meetgeometrie

Meetgeometrie is a Dutch-language term most often used to denote the study of metric geometry, the branch of mathematics concerned with geometric properties that arise from a notion of distance. It emphasizes structures in which distance, rather than coordinate systems or algebraic relations, is the primary datum. The subject encompasses both abstract metric spaces and concrete geometric settings such as Euclidean space, Riemannian manifolds and discrete networks.

Foundational concepts include the metric (distance function), triangles and the triangle inequality, geodesics (shortest paths), concepts of curvature formulated in metric terms, and notions of convergence of spaces such as Gromov–Hausdorff convergence. Meetgeometrie interacts with topology, analysis and combinatorics: properties like completeness, compactness and continuity are studied alongside isometries, embeddings and quasi-isometries.

Key themes include comparison geometry (relating curvature bounds to global shape), rigidity and stability results, and the study of spaces with singularities where classical differential tools fail. Applications span Riemannian geometry, geometric group theory, optimal transport, computer science (network geometry and algorithms) and applied fields that require distance-based modeling.

As a term, meetgeometrie is used in Dutch academic literature and teaching to refer broadly to metric-oriented approaches to geometry, often overlapping with international research labeled metric geometry. The field continues to evolve through interaction with analysis, topology and computational methods.