Normal Lines Drawn to Ellipses and Elliptic IntegralsTilak de Alwis
Department of Mathematics
Southeastern Louisiana University
Hammond, LA 70402, USA
Consider the ellipse in the standard position, and P, an arbitrary point on the plane. Finding the minimum distance from P to the ellipse is a well-known problem. One can easily show that the minimum distance path lies along a normal line to the ellipse, passing through P. This paper deals with a study of all the normal lines drawn from point P to the ellipse. We have used Mathematica to illustrate and discover several aspects of these normal lines. Mathematica can be used in contemporary mathematical research and education as a computational, visualization, experimentation and conjecture-forming tool. The paper well illustrates such usage via a study of the normal lines to the ellipse. We used Mathematica 3.0 on a Windows 95 platform.
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