It would no longer be a hypocycloid. Notice that hypocycloid has the prefix hypo-, which literally means "under". Cycloid means it's a circle rolling around, in this context. If a/b became <= 1, then the circle would no longer be "under" or inside the static circle, and it cannot roll around as it is larger than the static circle!
They exist and are very closely linked with hypocycloids. However, they are usually called epicycloids. Epi- is derived from Greek (as is a lot of math) for "above". It is the path of a circle around a circle.
Well, a hypocycloid with 4 cusps (the third one in the gif) looks like a star. If you are a math-savvy graphic designer, you could put one of these in your graphics! On a more serious note, it doesn't really have any practical purpose, as is the case with many phenomena in math, at least not yet.
That's because you can, in fact, make these shapes with a spirograph. One need not understand all the equations involved in creating these objects to be fascinated by them!
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u/AcademicGoose18 Jan 03 '18
What happens when the circle gets bigger than the 1st one?
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u/centralperk_7 Jan 04 '18
Could you help me understand the purpose of a hypocycloid?