Difference between revisions of "Cylindrical coordinates"

Latest revision as of 19:08, December 14, 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 $r$ , the angle measured in the x-y plane between the point and the x axis $\theta$ , the distance perpendicular to the x-y plane: $(r,\theta .z)$

In a sense, cylindrical coordinates are polar coordinates with a third dimension added: $(r,\theta )$ 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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r^2 = x^2 + y^2}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tan{\theta} = \frac{y}{x}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x = r \cos{\theta}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = r \sin{\theta}}

In cylindrical coordinates, the Jacobian is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} so that Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \text{d}x \, \text{d}y \, \text{d}z = r \text{d}r \, \text{d} \theta \, \text{d}z} .

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-{{jargon}}
+'''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>
-'''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).
+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.
-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:
+:<math>r^2 = x^2 + y^2</math>
-:r<sup>2</sup> = x<sup>2</sup> + y<sup>2</sup>
+:<math>\tan{\theta} = \frac{y}{x}</math>
-:tan(θ) = y/x
+:<math>x = r \cos{\theta}</math>
-:x = r*cos(θ)
+:<math>y = r \sin{\theta}</math>
-:y = r*sin(θ)
+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]]

Difference between revisions of "Cylindrical coordinates"

Latest revision as of 19:08, December 14, 2016

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