In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.

Jan 9, 2024 · Non-Euclidean geometry is a branch of geometry that explores geometric systems deviating from classical Euclidean geometry. It includes hyperbolic and elliptic geometries, where alterations to Euclid's parallel postulate lead to distinct geometric properties and theorems.

Jan 22, 2025 · Non-Euclidean geometry, literally any geometry that is not the same as Euclidean geometry. Although the term is frequently used to refer only to hyperbolic geometry, common usage includes those few geometries (hyperbolic and spherical) that differ from but are very close to Euclidean geometry.

Sep 12, 2020 · In a small triangle on the face of the earth, the sum of the angles is very nearly 180°. Image is used under a CC BY-SA 3.0 license. It is called "Non-Euclidean" because it is different from Euclidean geometry, which was developed by …

Euclidean geometry is flat (curvature = 0) and any triangle angle sum = 180 degrees. The non-Euclidean geometry of Lobachevsky is negatively curved, and any triangle angle sum < 180 degrees. The geometry of the sphere is positively curved, and any triangle angle sum > …

Each Non-Euclidean geometry is a consistent system of definitions, assumptions, and proofs that describe such objects as points, lines and planes. The two most common non-Euclidean geometries are spherical geometry and hyperbolic geometry.

The organization of this visual tour through non-Euclidean geometry takes us from its aesthetical manifestations to the simple geometrical properties which distinguish it from the Euclidean geometry. There are two main types of non-Euclidean …

In non-Euclidean geometry, the concept corresponding to a line is a curve called a geodesic. In non-Euclidean geometry a shortest path between two points is along such a geodesic, or "non-Euclidean line".

Jun 6, 2020 · The major non-Euclidean geometries are hyperbolic geometry or Lobachevskii geometry and elliptic geometry or Riemann geometry — it is usually these that are meant by "non-Euclidean geometries" .

There exists two lines parallel to a given line through a given point not on the line. Developed trig identities, hyperbolic geometry. Every line through a point not on a given line meets the line. Eugenio Beltrami (1835-1900) Published interpretations of non-Euclidean geometry -introduced pseudosphere in 1868.