Polar curves are not drawn using the (x, y) coordinates corresponding to horizontal and vertical axes (called Cartesian coordinates).
Instead, polar curves are drawn using polar coordinates. The first of the polar coordinates of a point is r: the distance between the point
and the pole (the pole is another name for the origin (0, 0), and this distance r is often referred to as the radius).
The second of the polar coordinates is
A common type of polar curve is a rose curve which has quite a bit of history.
The simplicity and symmetry of Rhodonea or rose curves have fascinated mathematicians since they were first named by the
Italian mathematician Guido Grandi in the 1700s. These curves created fascination due to the interesting patterns for the number of petals of the curves.
The functions in this case are trigonometric expressions
The following is a gallery
of demos for illustrating selected families of functions. These figures and animations can be used by instructors in a classroom setting or by
students to aid in acquiring a visualization background relating to the change
of parameters in expressions for functions. Two file formats, gif and MP4, are used and should run on most systems. Originally, see the NOTES below the
gallery of animations, the animations were gif files which had no control for a user. The animations are now MP4 files which allow the user to easily control features
like stop and go, restart, and change the animation screen size. The controls are similar to those in You Tube. Click this thumbnail
to see an example.
![]() |
Vary a
MP4 Animation Tracing: MP4 Animation |
|
![]() |
Vary a
MP4 Animation Vary b MP4 Animation Tracing: MP4 Animation |
|
![]() |
Vary a
MP4 Animation Vary b MP4 Animation Tracing: MP4 Animation |
|
![]() |
Vary a
MP4 Animation |
|
![]() |
Vary a
MP4 Animation Vary b MP4 Animation |
|
![]() |
Vary a
MP4 Animation |
|
![]() |
Vary a
MP4 Animation |
|
![]() |
Vary a
MP4 Animation |
|
![]() |
Vary a
MP4 Animation |
|
![]() |
Vary k
MP4 Animation Vary e MP4 Animation |
|
|
Vary ALL of c, a, b
MP4 Animation |
NOTES
Some Sources for Rose Curves
Other Sources for Polar Curves