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
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 also6-Sphere Coordinates
, Barth Sextic
, Sextic Equation
, Six Circles Theorem
, Six Exponentials Theorem
This entry contributed by Margherita
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ReferencesChandrasekharan, K. Hermann Weyl (1885-1985): Centenary Lectures. Berlin: Springer-Verlag, 1986.Descartes,
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.
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.