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 x2/3+ y2/3= 1
Number of Ellipses
How they come out will depend on your browser. Internet Explorer 8 renders them with ugly clumps of multiple pixels in XP but they come out just fine in Windows 7, Chrome and Firefox.
Created 29 November 2010, Last Update 05 February 2012
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