From: chavey@beloit.edu (Darrah Chavey) Newsgroups: sci.math Subject: Re: symmetry Date: Mon, 22 Jan 1996 11:43:49 -0600 In article <30FD182E.41C67EA6@discover.wright.edu>, ISAAC FORQUER wrote: > Hi, > I am just nearly above a laymen when it comes to mathematics. > I know some fundamentals of calculus and other wierd mostly > non-applicable stuff. I'm a biology student. I read an article about > there being seven different forms of symmetry and was wondering if > anyone could enlighten me as to what they are. Sounds like a reference to the seven different one dimensional symmetry groups. If you have a repetition along a straight line or band, then there you can have the following symmetry elements: Horizontal (top-bottom) reflection: B B B B B B B B ... Vertical (left-right) reflection: T T T T T T T T ... Rotation around a center: S S S S S S S S ... Glide-reflection, which is a top-bottom reflection followed by a "glide" to the right or left: p b p b p b p b ... These symmetry operations can be combined in seven possible arrangements: the four listed above, which each have a single symmetry operation, a repeating pattern with no symmetry operations: F F F F F F F F F ... One with everything except horizontonal reflection: /\/\/\/\/\/\/\/\/\/... And one with every symmetry operation: X X X X X X X X X X... Darrah Chavey Those who do not understand Unix are Math/CS Dept. condemned to reinvent it, poorly. Beloit College -- Henry Spencer, Univ. Toronto Unix hack 700 College St. Beloit, WI 53511