A structured visual guide to the major mathematical areas and their relationships.
Search by code, branch, topic, subtopic, or a keyword from the descriptions.
This subtopic introduces the core ideas in analytic and projective geometry, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Descriptive geometry represents three-dimensional objects through planar projections and constructions.
Wikipedia: Descriptive geometry
Foundational in technical drawing and geometric visualization.
Affine analytic geometry studies coordinate geometry with affine transformations and invariants as the primary symmetry class.
Useful for modeling geometric problems where ratios on parallel lines are meaningful but distances are not fixed.
Projective analytic geometry combines coordinate methods with projective invariants and homogeneous coordinates.
Core for modern geometric vision and many algebraic geometry preliminaries.
Euclidean analytic geometry studies geometric figures via Cartesian coordinates, equations, and metric invariants.
Widely used as an entry point to modern geometry and modeling.
This area extends analytic geometry by replacing Euclidean symmetries with alternative transformation groups and corresponding invariants.
Useful for unifying many geometries through symmetry principles.
Classical matrix groups such as orthogonal, unitary, and symplectic groups are studied through their geometric actions and invariants.
Connects analytic geometry with representation theory and mathematical physics.
This subtopic addresses classical algebraic-geometric questions using analytic-geometric techniques and coordinate methods.
Used to bridge computational and conceptual viewpoints between algebraic and analytic geometry.