Questions tagged [geometry]

Geometry is one of the classical disciplines of math. It is derived from two Latin words, "geo" + "metron" meaning earth & measurement. Thus it is concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs. Since its earliest days, geometry has served as a practical guide for measuring lengths, areas, and volumes, and geometry is still used for this purpose today. Geometry is important because the world is made up of different shapes and spaces.

Geometry has applications to many fields, including art, architecture, physics, as well as to other branches of mathematics.

Sub-fields of contemporary geometry:

$1.\quad$ Algebraic geometry – is a branch of geometry studying zeroes of multivariate polynomials. It includes the linear and polynomial algebraic equations used for finding these sets of zeros. The applications of algebraic geometry include cryptography, string theory, etc.

$2.\quad$ Discrete geometry – is concerned with the relative positions of simple geometric objects, such as points, lines, triangles, circles etc.

$3.\quad$ Differential geometry – uses techniques of algebra and calculus for problem-solving. The applications of differential geometry include general relativity in physics, etc.

$4.\quad$ Euclidean geometry – The study of plane and solid figures on the basis of axioms and theorems including points, lines, planes, angles, congruence, similarity, solid figures. It has a wide range of applications in computer science, modern mathematics problem solving, crystallography etc.

$5.\quad$ Convex geometry – includes convex shapes in Euclidean space using techniques of real analysis. It has application in optimization and functional analysis in number theory.

$6.\quad$ Topology – is concerned with properties of space under continuous mapping. Its application includes consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.

$7.\quad$ Plane geometry – This wing of geometry deals with flat shapes which can be drawn on a piece of paper. These include lines, circles & triangles of two dimensions.

$8.\quad$ Solid geometry – It deals with $3$-dimensional objects like cubes, prisms, cylinders & spheres.

Reference:

https://en.wikipedia.org/wiki/Geometry