DBpedia – Linked Data Fragments

Matches in DBpedia 2015-10 for { ?s ?p "A one-dimensional symmetry group is a mathematical group that describes symmetries in one dimension (1D). A pattern in 1D can be represented as a function f(x) for, say, the color at position x.The only nontrivial point group in 1D is a simple reflection. It can be represented by the simplest Coxeter group, [ ], or Coxeter-Dynkin diagram File:CDel node.png.Affine symmetry groups represent translation. Isometries which leave the function unchanged are translations x + a with a such that f(x + a) = f(x) and reflections a − x with a such that f(a − x) = f(x). The reflections can be represented by the affine Coxeter group [∞], or Coxeter-Dynkin diagram File:CDel node.pngFile:CDel infin.pngFile:CDel node.png representing two reflections, and the translational symmetry as [∞]+, or Coxeter-Dynkin diagram File:CDel node h2.pngFile:CDel infin.pngFile:CDel node h2.png as the composite of two reflections."@en }

• One-dimensional_symmetry_group abstract "A one-dimensional symmetry group is a mathematical group that describes symmetries in one dimension (1D). A pattern in 1D can be represented as a function f(x) for, say, the color at position x.The only nontrivial point group in 1D is a simple reflection. It can be represented by the simplest Coxeter group, [ ], or Coxeter-Dynkin diagram File:CDel node.png.Affine symmetry groups represent translation. Isometries which leave the function unchanged are translations x + a with a such that f(x + a) = f(x) and reflections a − x with a such that f(a − x) = f(x). The reflections can be represented by the affine Coxeter group [∞], or Coxeter-Dynkin diagram File:CDel node.pngFile:CDel infin.pngFile:CDel node.png representing two reflections, and the translational symmetry as [∞]+, or Coxeter-Dynkin diagram File:CDel node h2.pngFile:CDel infin.pngFile:CDel node h2.png as the composite of two reflections.".