# non-Euclidean geometry

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## non-Euclidean geometry

n
(Mathematics) the branch of modern geometry in which certain axioms of Euclidean geometry are restated. It introduces fundamental changes into the concept of space
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 Noun 1 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"math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementgeometry - the pure mathematics of points and lines and curves and surfaceshyperbolic geometry - (mathematics) a non-Euclidean geometry in which the parallel axiom is replaced by the assumption that through any point in a plane there are two or more lines that do not intersect a given line in the plane; "Karl Gauss pioneered hyperbolic geometry"elliptic geometry, Riemannian geometry - (mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle; "Bernhard Riemann pioneered elliptic geometry"
References in periodicals archive ?
The book has three sections: The first deals with euclidean geometry and geometric constructions; the second covers noneuclidean geometry, including hyperbolic, elliptic, taxicab, and finite geometries; and the final section covers symmetry.
He then moves to applications in Fourier series, including strings and springs, and devotes the rest of the text to the calculus of variations, including Euler's Equation, harmonic functions, Hamilton's Action and Lagranges' Equation, finishing with nonEuclidean geometry and some fun with relativity.

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