Euclidean And Non Euclidean

Euclidean And Non Euclidean. Elements of R2, that is ordered pairs (x,y) of real numbers, are called points Space is not perfectly "flat", or Euclidean; the force of gravity gives it a curvature, especially in the vicinity of massive objects.

The first thread started with the search to understand the movement of stars and planets in the apparently hemispherical sky 1.2 Non-Euclidean Geometry: non-Euclidean geometry is any geometry that is different from Euclidean geometry

Each Non-Euclidean geometry is a consistent system of definitions, assumptions, and proofs that describe such objects as points, lines and planes While many of Euclid's findings had been previously stated by earlier Greek mathematicians, Euclid Consider directed segments (also called "arrows") between points of the plane.

. Chapter 2 Affine and Euclidean Geometry 2.1 Points and vectors First we recall coordinate plane geometry from Calculus The non-Euclidean geometries developed along two different historical threads

. A non-Euclidean geometry is a rethinking and redescription of the properties of things like points, lines, and other shapes in a non-flat world discoverers of Non-Euclidean Geometries, the Elliptic and Hyperbolic Geometries themselves, being the most outstanding among all the Non-Euclidean, and even some models of its representations