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The Kappa Curve as a Locus

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The kappa curve looks vaguely like a curly kappa, , and was studied by Newton, Bernoulli, and Gutschoven. Sometimes called Gutschoven's curve, its double cusp form can be represented as .

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Let be the point (magenta). Let be the intersection point (blue) of the horizontal line with a line rotating about the origin . The kappa curve is the locus of points (red) on the rotating line such that distances (green segments).

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Contributed by: Roberta Grech (July 2013)
Open content licensed under CC BY-NC-SA

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[1] T. Heard, D. Martin, and B. Murphy, A2 Further Pure Mathematics, 3rd ed., London: Hodder Education, 2005 p. 209, question 13.

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