Riemannian geometry


Rie·​mann·​ian geometry rē-ˈmä-nē-ən- How to pronounce Riemannian geometry (audio)
: a non-Euclidean geometry in which straight lines are geodesics and in which the parallel postulate is replaced by the postulate that every pair of straight lines intersects

Examples of Riemannian geometry in a Sentence

Recent Examples on the Web Certain phenomena—such as projecting flight paths around planets onto 2D spaces, or the space between two vertices of a graph—violate Euclidean (or coordinate) geometry; luckily, Riemannian geometry, frequently used to study the curvature of surfaces, can still model them. Adrienne Bernhard, Popular Mechanics, 20 Mar. 2023 In the new study, Bujack and her colleagues discovered that the longstanding application of Riemannian geometry overestimates perception of large color differences. Adrienne Bernhard, Popular Mechanics, 20 Mar. 2023

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'Riemannian geometry.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History


G. F. B. Riemann

First Known Use

1896, in the meaning defined above

Time Traveler
The first known use of Riemannian geometry was in 1896

Dictionary Entries Near Riemannian geometry

Cite this Entry

“Riemannian geometry.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/Riemannian%20geometry. Accessed 30 May. 2024.

Love words? Need even more definitions?

Subscribe to America's largest dictionary and get thousands more definitions and advanced search—ad free!