Difference between revisions of "Cylindrical coordinates"

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'''Cylindrical coordinates''' refers to a three-dimensional coordinate system used to describe the location of a point in space based on the distance from the origin in the x-y plane "r", the angle measured in the x-y plane between the point and the x axis "θ", the distance perpendicular to the x-y plane:  (r,θ,z).  
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'''Cylindrical coordinates''' refers to a three-dimensional coordinate system used to describe the location of a point in space based on the distance from the origin in the x-y plane <math>r</math>, the angle measured in the x-y plane between the point and the x axis <math>\theta</math>, the distance perpendicular to the x-y plane:  <math>(r, \theta. z)</math>  
  
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.
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In a sense, cylindrical coordinates are polar coordinates with a third dimension added: <math>(r, \theta)</math> correspond to the polar coordinates for <math>(x, y)</math>. This is in contrast to [[spherical coordinates]], where <math>z</math> 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:
  
:r<sup>2</sup> = x<sup>2</sup> + y<sup>2</sup>
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:<math>r^2 = x^2 + y^2</math>
  
:tan(θ) = y/x
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:<math>\tan{\theta} = \frac{y}{x}</math>
  
:x = r*cos(θ)
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:<math>x = r \cos{\theta}</math>
  
:y = r*sin(θ)
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:<math>y = r \sin{\theta}</math>
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In cylindrical coordinates, the Jacobian is <math>r</math> so that <math>\text{d}x \, \text{d}y \, \text{d}z = r \text{d}r \, \text{d} \theta \, \text{d}z</math>.
  
 
[[Category:Mathematics]]
 
[[Category:Mathematics]]
 
[[Category:Geometry]]
 
[[Category:Geometry]]

Latest revision as of 14:08, 14 December 2016

Cylindrical coordinates refers to a three-dimensional coordinate system used to describe the location of a point in space based on the distance from the origin in the x-y plane , the angle measured in the x-y plane between the point and the x axis , the distance perpendicular to the x-y plane:

In a sense, cylindrical coordinates are polar coordinates with a third dimension added: correspond to the polar coordinates for . This is in contrast to spherical coordinates, where is replaced by an angle, just like x and y are in polar coordinates.

The equations converting the parameters are as follows:

In cylindrical coordinates, the Jacobian is so that .