Branches of Geometry

The branches of geometry are categorized as:

• Algebraic geometry
• Discrete geometry
• Differential geometry
• Euclidean geometry
• Convex geometry
• Topology

Algebraic Geometry

It is a branch of geometry studying zeros of the multivariate polynomial. It includes linear and polynomial algebraic equations that are used for solving the sets of zeros. The application of this type comprises Cryptography, string theory, etc.

Discrete Geometry

It is concerned with the relative position of simple geometric objects, such as points, lines, triangles, circles etc.

Differential Geometry

It uses techniques of algebra and calculus for problem-solving. The various problems include general relativity in physics etc.

Euclidean Geometry

The study of plane and solid figures based on 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.

Convex Geometry

It includes convex shapes in Euclidean space using techniques of real analysis. It has application in optimization and functional analysis in number theory.

Topology

It is concerned with the 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, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.