This entry contributed by Margherita Barile
The smallest composite squarefree number (
), and the third triangular number (
). It is the also smallest perfect number, since 
.
,
(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).
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
Chandrasekharan, K. Hermann Weyl (1885-1985): Centenary Lectures. Berlin: Springer-Verlag, 1986.
Descartes, R. 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.
 |
|||
|
|
||