Cardioids and Limacons

Steven Dutch, Natural and Applied Sciences,  University of Wisconsin - Green Bay
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A Cardioid is named from its somewhat heart-like shape. It can be constructed by taking a fixed circle and a point on the circle, and drawing circles through the point with centers on the fixed circle.

If the fixed point is not on the circle, we can get curves with or without loops. In the diagram below, the radius of the point is the distance from the center of the fixed circle in terms of the radius of the fixed circle. If the radius is greater than 1, that is the fixed point is outside the circle, we get a curve with a loop. If the radius is less than 1 (point inside the circle), then there is no loop. These generalized curves are called Limacons.

If you set the radius to zero, you get circles passing through the center of the fixed circle. Pretty, but not very significant. However, if you select six circles, you get the well known compass construction for a hexagon.

Radius of Point: Number of Circles:

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Created 29 November 2010, Last Update 11 February 2012

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