A polar plot is a plot of a polar equation, namely a function expressed in polar
coordinates with radius 
as a function of angle 
. Polar plots can be drawn in the
Wolfram Language using PolarPlot[r,
t, tmin, tmax
]. The plot above is a polar plot of the
polar equation 
, giving a cardioid.
Polar plots of 
give curves known as roses, while polar plots of 
produce what's known as Archimedes' spiral, a special case of the Archimedean
spiral 
corresponding to 
.
When 
, other specially named Archimedean
spirals include the lituus when 
, the hyperbolic spiral
when 
, and Fermat's
spiral when 
.
Note that lines through the origin
and circles are easily-expressed in polar
coordinates as
 |
(1)
|
and
 |
(2)
|
for the circle with center 
and radius 
, respectively. The equation (2)
describes a circle with arbitrary center.
In a different polar representation, with the origin at
a focus and the polar axis along its axis
of symmetry, the equation
 |
(3)
|
defines a conic section of eccentricity 
and semilatus
rectum 
.
In particular, the circle centered at the origin
is obtained with eccentricity 
, while 
yields a general ellipse,
a parabola,
and 
a hyperbola.
The plotting of a complex number 
in terms of its complex
modulus 
and its complex argument 
is closely related to polar
coordinates due, e.g., to the Euler formula.
As such, the plotting of complex numbers in the
Cartesian plane by way of an Argand
diagram can be viewed as a specialized polar plot.
