A Parameterized Curve Applet

This applet is designed to build intuition about parameterized curves.
• The applet has a control window and Parameterized Curve window.
• The control window lets you define x, y, and z as functions of t.  (For curves in 2 variables, z(t)=t is used.)  One can also scroll the point t0.  Readouts let you see the values of the point P0, and the tangent and normal vectors at that point.
• The parameterized curve window shows the curve along with the point P0 and the unit tangent and normal vectors at that point.

Things to notice:
• One can rotate the Parameterized Curve window by dragging.  Looking up the z-axis gives the curve in x and y.  If z(t)=t, then looking up the x-axis gives shows y as a function of t while looking down the y axis shows x as a function of t.  (You may want to use the view menu instead of dragging.
• As long as z(t) covers the same interval, the x-y view is not changed.  Try t^2, t^5, t^20, and sin(Pi*t) for z(t) while viewing "up the z-axis".  The view should remain unchanged.  With the same changes viewing "up the x axis" we get noticeable changes.

This applet was designed as by modifying an applet from a demo by Tom Banchoff at Brown University.  It is used with permission.   Go to the Banchoff Applet Help page.

Return to the Banchoff Applet page.
Return to the SLU Calculus Applet page.

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Last updated By Mike May, S.J. ,  November 18, 2006.