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Be Careful What You Assign: Constant Speed Parametrizations

Michelle L. Ghrist and Eric E. Lane
Mathematics Magazine
Vol. 86, No. 1 (February 2013), pp. 3-14
DOI: 10.4169/math.mag.86.1.003
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Page Count: 12
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Be Careful What You Assign: Constant Speed Parametrizations
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Summary We explore one aspect of a multivariable calculus project: parametrizing an elliptical path for an airplane that travels at constant speed. We find that parametrizing a constant speed elliptical path is significantly more complicated than a circular path and involves taking the inverse of the elliptic integral of the second kind. We compare our constant-speed parametrization to the standard ellipse parametrization (x(t) = a cos wt, y(t) = b sin wt) and generalize to parametrizing other constant-speed curves.

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