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Beyond the Ellipse

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Author:Ivars Peterson (MathLand)
Description: There's a simple trick one can use to draw an ellipse. Tie the ends of a length of string to two pins (or thumbtacks) stuck in a sheet of paper on a drawing board. Then, keeping the string taut with the point of a pencil, allow the pencil to trace a path around the pins. The resulting curve is an ellipse, with the two pins, or fixed points, representing its foci. One can also ask what curve results when the total distance from three given points is kept the same. That's what Bilge Demirkoz, a 16-year-old high school student in Istanbul, Turkey, did to investigate what happens for not only three but also four fixed points. She presented a guided tour of her findings in this neglected corner of mathematics one evening at a Seattle Mathcamp...

Levels: Middle School (6-8), High School (9-12), College
Languages: English
Resource Types: Manipulatives, Articles
Math Topics: Conic Sections and Circles

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