Astroid

A astroid is a plane curve, which can be defined in several ways. In particular, it is possible to obtain it while making roll a Cercle of ray ¼ inside a circle of radius 1. For this reason, the astroid is a Hypocycloïde of circle at four points of reflection.

An astroid can be defined by the parametric equation following:

$\backslash \; begin\; \{boxes\}\; X\; (T)\; =\; \backslash \; cos^3\; (T)\; \backslash \; \backslash \; there\; (T)\; =\; \backslash \; sin^3\; (T)\; \backslash \; end\; \{boxes\}$

On the figure opposite was traced in green a segment length 1 connecting a point of the x-axis to a point of the y-axis. It is tangent with the astroid. For this reason, the astroid can be seen like the curve envelope of the family of the segments checking these properties. To describe this family by an image, one often evokes a scale slipping along a wall.

The astroid admits for Cartesian equation

$(x^2+y^2-1)\; ^3+27x^2y^2=0.$

It is a algebraic Courbe of degree equal to six and of kind zero (a rational Sextique).

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