The polar equation

The polar equation of a curve is an equation in which the modulus (this is the distance from a point of the curve to the origin) is expressed in terms of the argument (this is the angle between the straight line through the point and the origin and the x-axis). The modulus is denoted by r and the argument by u. As with the parameter equation, a range for the parameter u must be given. Below, this is illustrated:

Polar coordinates

The curve with polar equation r(u) = u/3 with u in the interval (0, 8*pi) is given here:

A linear spiral