Doug Ensley's Envelope Applet
In the window below, you can explore envelopes of families of
lines. The interaction is a Flash applet by Doug Ensley, created as
part of the Flash and
Math Project. Each family of lines is defined by an equation
of the form
where a(p) and b(p)
are functions of the parameter p.
For any value of p, the
equation produces a straight line whose x and y intercepts are a(p)
and b(p), respectively. Varying p produces a collection of lines --
the family of lines for the given equation. In the applet you can
specify a(p)
and b(p) and then generate a sample of
lines from the family. You can also display the envelope for the
family of lines. Can you find the equation of the
envelope? The applet permits you to specify a solution, either
implicitly or as a parameterized curve, and will add your solution to
the graph.
To begin immediately, scroll down to the applet window. Or if you
prefer, view some more detailed
instructions first. You may also wish to read more about envelopes and methods for finding their equations.
