Infobox number Template:Sister project 51 (fifty-one) is the natural number following 50 and preceding 52.

In mathematics

Fifty-one is

• a pentagonal number<ref>{{#invoke:citation/CS1|citation

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• 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>{{#invoke:citation/CS1|citation

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• a Perrin number,<ref>{{#invoke:citation/CS1|citation

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• a Størmer number, since the greatest prime factor of 51² + 1 = 2602 is 1301, which is substantially more than 51 twice.<ref>{{#invoke:citation/CS1|citation

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• 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.

References

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