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.