Euclidean and Non-Euclidean Geometry

Synthetic geometry, hyperbolic and spherical geometry, and the parallel postulate.

foundation tier

Euclidean and Non-Euclidean Geometry. Synthetic geometry, hyperbolic and spherical geometry, and the parallel postulate. 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 euclidean and non-euclidean 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.

Open methodological questions for euclidean and non-euclidean 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 · 2000
    Geometry: Euclid and Beyond
    hartshorne-2000b

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Explore

  1. 01

    Hyperbolic Geometry

    Poincaré disk, upper half-plane, and isometries of hyperbolic space.
  2. 02

    Projective Geometry

    Projective spaces, duality, and cross-ratio.
  3. 03

    Inversive and Möbius Geometry

    Conformal transformations of the sphere and circle inversions.

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