Editing Coordinate system (section)

==Coordinates of geometric objects==
Coordinates systems are often used to specify the position of a point, but they may also be used to specify the position of more complex figures such as lines, planes, [[circle]]s or [[sphere]]s. For example, [[Plücker coordinates]] are used to determine the position of a line in space.<ref>{{cite book
| last= Hodge
| first= W.V.D.
| author-link= W. V. D. Hodge
| author2=[[D. Pedoe]]
| title= Methods of Algebraic Geometry, Volume&nbsp;I (Book&nbsp;II)
| publisher= [[Cambridge University Press]]
| year= 1994
| isbn= 978-0-521-46900-5
| orig-year= 1947}}</ref> When there is a need, the type of figure being described is used to distinguish the type of coordinate system, for example the term ''[[line coordinates]]'' is used for any coordinate system that specifies the position of a line.

It may occur that systems of coordinates for two different sets of geometric figures are equivalent in terms of their analysis. An example of this is the systems of homogeneous coordinates for points and lines in the projective plane. The two systems in a case like this are said to be ''dualistic''. Dualistic systems have the property that results from one system can be carried over to the other since these results are only different interpretations of the same analytical result; this is known as the ''principle of [[duality (mathematics)|duality]]''.<ref>Woods p. 2</ref>