Geometr

Geometr is not a standard term in mathematics. If you encounter it, it is most likely a misspelling or shorthand for geometry, the branch of mathematics that studies the properties and relations of points, lines, surfaces, and solids.

Geometry is the branch of mathematics that studies properties and relations of points, lines, surfaces, and solids. From Greek roots ge and metron, the subject concerns measurements and shapes in space and the invariants that survive changes in form or position. It provides a framework for describing space, size, and relative position, using definitions, axioms, and proofs to establish theorems.

Classical geometry focuses on figures in the plane and in space, using an axiomatic approach to derive results. Major subfields include Euclidean geometry, which assumes the parallel postulate and forms the basis of much of school mathematics; non-Euclidean geometries such as hyperbolic and elliptic geometry, which arise when the parallel postulate is modified; differential geometry, which applies calculus to curved spaces; and algebraic geometry, which studies solution sets of polynomial equations using algebraic methods. Computational geometry applies geometric techniques to algorithms and computer graphics. Geometry is closely related to trigonometry, topology, and linear algebra, and often intersects with physics and engineering.

Historically, geometry originated in ancient Greece with Euclid’s Elements; later developments by Gauss, Bolyai, and Lobachevsky challenged Euclid’s postulates, and Riemann’s work generalized geometry to curved spaces. Geometry remains essential in science and engineering, informing design, analysis, and visualization across many disciplines.