non-Euclidean geometry


  • WordNet 3.6
    • n non-Euclidean geometry (mathematics) geometry based on axioms different from Euclid's "non-Euclidean geometries discard or replace one or more of the Euclidean axioms"
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In literature:

In their non-Euclidean geometry the part is always greater than the whole.
"The Open Secret of Ireland" by T. M. Kettle
Non-Euclidean geometry, II, 83.
"A Budget of Paradoxes, Volume II (of II)" by Augustus de Morgan
The history of non-Euclidean geometry has been aptly divided by Felix Klein into three very distinct periods.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6" by Various

In science:

Some years before, during the second half of the XIX century, mathematicians saw the birth of non-Euclidean Geometries.
Higher-Order Theories of Gravitation
We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry.
Hyperbolic planforms in relation to visual edges and textures perception
Rylov, Non-Euclidean method of the generalized geometry construction and its application to space-time geometry in Pure and Applied Differential geometry pp.238-246. eds.
General relativity extended to non-Riemannian space-time geometry
Given that we have found that a finite temperature characterizes the quantum geometry with non-zero mass, it would be desirable to continue to the Euclidean theory to implement the finite temperature partition function as a path integral in Euclidean quantum gravity.
Newtonian gravity in loop quantum gravity
However, in the non-Euclidean geometry one succeeds to agree properties of different fundamental quantities not always.
Monistic conception of geometry