hypocycloid: a curved, multi-pointed shape (with a complex geometrical definition)

Your eyes are not deceiving you. That's the Pittsburg Steelers logo. No, I'm not a fan. (I'm also not not a fan. Team sports do nothing for me.)

I chose it because it features not one but three hypocycloids. In this case, they're diamond shapes with curved sides instead of straight.

What makes them hypocycloids is that those lines were created by tracing a smaller circle inside the bigger (silver) circle. You can see it most clearly half-encircling the word, to its right, where the blue and yellow curves clearly create the half circle. That circle-in-a-circle quality is what turns these simple diamonds into hypocycloids.

But a hypocycloid is not limited to specifically four points. There can be three; there can be dozens! They can come in all different shapes and sizes. The easiest way to think of them is that they're what you get when you draw with a Spirograph. The way the smaller piece rolls inside of the big circle, making further circles as it goes, is what makes it a hypocycloid.

That said, it's worth noting that the term can also be used to refer to just an inner curve that makes up the shape, and not just the shape itself. In fact, if you look it up, the definitions that come up first will most likely refer to those individual curves.

Okay, already... If you insist on seeing such an official definition for yourself--and don't say I didn't warn you--here's what Merriam-Webster says:

hypocycloid: a curve traced by a point on the circumference of a circle rolling internally on the circumference of a fixed circle

And that's probably the one that's easiest to understand.

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