## Projective plane |

In
**projective plane** is a geometric structure that extends the concept of a
*any* two distinct lines in a projective plane intersect in one and only one point.

**extended Euclidean plane**.^{
[1]} This example, in slightly different guises, is important in
**R**), **RP**^{2}, or **P**_{2}(**R**) among other notations. There are many other projective planes, both infinite, such as the

A projective plane is a 2-dimensional

- definition
- some examples
- vector space construction
- subplanes
- affine planes
- degenerate planes
- collineations
- plane duality
- correlations
- finite projective planes
- projective planes in higher-dimensional projective spaces
- see also
- notes
- references
- external links

A **projective plane** consists of a set of **lines**, a set of **points**, and a relation between points and lines called **incidence**, having the following properties:^{
[2]}

- Given any two distinct points, there is exactly one line incident with both of them.
- Given any two distinct lines, there is exactly one point incident with both of them.
- There are four points such that no line is incident with more than two of them.

The second condition means that there are no
* degenerate* cases (see
below). The term "incidence" is used to emphasize the symmetric nature of the relationship between points and lines. Thus the expression "point

Other Languages

العربية: مستوى إسقاط

čeština: Projektivní rovina

Deutsch: Projektive Ebene

español: Plano proyectivo

français: Plan projectif

한국어: 사영 평면

italiano: Piano proiettivo

עברית: מישור פרויקטיבי

Nederlands: Projectief vlak

日本語: 射影平面

norsk: Projektivt plan

português: Plano projectivo

русский: Проективная плоскость

slovenščina: Projektivna ravnina

suomi: Projektiivinen taso

svenska: Projektivt plan

українська: Проективна площина

中文: 射影平面