Difference between revisions of "Cylindrical coordinates"
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'''Cylindrical coordinates''' are a way to describe the location of a point in three-dimensional space based on "r", the distance from the origin in the x-y plane, "θ", the angle from the origin in the x-y plane, and z, the distance perpendicular to the x-y plane: (r,θ,z). | '''Cylindrical coordinates''' are a way to describe the location of a point in three-dimensional space based on "r", the distance from the origin in the x-y plane, "θ", the angle from the origin in the x-y plane, and z, the distance perpendicular to the x-y plane: (r,θ,z). | ||
| − | In a sense, cylindrical coordinates are [[polar coordinates]] with a third dimension added: (r,θ) correspond to the polar coordinates for (x,y). | + | In a sense, cylindrical coordinates are [[polar coordinates]] with a third dimension added: (r,θ) correspond to the polar coordinates for (x,y). This is in contrast to [[spherical coordinates]], where z is replaced by an angle, just like x and y are in polar coordinates. |
The equations converting the parameters are as follows: | The equations converting the parameters are as follows: | ||
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[[Category:mathematics]] | [[Category:mathematics]] | ||
| + | [[Category:Geometry]] | ||
Revision as of 22:34, November 29, 2009
Cylindrical coordinates are a way to describe the location of a point in three-dimensional space based on "r", the distance from the origin in the x-y plane, "θ", the angle from the origin in the x-y plane, and z, the distance perpendicular to the x-y plane: (r,θ,z).
In a sense, cylindrical coordinates are polar coordinates with a third dimension added: (r,θ) correspond to the polar coordinates for (x,y). This is in contrast to spherical coordinates, where z is replaced by an angle, just like x and y are in polar coordinates.
The equations converting the parameters are as follows:
- r2 = x2 + y2
- tan(θ) = y/x
- x = r*cos(θ)
- y = r*sin(θ)