ISOMetrische

Isometrische is the German or Dutch adjective corresponding to the English isometric. In mathematics, an isometry is a distance-preserving map between metric spaces. An isometric transformation preserves the distance between any two points and therefore also preserves lengths, angles and the overall shape of objects. In Euclidean space, examples include translations, rotations, reflections, and glide reflections; any composition of such maps is again an isometry.

Isometric projection is a type of parallel projection used in technical drawing, map rendering and pixel art. In an isometric projection the three coordinate axes appear equally foreshortened, giving a visually balanced representation of a 3D object on a 2D plane. It is distinct from perspective projection, which creates vanishing points and depth cues.

In differential geometry, an isometric immersion or embedding is a smooth map between Riemannian manifolds that preserves the metric: the pullback of the target metric equals the source metric. Isometries locally preserve distances and angles, making them fundamental for comparing geometric structures.

In biology and physiology, isometric growth describes proportional growth where body parts maintain their relative sizes. In exercise science, isometric contractions generate force without changing the length of the muscle. The term isometrische is used across languages to denote these same underlying ideas of preserving structure, distance or proportionality in different contexts.