Editing Non-Euclidean geometry (section)

==Importance==
Before the models of a non-Euclidean plane were presented by Beltrami, Klein, and Poincaré, Euclidean geometry stood unchallenged as the [[mathematical model]] of [[space]]. Furthermore, since the substance of the subject in [[synthetic geometry]] was a chief exhibit of rationality, the Euclidean point of view represented absolute authority.

The discovery of the non-Euclidean geometries had a ripple effect which went far beyond the boundaries of mathematics and science. The philosopher [[Immanuel Kant]]'s treatment of human knowledge had a special role for geometry. It was his prime example of synthetic [[a priori]] knowledge; not derived from the senses nor deduced through logic&nbsp;— our knowledge of space was a truth that we were born with. Unfortunately for Kant, his concept of this unalterably true geometry was Euclidean. Theology was also affected by the change from absolute truth to relative truth in the way that mathematics is related to the world around it, that was a result of this paradigm shift.<ref>Imre Toth, "Gott und Geometrie: Eine viktorianische Kontroverse," ''Evolutionstheorie und ihre Evolution'', Dieter Henrich, ed. (Schriftenreihe der Universität Regensburg, band 7, 1982) pp. 141–204.</ref>

Non-Euclidean geometry is an example of a [[paradigm shift|scientific revolution]] in the [[history of science]], in which mathematicians and scientists changed the way they viewed their subjects.<ref>see {{harvnb|Trudeau|2001|loc=pp. vii–viii}}</ref> Some geometers called [[Nikolai Lobachevsky|Lobachevsky]] the "[[Copernicus]] of Geometry" due to the revolutionary character of his work.<ref>{{citation|last=Bell|first=E. T.|author-link=E. T. Bell|title=Men of Mathematics|year=1986|publisher=Touchstone Books|isbn=978-0-671-62818-5|page=294}} Author attributes this quote to another mathematician, [[William Kingdon Clifford]].</ref><ref>This is a quote from G. B. Halsted's translator's preface to his 1914 translation of ''The Theory of Parallels'': "What [[Vesalius]] was to [[Galen]], what [[Copernicus]] was to [[Ptolemy]] that was Lobachevsky to [[Euclid]]." &mdash; [[William Kingdon Clifford|W. K. Clifford]]</ref>

The existence of non-Euclidean geometries impacted the intellectual life of [[Victorian England]] in many ways<ref>{{Harvard citation|Richards|1988}}</ref> and in particular was one of the leading factors that caused a re-examination of the teaching of geometry based on [[Euclid's Elements]]. This curriculum issue was hotly debated at the time and was even the subject of a book, ''[[Euclid and his Modern Rivals]]'', written by Charles Lutwidge Dodgson (1832–1898) better known as [[Lewis Carroll]], the author of ''[[Alice's Adventures in Wonderland|Alice in Wonderland]]''.