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In three dimensions there are two analogues of polar coordinates. In cylindric coordinates, x and y are described by r and exactly as in two dimensions, while the third dimension, z is treated as an ordinary coordinate. r then represents distance from the z axis. In spherical coordinates, a general point
is described by two angles and one radial
variable, ,
which represents distance to the origin: Exercises:3.12 Express the parameters of cylindric and spherical coordinates in terms of x, y and z. 3.13 Construct a spreadsheet converter which takes coordinates x, y and z and produces the three parameters of spherical coordinates; and vice versa. Verify that they work by substituting the result from one as input into the other. |