The name pretzel curve has two uses. It is an alternate name for the knot curve, but it also denotes the distinct quartic
curve studied by Hašek (2017, pp. 40-42). Here it denotes Hašek's
rational curve, illustrated above for 
, with Cartesian equation
 |
(1)
|
where 
.
Its polar equation is
 |
(2)
|
where the radial coordinate 
is signed and 
. A parametrization is given by the parametric equations
 |  |  |
(3)
|
 |  |  |
(4)
|
where 
ranges over the real numbers (Hašek 2017, p. 41).
The curve has three ordinary double points,
at 
, 
, and 
.
