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Parametric Plots: A Creative Outlet

Judy Holdener and Keith Howard

Notes to Instructor

 Created by Atul Varma (Class of 2001, Kenyon College)

 Created by Atul Varma
(Class of 2001, Kenyon College)

Many of us have fond childhood memories of creating wiggly lines, circles, and other doodles on the magic screen of an Etch A Sketch®, a toy that first appeared in the early 1960's. In this module, you will get the chance to relive those endless hours of etching fun through the use of parameterizations and MAPLE.

A parameterization of a curve in the plane is a pair of functions, x(t) and Y = y(t), that describe the motion of a particle in the plane. The function x(t) serves the same role as the left-hand dial on the Etch A Sketch; it describes the motion of the particle in the x-direction. The function y(t), like the right-hand dial, dictates the motion in the y-direction. At any given value of time t, the pair (x(t), y(t)) determines the particle's exact location at that time.

As you will soon discover, MAPLE's parametric plotting capabilities are more conducive to creative doodling than those familiar white dials ever were. In fact, by working through each of the sections listed below, you will learn how to draw almost anything you wish. In the final section of this project, you will then be asked to show off your new skills by creating your own elaborate doodle.

Judy Holdener is Associate Professor of Mathematics and 
Keith Howard  is Assistant Professor of Mathematics, both at Kenyon College.

Copyright © 2004 by Judy Holdener and Keith Howard

Published June, 2004

Judy Holdener and Keith Howard, "Parametric Plots: A Creative Outlet," Convergence (August 2004)