Quadratischem

Quadratischem is the dative singular form of the German adjective quadratisch, meaning square-shaped or quadratic. It is used to describe a noun in the dative case when there is no definite article or other determiner providing a weak ending. In that context, quadratischem appears with masculine or neuter nouns.

In practical use, quadratischem occurs in phrases such as mit quadratischem Rand (with a square edge) or in quadratischem Raum (in a square-shaped room). When a definite article is present, the ending changes to dem quadratischen, not quadratischem, for example, dem quadratischen Rand. This illustrates how German adjective endings depend on case, gender, number, and the presence of articles.

Etymology and meaning: The word quadratisch comes from Quadrat, the German word for a square, which itself derives from Latin quadratus. The suffix -isch forms adjectives meaning “-ish” or “relating to.” The form quadratischem is simply the inflected dative singular used under appropriate syntactic conditions.

In broader usage, quadratischem is a grammatical inflection rather than a separate semantic term. The base adjective quadratisch is also used in mathematics and geometry to mean quadratic, such as in eine quadratische Gleichung (a quadratic equation) or eine quadratische Form (a quadratic form). In those mathematical phrases, the accompanying article and case determine the exact ending of the adjective, with quadratischem appearing only in the appropriate dative contexts without a determiner.