CisGeometrie

CisGeometrie is a term used in some mathematical and educational contexts to describe a branch of geometry focused on cis relationships—situations in which geometric elements lie on the same side of a reference line, plane, or hyperplane. The concept is analogous to the chemical notion of cis isomerism and is often used as a pedagogical metaphor to illustrate half-space partitions and orientation.

Definitions vary by source, but a common thread is the study of configurations preserved under transformations that do not cross the reference boundary, i.e., cis-preserving transformations. The central object of study is the cis relation, which partitions space into cis and trans regions relative to a chosen reference. Methods from Euclidean, affine, and oriented geometry are employed to classify cis configurations, determine invariants, and construct examples.

Applications include visualization and teaching of half-spaces, analysis of spatial data with side information, and, in some models, the geometric interpretation of molecular conformations in chemistry-inspired pedagogy. The field often emphasizes intuitive diagrams and concrete constructions to convey how a configuration changes when the reference boundary is moved or rotated.

Relationship to other fields: CisGeometrie relates to half-space geometry, oriented geometry, and chiral or asymmetric configurations. It may intersect with incidence geometry and concepts like oriented matroids when formalizing the cis relation.

History: The term appears in a limited set of supplementary texts and online glossaries and is not part of a standard, widely adopted branch of geometry.

See also: cis-trans isomerism, half-space, oriented geometry, incidence geometry, chiral geometry.