Riemannian Geometry

Pronunciation: /ˈriˌmɑn.i.ən dʒiˈɒ.mɪ.tri/ Explain

Click on the blue points and drag them to change the figure. Manipulative 1 - Riemannian Geometry Created with GeoGebra.

Riemannian geometry is a non-Euclidean geometry. It can be visualized as taking place on the surface of a sphere. In Riemannian geometry, lines are the great circles on the sphere. As a consequence, every pair of distinct lines intersect in Riemannian geometry. The points of intersection are antipodal, are diametrically opposed. Riemannian geometry is also called Elliptic Geometry.

References

1. McAdams, David E.. All Math Words Dictionary, riemannian geometry. 2nd Classroom edition 20150108-4799968. pg 156. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Riemannian geometry. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 12/4/2018. http://www.merriam-webster.com/dictionary/Riemannian geometry. Buy the book

More Information

• Euclid of Alexandria. Elements. Clark University. 9/6/2018. https://mathcs.clarku.edu/~djoyce/elements/elements.html.

Cite this article as:

McAdams, David E. Riemannian Geometry. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/r/riemanniangeometry.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/5/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra app. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
12/17/2008: Initial version. (McAdams, David E.)