Space (mathematics) projective geometry nor defined from the notions mentioned there. The question "what is the sum of the three angles of a triangle" is meaningful in Euclidean geometry but meaningless in projective geometry. A different situation appeared in the 19th century: in some geometries the sum of the three angles of a triangle is well-defined but different from the classical value (180 degrees). Non-Euclidean hyperbolic geometry, introduced by Nikolai Lobachevsky in 1829 and János Bolyai in 1832 (and Carl Friedrich Gauss in 1816, unpublished) stated that the sum depends on the triangle and is always less than 180 degrees. Eugenio Beltrami
Angles at the centre of the Angle homeland in the northeastern portion of the modern German "Bundesland" of Schleswig-Holstein, on the Jutland Peninsula. There, a small peninsular area is still called Anglia today and is formed as a triangle drawn roughly from modern Flensburg on the Flensburger Fjord to the City of Schleswig and then to Maasholm, on the Schlei inlet. Attribution: Angles The Angles () were one of the main Germanic peoples who settled in Great Britain in the post-Roman period. They founded several of the kingdoms of Anglo-Saxon England, and their name is the root of the name England.