Astroid

: This page is about the geometrical concept. An asteroid is a small, solid object in the solar system.

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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.

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Its modern name comes from the Greek word for "star". The curve had a variety of names, including tetracuspid (still used), cubocycloid, and paracycle.

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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

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:x = cos3θ

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:y = sin3θ

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The evolute of an astroid is an astroid twice as large.

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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.

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Curve: In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. Simple examples are the circle or the straight line. A large number of other curves have been studied in geometry....

Hypocycloid: In geometry, a hypocycloid is a special plane curve, a roulette, generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the cycloid but instead of the circle rolling along a line, it rolls within a circle....

Cusp: In common parlance, a cusp is an important moment usually regarded as a decision point upon which consequent events are determined....