Definition:Polar Equation

Definition

A polar equation is an equation defining the locus of a set of points in the polar coordinate plane.

Such an equation is generally presented in terms of the variables:

$r$: the radial coordinate

$\theta$: the angular coordinate

Examples

Circle

The polar equation:

$r = 2 \cos \theta$

defines the locus of the circle whose Cartesian equation is:

$\paren {x - 1}^2 + y^2 = 1$

Also see

• Results about polar equations can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): polar equation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): polar equation
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): polar equation