X-Nico

unusual facts about Non-Euclidean geometry


Non-Euclidean geometry

Bernard H. Lavenda, (2012) " A New Perspective on Relativity : An Odyssey In Non-Euclidean Geometries", World Scientific, pp.


Ex-tangential quadrilateral

Daniel Pedoe named it the most elementary theorem in Euclidean geometry since it only concerns straight lines and distances.

Foundations of mathematics

Later in the 19th century, the German mathematician Bernhard Riemann developed Elliptic geometry, another non-Euclidean geometry where no parallel can be found and the sum of angles in a triangle is more than 180°.

Parabolic geometry

Euclidean geometry, where Euclidean space is viewed as the natural representation space of the group of Euclidean motions E(n) = O(n) \ltimes \mathbb{R}^n

Rytz's construction

Rytz’s construction is a classical construction of Euclidean geometry, in which only compass and ruler are allowed as aids.

Stephen F. Barker

Its five chapters concern Euclidean and non-Euclidean geometry, and literalist and non-literalist views on the meaning of numbers.


see also

Giovanni Girolamo Saccheri

Martin Gardner, Non-Euclidean Geometry, Chapter 14 of The Colossal Book of Mathematics, W. W.Norton & Company, 2001, ISBN 0-393-02023-1

Squeeze mapping

Edwin Bidwell Wilson & Gilbert N. Lewis (1912) "The space-time manifold of relativity. The non-Euclidean geometry of mechanics and electromagnetics", Proceedings of the American Academy of Arts and Sciences 48:387–507.