Astroid, how it is formed - This page is about the geometrical concept. An asteroid is a small, solid object in the solar system.
In mathematics, an astroid is a particular type of curve: a hypocycloid with four cusps, or a super ellipse with n=2/3 and a=b.
A circle of radius 1/4 rolls around inside a circle of radius 1 and a point on its circumference traces an astroid. A line segment of length 1 slides with one end on the x-axis and the other on the y-axis, so that it is tangent to the astroid (which is therefore an envelope). The parametric equation is
- x = cos3θ, y = sin3θ.
The evolute of an astroid is an astroid twice as large.
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