14 Facts About Non-Euclidean geometries

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

Euclidean geometry, named after the Greek mathematician Euclid, includes some of the oldest known mathematics, and Non-Euclidean geometries that deviated from this were not widely accepted as legitimate until the 19th century.

Non-Euclidean geometries finally reached a point where he believed that his results demonstrated the impossibility of hyperbolic geometry.

Non-Euclidean geometries's claim seems to have been based on Euclidean presuppositions, because no logical contradiction was present.

Non-Euclidean geometries worked with a figure now known as a Lambert quadrilateral, a quadrilateral with three right angles .

Related searches

Non-Euclidean geometries quickly eliminated the possibility that the fourth angle is obtuse, as had Saccheri and Khayyam, and then proceeded to prove many theorems under the assumption of an acute angle.

Non-Euclidean geometries had proved the non-Euclidean result that the sum of the angles in a triangle increases as the area of the triangle decreases, and this led him to speculate on the possibility of a model of the acute case on a sphere of imaginary radius.

Non-Euclidean geometries constructed an infinite family of non-Euclidean geometries by giving a formula for a family of Riemannian metrics on the unit ball in Euclidean space.

Non-Euclidean geometries was referring to his own work, which today we call hyperbolic geometry.

Euclidean and non-Euclidean geometries naturally have many similar properties, namely those that do not depend upon the nature of parallelism.

Discovery of the non-Euclidean geometries had a ripple effect which went far beyond the boundaries of mathematics and science.

Non-Euclidean geometries geometry is an example of a scientific revolution in the history of science, in which mathematicians and scientists changed the way they viewed their subjects.

Existence of non-Euclidean geometries impacted the intellectual life of Victorian England in many ways and in particular was one of the leading factors that caused a re-examination of the teaching of geometry based on Euclid's Elements.

Non-Euclidean geometries realized that the submanifold, of events one moment of proper time into the future, could be considered a hyperbolic space of three dimensions.