View source for Non-Euclidean geometry

You do not have permission to edit this page, for the following reason:

You currently can not change pages on Wikipedia.

The ability to change pages on all Wikimedia wikis has been removed from this account, IP address or IP address range by ‪Jon Kolbert‬. The following reason(s) were given for this block:

Open proxy/Webhost: See the help page if you are affected

Your IP address is 54.164.230.42. This block began on 18:27, 12 November 2023 and has been set to finish on: 18:27, 12 November 2028.

You are not blocked from reading pages, only from changing or creating them.
If you have just clicked a red link, you were blocked from creating a new page as no article on that topic is there yet.

If you think you were not blocked fairly, you may make unblock requests or file appeals at meta:Steward requests/Global.

You can view and copy the source of this page.

[[File:noneuclid.svg|right|thumb|300px|Behavior of lines with a common perpendicular in each of the three types of geometry]]
'''Non-Euclidean geometry''' is a type of [[geometry]]. Non-Euclidean geometry only uses some of the "[[postulate]]s" ([[wikt:assume|assumptions]]) that [[Euclidean geometry]] is based on. In normal geometry, [[parallel (geometry)|parallel]] lines can never meet. In non-Euclidean geometry they can meet, either infinitely many times ([[elliptic geometry]]), or never ([[hyperbolic geometry]]).

An example of Non-Euclidian geometry can be seen by drawing lines on a [[ball]] or [[Globe|other round object]], straight lines that are parallel at the equator can meet at the poles.

== Origin ==
It is called "Non-Euclidean" because it is different from Euclidean geometry, which was discovered by an [[Ancient Greek]] mathematician called [[Euclid]]. The different names for non-Euclidean geometries came from thinking of "straight" lines as curved lines, either curved inwards like an [[ellipse]], or outwards like a [[hyperbola]].

The first authors of non-Euclidean geometries were the [[Hungary|Hungarian]] mathematician [[János Bolyai]] and the [[Russia]]n mathematician [[Nikolai Ivanovich Lobachevsky]], who separately published treatises on hyperbolic geometry around 1830. As well [[Eugenio Beltrami]] published book on non-Eucludean geometry in [[1868]]. Others, such as [[Carl Friedrich Gauss]], had earlier ideas, but did not publish their ideas at the time.


{{math-stub}}
{{authority control}}
[[Category:Fields of geometry]]

Templates used on this page:

Template:Authority control (view source) (semi-protected)
Template:Math-stub (view source) (semi-protected)
Template:Stub-template (view source) (protected)
Template:Tooltip (change)
Template:Tooltip/styles.css (change)
Template:Yesno (view source) (protected)
Template:Yesno-no (view source) (semi-protected)
Template:Yesno-yes (view source) (semi-protected)
Module:Authority control (view source) (semi-protected)
Module:Authority control/auxiliary (view source) (semi-protected)
Module:Authority control/config (view source) (semi-protected)
Module:Check for unknown parameters (view source) (protected)
Module:EditAtWikidata (view source) (protected)
Module:Navbar (view source) (protected)
Module:Navbar/configuration (view source) (protected)
Module:Navbox (view source) (protected)
Module:Navbox/configuration (view source) (protected)
Module:Navbox/styles.css (view source) (protected)
Module:String (view source) (protected)

Return to Non-Euclidean geometry

Retrieved from "https://simple.wikipedia.org/wiki/Non-Euclidean_geometry"