Geometry
Euclidean, differential, algebraic, computational, and discrete geometry.
Geometry. Euclidean, differential, algebraic, computational, and discrete geometry. This page collects canonical references that organise the subject and provide entry points to its main techniques.
Foundations and canonical references
The standard treatments of geometry approach the subject from complementary angles. Hartshorne, Geometry: Euclid and Beyond (2000) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Coxeter, Geometry (1969) offers an alternative presentation that complements the primary references and is useful for triangulating definitions and proof techniques.
Open methodological questions for geometry include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2000Geometry: Euclid and Beyondhartshorne-2000b
- textbook · supporting · 1969Geometrycoxeter-1969
In context
Where this topic sits in the prerequisite graph. Click any node to jump.
Explore
- 01
Euclidean and Non-Euclidean Geometry
Synthetic geometry, hyperbolic and spherical geometry, and the parallel postulate.
- 02
Differential Geometry
Smooth manifolds, connections, curvature, and Riemannian geometry.
- 03
Algebraic Geometry
Varieties, schemes, sheaves, and cohomological methods.
- 04
Computational Geometry
The algorithmic study of geometric objects — manifolds, meshes, point clouds, and convex bodies — with explicit attention to representation, complexity, and numerical stability.
- 05
Discrete Geometry
Polytopes, packings, coverings, and incidence geometry.
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