Cylindrical Coordinates

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Hook

Polar, now with altitude

A soup can, a pipe, a tree trunk — round in cross-section and extended upward. Cartesian coordinates make these miserable. Cylindrical coordinates fix it the lazy-genius way: keep polar (r, θ) for the circular floor and just bolt on z for height. A point is (r, θ, z).

x = r·cos θ, y = r·sin θ, z = z. Polar in the plane, plain height up.

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