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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