Rúmfræði

Rúmfræði, the Icelandic term for geometry of space, is a branch of mathematics that studies the properties and relations of points, lines, surfaces, and solids. It concerns the measurement, classification, and transformation of space, and it develops its results through logical deduction from axioms. Rúmfræði covers two classical domains—plane geometry, which deals with flat, two‑dimensional figures, and solid geometry, which concerns three‑dimensional bodies—while also extending to higher dimensions.

Key notions include distance, angle, area and volume, shape, and congruence, as well as the study of geometric transformations that preserve these properties, such as rotations, translations, and reflections. The subject has several major branches. Euclidean geometry follows the parallel postulate and governs ordinary flat space. Non‑Euclidean geometries, such as spherical and hyperbolic geometry, explore curved spaces. Differential geometry applies calculus to curves and surfaces, leading to the study of curvature and geodesics on manifolds. Algebraic geometry investigates geometric properties of solution sets of polynomial equations, often in higher-dimensional spaces.

Rúmfræði has broad applications in science and engineering. It underpins physics, notably general relativity, computer graphics and computer-aided design, architecture, robotics, and geographic information systems. It also provides foundational concepts for more advanced mathematical theories.

Etymology: rúm means space, fræði means science or field. The discipline has a long history, from ancient geometry to modern, abstract theories that model complex spatial structures.