Believe!

In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the cycloid but instead of the circle rolling along a line, it rolls within a circle.
The red curve is a hypocycloid traced as the smaller black circle rolls around inside the larger blue circle (parameters are R=3.0, r=1.0, and so k=3), giving a deltoid.

If the smaller circle has radius r, and the larger circle has radius R = kr, then the parametric equations for the curve can be given by either:

x (\theta) = (R - r) \cos \theta + r \cos \left( \frac{R - r}{r} \theta \right)
y (\theta) = (R - r) \sin \theta - r \sin \left( \frac{R - r}{r} \theta \right),

or:

x (\theta) = r (k - 1) \cos \theta + r \cos \left( (k - 1) \theta \right) \,
y (\theta) = r (k - 1) \sin \theta - r \sin \left( (k - 1) \theta \right). \,

If k is an integer, then the curve is closed, and has k cusps (i.e., sharp corners, where the curve is not differentiable). Specially for k=2 the curve is a straight line and the circles are called Cardano circles. Girolamo Cardano was the first to describe these hypocycloids, which had applications in the technology of high-speed printing press.

If k is a rational number, say k = p/q expressed in simplest terms, then the curve has p cusps.

If k is an irrational number, then the curve never closes, and fills the space between the larger circle and a circle of radius R − 2r.

I have no idea what any of that means but when you put 3 hypocycloids together it strikes fear into the hearts of some and causes the hearts of others to soar.

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