astroid

thumb|Astroid thumb|The hypocycloid construction of the astroid. thumb|Astroid as the common Envelope (mathematics)|envelope of a family of [[ellipses of equation , where .]] [[File:sliding_ladder_in_astroid.svg|thumb|link=|The envelope of a ladder (coloured lines in the top-right quadrant) sliding down a vertical wall, and its reflections (other quadrants) is an astroid. The midpoints trace out a circle while other points trace out ellipses similar to the previous figure. [ ] hover over a ladder to highlight it.]] thumb|right|Astroid as an evolute of ellipse

In mathematics, an astroid is a particular type of roulette curve: a hypocycloid with four cusps. Specifically, it is the locus of a point on a circle as it rolls inside a fixed circle with four times the radius. By double generation, it is also the locus of a point on a circle as it rolls inside a fixed circle with 4/3 times the radius. It can also be defined as the envelope of a line segment of fixed length that moves while keeping an end point on each of the axes. It is therefore the envelope of the moving bar in the Trammel of Archimedes.