# Riemannian geometry

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## Rie·mann·ian geometry

(rē-män′ē-ən)*n.*

A non-Euclidean system of geometry based on the postulate that within a plane every pair of lines intersects.

[After Georg Friedrich Bernhard

**Riemann**.]American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## Riemannian geometry

*n*

(Mathematics) a branch of non-Euclidean geometry in which a line may have many parallels through a given point. It has a model on the surface of a sphere, with lines represented by great circles. Also called:

**elliptic geometry**Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## Riemann′ian geom′etry

*n.*

the branch of non-Euclidean geometry that replaces the parallel postulate of Euclidean geometry with the postulate that in a plane every pair of distinct lines intersects.

[1915–20; after German.French.B. Riemann]

Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.

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Noun | 1. | 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"math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement 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" |

Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.

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