archimedische

Archimedische is a German adjective meaning “Archimedean” in English. It is used in mathematical contexts to refer to concepts named after the ancient Greek mathematician Archimedes or to properties associated with him. In German-language math literature, it can describe both structural objects and foundational properties that carry Archimedean lineage.

One prominent use is the Archimedische Eigenschaft, or Archimedean property, which appears in ordered algebraic structures such as fields and groups. Roughly, an ordered field is Archimedean if for every positive element x and every element y there exists a natural number n with ny exceeding y (equivalently, the natural numbers are unbounded within the field). This property distinguishes Archimededean fields from non-Archimedean constructions that admit infinitesimal or infinitely large elements. The concept extends similarly to ordered abelian groups.

Another well-known application is Archimedische Körper, or Archimedean solids, a family of 13 semiregular convex polyhedra described by Archimedes. These solids have regular faces but more than one face type and are vertex-transitive, combining symmetry with variety in face structure. They are named for their historical connection to Archimedes and remain a classical topic in geometry and mathematical art.

Archimedische Spirale, or Archimedean spiral, is a polar curve defined by r = aθ. In this spiral, the distance between successive turns is constant, yielding a simple, uniform winding that is frequently discussed in geometry and applied contexts.

See also: Archimedes, Archimedean property, Archimedean solids, Archimedean spiral.