David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735

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Investigate Parametric Curves

The following applet graphs curves defined parametrically by x=x(t) and y=y(t) for a ≤ t ≤ b. Simply enter the functions x(t) and y(t) and the values a and b. The parametric curve is drawn in the main window, while the graphs of x(t) and y(t) are drawn individually in the pulldown window.

The values a and b can be changed by simply typing a new value, such as "1.2345", "pi/2", "sqrt(5)+cos(3)", etc. You may also change these values by using the up/down arrow keys or dragging the corresponding point left or right. To move the center of the graph, simply drag any point to a new location. To label the x-axis in radians (i.e. multiples of pi), click on the graph and press "control-r". To switch back, simply press "control-r" again.

Here is a list of functions that can be used with this applet.

Use the above applet to:

  • investigate the number of loops in the parametric curve
    x(t) = cos(At) + cos(Bt)
    y(t) = sin(At) - sin(Bt)
    for various values of A and B.
  • draw the curve
    x(t) = t + sin(2t)
    y(t) = sin(3t)cos(t)
    Surf's Up!
  • Draw your favorite SpiroGraphs using the the following parametric equations
    x(t) = (R+r)cos(t) - p*cos((R+r)t/r)
    y(t) = (R+r)sin(t) - p*sin((R+r)t/r)
    for various values of R,r and p.

© 2005 David P. Little
Download this applet for off-line viewing (includes source code). The above applet uses the Java Math Expression Parser (JEP) developed by Singular Systems