Kreises

Kreises is the genitive singular form of the German noun Kreis, which can refer to a geometric circle or to an administrative district in German-speaking regions. As a root term, Kreis shares its origin with the English word circle, and its inflected forms follow standard German grammar.

In geometry, Kreis denotes a circle. Kreises is used when describing possession or relation involving a circle, for example in phrases like die Fläche des Kreises (the area of the circle) or der Umfang des Kreises (the circumference of the circle). In mathematical writing you will typically see des Kreises in contexts that require a possessive form.

In geographic and administrative contexts, Kreis historically referred to a district or county within a state or region. In modern Germany, the practical administrative level is often called Landkreis or Kreis, with kreisfreie Städte as independent cities. The genitive Kreises appears in official text when referring to a specific district and its attributes, such as die Verwaltung des Kreises or die Geschichte des Kreises. The term remains common in historical documents and formal writing, even as administrative terminology evolves.

Usage notes: Kreises should not be treated as a separate noun beyond its grammatical role as the genitive singular of Kreis. It is not the plural form; Kreise is the plural nominative and accusative form of Kreis. Care should be taken to distinguish context (geometry vs. administrative division) to interpret the meaning accurately.