The smallest composite squarefree number (2·3), and the third triangular number (3(3+1)/2). It is the also smallest perfect number, since 6=1+2+3. The number 6 arises in combinatorics as the binomial coefficient (4; 2), which appears in Pascal's triangle and counts the 2-subsets of a set with 4 elements. It is also equal to 3!=1·2·3 (3 factorial), the number of permutations of three objects, and the order of the symmetric group S_3 (which is the smallest non-Abelian group).

Six is indicated by the Latin prefix sex-, as in sextic, or by the Greek prefix hexa- (epsilon^'xialpha-), 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

Explore with Wolfram|Alpha


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.

Subject classifications