Polar Plot
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.
Contact the MathWorld Team
polar plot
