Astroid

The astroid (also called star curve) is a plane curve, which is a parameter by parameter equations

Or by the implicit equation

Be described, where a is a fixed positive real number. For its area A

The length of the entire curve. Within a quarter curve applies to the arc length

And the radius of curvature

The astroid is also a special case of the hypocycloid. It is also similar to check on ordinary playing cards.

Center of gravity

* When rotation about the X-axis

Skew astroid

A generalization is the crooked astroid, which is characterized by the parametric equations

Or by the implicit equation

Can be described. The evolute of an ellipse is also a skew astroid.