Polar and Spherical Coordinates
New, dedicated functions are available to convert between Cartesian and the two most important non-Cartesian coordinate systems: polar coordinates and spherical coordinates.
Convert between Cartesian and polar coordinates.
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ToPolarCoordinates[{x, y}]
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FromPolarCoordinates[{r, \[Theta]}]
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Convert between Cartesian and spherical coordinates.
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ToSphericalCoordinates[{x, y, z}]
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FromSphericalCoordinates[{r, \[Theta], \[CurlyPhi]}]
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Polar coordinates naturally generalize to higher dimensions.
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ToPolarCoordinates[{w, x, y, z}]
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FromPolarCoordinates[{r, \[Theta]1, \[Theta]2, \[Theta]3, \
\[CurlyPhi]}]
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Plot curves expressed in polar and spherical coordinates.
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ParametricPlot[
FromPolarCoordinates[{Exp[-t/10], t}] // Evaluate, {t, 0, 50},
PlotRange -> All]
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ParametricPlot3D[
FromSphericalCoordinates[{1, TriangleWave[{0, Pi}, p/(2 Pi)], p}] //
Evaluate, {p, 0, 2 Pi}]
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