Langara College - Department of Mathematics and Statistics

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Internet Resources for the Calculus Student - Topics in Precalculus

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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.