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: Size
Created 07 February 2012, Last Update 11 February 2012
Not an official UW Green Bay site