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

2025年1月22日 · 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.

2024年1月9日 · Non-Euclidean Geometry refers to the branch of mathematics that deals with the study of geometry on Curved Surfaces. It is a different way of studying shapes compared to what Euclid, an ancient mathematician, taught. There are …

2020年9月12日 · Is Euclidean geometry true or false? The answer to this last question is “It depends.” If you assume all five axioms of Euclid, you get plane geometry, just as you learned in high school. If you decide not to assume Euclid’s Fifth, …

In non-Euclidean geometry they can meet, either infinitely many times (elliptic geometry), or never (hyperbolic geometry). An example of Non-Euclidian geometry can be seen by drawing lines on a ball or other round object, straight lines that are parallel at the equator can meet at the poles.

5 天之前 · The "flat" geometry of everyday intuition is called Euclidean geometry (or parabolic geometry), and the non-Euclidean geometries are called hyperbolic geometry (or Lobachevsky-Bolyai-Gauss geometry) and elliptic geometry (or Riemannian geometry).

2020年6月6日 · 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" .

2024年6月25日 · Non-Euclidean geometry offers new ways of looking at shapes. It is used in topology to study shapes that keep their properties when we change them. This study opens doors to understanding the universe better.

One of Gauss' most important insights was that we can tell the shape of the space we are in by measuring angle sums for triangles, not just in two dimensions, but also in three-dimensional space. To show that space is non-Euclidean, all we have to do is find a triangle with an angle sum observably different from 180 degrees.

The study of non Euclidean figures is known as non Euclidean geometry. The great mathematician Carl Friedrich Gauss brought the concept of non Euclidean geometry. It includes the study of hyperbola, ellipse, sphere, and other non Euclidean.