The astroid curve is a fascinating and famous curve — but why do we care?
Several famous mathematicians and physics worked on it, like Roemer, Bernoulli, and Leibnitz, but why? Is it simply for investigating mathematical properties of the curve, or is there some practical application?
In my research, I have found very little real-world applications of the astroid curve, and only in very high-level physics (for example, caustics in gravitational lensing).
Since the astroid curve has been so extensively studied, is there some simple application I am missing?
Consider all rhombuses with side length 2 whose centers are the origin and vertices lie on the coordinate axes. An astroid curve is the envelope of these rhombuses.
Likewise it is the exterior of all points swept out by a linear "ladder" sliding down a wall.