The smallest composite squarefree number (triangular
number (perfect number , since combinatorics
as the binomial coefficient Pascal's
triangle and counts the 2-subsets of a set with 4 elements. It is also equal
to factorial ),
the number of permutations of three objects, and the order of the symmetric
group
Six is indicated by the Latin prefix sex- , as in sextic, or by the Greek prefix hexa- (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
References Chandrasekharan, K. Hermann Weyl (1885-1985): Centenary Lectures. Descartes,
R. Discours
de la méthode: Les météores. 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. Weyl, H. Symmetry.
Cite this as:
Barile, Margherita . "6." From MathWorld Eric W. Weisstein .
https://mathworld.wolfram.com/6.html
Subject classifications
), 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).
-), as in hexagon,
hexagram, or hexahedron.
