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Geometry is a branch of mathematics that studies the properties and relationships of space, including the distance, shape, size, position, angles, and dimensions of figures. Its foundational objects include points, lines, planes, curves, surfaces, solids, and spaces. Traditionally, geometry focused mainly on Euclidean space and concepts such as length, area, volume, and parallelism, using axioms, definitions, theorems, and proofs to establish results rigorously. The scope of geometry has expanded substantially beyond classical Euclidean geometry. It now includes non-Euclidean, differential, algebraic, projective, affine, computational, discrete, and topological geometries, each emphasizing different properties or methods. Modern geometry can study spaces of any dimension, including abstract manifolds, and has applications in science, physics, engineering, architecture, art, and other areas of mathematics.
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