A plot of 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 
.
Other specially-named Archimedean spirals include
the lituus when 
, the hyperbolic spiral
when 
, and Fermat's
spiral when 
.
Note that lines and circles are
easily-expressed in polar coordinates as
 |
(1)
|
and
 |
(2)
|
for the circle with center 
and radius 
, respectively. Note that equation () is merely a particular
instance of the equation
 |
(3)
|
defining a conic section of eccentricity 
and semilatus
rectum 
.
In particular, the circle is the conic of 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.
