glijsymmetrie

Glijsymmetrie, also known as glide reflection, is a type of isometry in Euclidean geometry. It is a composite transformation that consists of a reflection across a line and a translation along that same line. The order of these two operations does not matter; a translation followed by a reflection along the same line results in the same final position as a reflection followed by a translation.

A glide reflection is characterized by two components: the line of reflection, also known as the glide line, and the translation vector, which specifies the distance and direction of the translation along the glide line. For a point to be invariant under a glide reflection, it would need to be on the glide line and the translation distance would need to be zero. In such a case, the glide reflection would simply be a reflection.

In two dimensions, glide reflections are responsible for creating patterns with translational symmetry where the repeating units are mirror images of each other. This is commonly seen in frieze patterns and wallpaper groups. For example, a row of footprints can exhibit glide symmetry if each footprint is a reflection of the preceding one, and there is a consistent distance between them.

Glide reflections are fundamental in understanding the classification of isometries. Along with translations, rotations, and reflections, glide reflections form the set of direct isometries when combined with reflections. In higher dimensions, glide reflection is also a valid geometric transformation.