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?

  • $\begingroup$ I don't know about the asteroid curve specifically, but a thing does not have to have any real application to captivate mathematicians. For an extreme example, see Fermat's last theorem, whose most important application as far as I know is to prove that $\sqrt[n]2$ is irrational for $n\geq3$. $\endgroup$ – Arthur Nov 19 '18 at 20:21
  • $\begingroup$ You will find some "applications" (please note the quotes) in {mathworld.wolfram.com/Astroid.html} in particular as an envelope. $\endgroup$ – Jean Marie Nov 19 '18 at 23:13

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.


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