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Internet Resources for the Calculus Student - Topics in Precalculus

Parametric Equations

Many interesting curves are not function graphs with y=f(x), but can be described by specifying both x and y as functions of a third variable (called a parameter). For example the circle x^2+y^2=1 can be described "parametrically" with x=cos(t) and y=sin(t). The path of any moving point can be described this way with the parameter, t, being the time.

Some interesting examples correspond to cases where the moving point is attached to a wheel:

The Cycloid arises when the point is on the rim and the wheel is rolling along a flat surface.
Spirograph is a child's toy that lets you draw the corresponding curves when the circle rolls inside or outside another circle. (The toy itself is actually used in our M183 calculus lab on parametric equations.)

Many of these Famous Curves are defined parametrically, as are also many of the ones in this Visual Dictionary of Special Plane Curves.

Here are some other sites dealing with parametric curves that have been found and reviewed by Langara students:

url:  http://members.aol.com/kchs99/calc/basics.html From: Kalamazoo College web site
(Reviewed by Amin Pirzadeh)

and: http://members.aol.com/kchs99/calc/focus.html also discusses projectile motion
(Reviewed by Amin Pirzadeh)

and this URL:http://members.aol.com/kchs99/calc/index.html was reviewed by Tony Wang

You might also check our 'raw list' (of links provided without comment) to see if there are any more examples there that we haven't yet included here.

If you have come across other good web-based illustrations of parametric curves,
     please do let us know and we will add them here.


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