- 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.
Its modern name comes from the Greek word for "star". The curve had a variety of names, including tetracuspid (still used), cubocycloid, and paracycle.
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.
The old U.S. Steel logo consisted of three astroids, one each of blue, yellow and red. It is now used as the logo for the Pittsburgh Steelers.