Polar coordinates: Difference between revisions

From Citizendium
Jump to navigation Jump to search
imported>Todd Coles
(subpages)
imported>Anthony Argyriou
(add direction angle is measured)
Line 1: Line 1:
{{subpages}}
{{subpages}}
[[Image:2D polar coordinates .png|right|thumb|250px|Two dimensional polar coordinates ''r'' and &theta; of vector <math>\scriptstyle \vec{\mathbf{r}}</math>]]
[[Image:2D polar coordinates .png|right|thumb|250px|Two dimensional polar coordinates ''r'' and &theta; of vector <math>\scriptstyle \vec{\mathbf{r}}</math>]]
In [[mathematics]] and [[physics]],  '''polar coordinates''' give the position of a vector <math>\scriptstyle \vec{\mathbf{r}}</math> in two-dimensional real space <math>\scriptstyle \mathbb{R}^2</math>.  A Cartesian system of two orthogonal axes is presupposed. One number (''r'') gives the length of the vector and the other number (&theta;)  gives the angle of the vector with the ''x''-axis of the Cartesian system.  
In [[mathematics]] and [[physics]],  '''polar coordinates''' give the position of a vector <math>\scriptstyle \vec{\mathbf{r}}</math> in two-dimensional real space <math>\scriptstyle \mathbb{R}^2</math>.  A Cartesian system of two orthogonal axes is presupposed. One number (''r'') gives the length of the vector and the other number (&theta;)  gives the angle of the vector with the ''x''-axis of the Cartesian system (measured in the direction of the positive y-axis).  
==Definition==
==Definition==
The polar coordinates are related to the [[Cartesian coordinates]] ''x'' and ''y''  through
The polar coordinates are related to the [[Cartesian coordinates]] ''x'' and ''y''  through

Revision as of 15:55, 22 January 2008

This article is developing and not approved.
Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
This editable Main Article is under development and subject to a disclaimer.
File:2D polar coordinates .png
Two dimensional polar coordinates r and θ of vector

In mathematics and physics, polar coordinates give the position of a vector in two-dimensional real space . A Cartesian system of two orthogonal axes is presupposed. One number (r) gives the length of the vector and the other number (θ) gives the angle of the vector with the x-axis of the Cartesian system (measured in the direction of the positive y-axis).

Definition

The polar coordinates are related to the Cartesian coordinates x and y through

so that for r ≠ 0,