See that small heart-shaped curve? It's a cardioid. You get it when you roll a circle on a circle that's the same size, and track the motion of a point on the rolling circle.
The other curves here, with more bumps, are epicycloids. You get them when you roll a circle on a circle that's 2 times as big, or 3 times as big, etc.
It turns out there's a nice way to 'roll' each epicycloid inside the next... and that's what you see here, in this image made by Gerard Westendorp.
However, as each one rolls inside the next, it has to slip, too, for the cusps (the sharp points) to line up.
For details and more pictures like this, see:
- Hedge Fund Business Manager, present
- Johns Hopkins1981 - 1985
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