The smallest composite squarefree number ( ), and the third triangular
number ( ). It is the also smallest perfect number , since . The number 6 arises in combinatorics
as the binomial coefficient , which appears in Pascal's
triangle and counts the 2-subsets of a set with 4 elements. It is also equal
to (3 factorial ),
the number of permutations of three objects, and the order of the symmetric
group (which is the smallest non-Abelian
group).

Six is indicated by the Latin prefix sex- , as in sextic, or by the Greek prefix hexa- ( -), as in hexagon ,
hexagram , or hexahedron .

The six-fold symmetry is typical of crystals such as snowflakes. A mathematical and physical treatment can be found in Kepler (Halleux 1975), Descartes (1637), Weyl (1952), and Chandrasekharan (1986).

See also 6-Sphere Coordinates ,

Barth Sextic ,

Cayley's
Sextic ,

Hexagon ,

Hexahedral
Graph ,

Hexahedron ,

Sextic
Curve ,

Sextic Equation ,

Sextic
Surface ,

Six Circles Theorem ,

Six-Color
Theorem ,

Six Exponentials Theorem ,

Wigner 6j -Symbol
This entry contributed by Margherita
Barile

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References Chandrasekharan, K. Hermann Weyl (1885-1985): Centenary Lectures. Berlin: Springer-Verlag, 1986. Descartes,
R. Discours
de la méthode: Les météores. Leyden, Netherlands, 1637. Kepler,
J. Étrenne ou la Neige sexangulaire. Translated from Latin by R. Halleux.
Paris, France: J. Vrin Éditions du CNRS, 1975. Wells, D.
The
Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England:
Penguin Books, pp. 67-69, 1986. Weyl, H. Symmetry.
Princeton, NJ: Princeton University Press, 1952.
Cite this as:
Barile, Margherita . "6." From MathWorld --A Wolfram Web Resource, created by Eric W. Weisstein .
https://mathworld.wolfram.com/6.html

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