The term "polar bear curve" can be used to refer to a bear-shaped polar curve. It can be constructed using polar coordinates
and truncated expansions in Chebyshev
polynomials of the first kind 
. The curve's name is a mathematical pun on using polar
coordinates to draw a bear.
The plot above shows a numerical reconstruction of the bear-shaped outline in Watt (2015), with parametric equations
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
,
and both the radial coordinate 
and a continuously tracked polar
angle 
are approximated by
 |  |  |
(3)
|
 |  |  |
(4)
|
where the radial scale is chosen so that 
and the polar angle need
not increase throughout the traversal, meaning that this representation does not
require a single-valued polar equation 
.
The plots above show the radial coordinate 
(left) and polar angle 
(right) as functions of the parameter
.
The plots above show the magnitudes of the coefficients 
(left) and 
(right) as functions of the index 
, using logarithmic vertical scales. Blue points indicate positive
coefficients and red points indicate negative coefficients.
This reconstruction uses many more coefficients than the compact representations of von Neumann's elephant. It could presumably be simplified to give a similar schematic bear shape using fewer coefficients.
