Steven Dutch, Natural and Applied Sciences, University
of Wisconsin - Green Bay

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The astroid (not "asteroid") is a curve that can be defined several ways. It is the envelope swept out by a line of constant length with ends that slide along the x- and y- axes. It is also the locus of a point on a circle that rolls around the inner circumference of a circle with four times the radius. That is, it's a hypocycloid.

Another interesting definition is that it's the envelope of ellipses centered at the origin whose major and minor axes sum to a constant. That's the form shown here.

The equation of the astroid is x^{2/3}+
y^{2/3}= 1

Number of Ellipses: Size

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*Created 07 February 2012, Last Update
13 July 2014
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