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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