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Geometry

Geometry is a branch of mathematics that deals with the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. Explore the various facets and applications of geometry across different fields.
Sub-categories:

Euclidean Geometry focuses on the study of plane and solid figures based on axioms and theorems employed by the Greek mathematician Euclid.

Non-Euclidean Geometry examines geometrical properties that are not based on the parallel postulate, such as hyperbolic and elliptic geometry.

Differential Geometry uses techniques of algebra and calculus for the study of curves, surfaces, and manifolds.

Algebraic Geometry investigates the geometric properties of solutions to polynomial equations, including curves, surfaces, and multidimensional spaces.

Computational Geometry focuses on algorithms to solve geometric problems in computer science and various engineering disciplines.

Coordinate Geometry, or analytic geometry, describes the link between geometry and algebra through graphs involving coordinates and equations.

Topology explores properties that are preserved under continuous deformations such as stretching and bending of objects.

Projective Geometry studies the properties of figures invariant under projection, providing foundations for perspective in art and advancements in science.

Discrete Geometry investigates combinatorial properties and constructive methods of discrete geometric objects, such as points, lines, and polyhedra.

Convex Geometry is the study of convex shapes in the Euclidean space and their properties, including convex sets and convex hulls.

Geometry of Numbers refers to the study of the structure of numbers using geometric methods, as in lattice point enumeration.

Incidence Geometry examines the relative position of lines and other geometric figures, primarily concerned with incidence properties.

Plane Geometry deals with shapes such as circles, triangles, and polygons that can exist in two dimensions, focusing on patterns and relationships.

Solid Geometry involves the study of three-dimensional figures like spheres, cubes, and cylinders, analyzing their properties and volumes.

Fractal Geometry examines self-similar patterns and complex shapes across different scales, with applications in various scientific fields.

Spherical Geometry explores figures on the surface of a sphere, used in navigation and astronomy, questioning Euclidean assumptions like parallel lines.