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.

Related Topics:
Mathematics - Curve - Hypocycloid - Cusp - Super ellipse

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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.

Related Topics:
Greek - Star

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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

Related Topics:
Circle - Line segment - X-axis - Y-axis - Envelope - Parametric equation

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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.

Related Topics:
U.S. Steel - Pittsburgh Steelers

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