# Riemannian geometry

- Also called elliptic geometry. 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.Compare hyperbolic geometry.
- the differential geometry of a metric space that generalizes a Euclidean space.

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## Origin of Riemannian geometry^{}

First recorded in 1915–20

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

## Riemannian geometry

- 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 circlesAlso called: elliptic geometry

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Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## Riemannian geometry

[rē-män′ē-ən]

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

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The American Heritage® Science Dictionary
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