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1. Constructing a Point on a Cassini Oval

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This Demonstration shows a ruler and compass construction of a point on a Cassini oval.

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Fix two points, and (the foci), a distance apart. A Cassini oval (or Cassini ellipse) is a quartic curve traced by a point such that the product of the distances is a constant .

Let be the circle with center at the center of the oval and radius . Let be the right apex of the oval. A ray from at an angle to the line meets at the points and . Let be the circle with center and radius and let be the circle with center and radius . Let the point be one of the intersections of and . Then the product of the radii and is equal to the product , so is on the oval.

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Contributed by: Izidor Hafner and Marko Razpet (March 2018)
Open content licensed under CC BY-NC-SA

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Details

The construction can be found in [2, pp. 189–190].

References

[1] E. W. Weisstein. "Cassini Ovals" from Wolfram MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/CassiniOvals.html (Wolfram MathWorld).

[2] A. A. Savelov, Plane Curves (in Croatian), Zagreb: Školska knjiga, 1979.

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