Definition:Hypocycloid/Generator

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Definition

Let a hypocycloid be generated by rolling circle $C_1$ around the inside of another (larger) circle $C_2$.


Hypocycloid.png


The circles $C_1$ and $C_2$ can be referred to as the generators of the hypocycloid.


Deferent

The circle $C_2$ can be referred to as the deferent of the hypocycloid.


Epicycle

The circle $C_1$ can be referred to as the epicycle of the hypocycloid.


Also known as

The generators of a hypocycloid can also be referred to as its generating circles.


Linguistic Note

The term generator of a hypocycloid was invented by $\mathsf{Pr} \infty \mathsf{fWiki}$.

As such, it is not generally expected to be seen in this context outside $\mathsf{Pr} \infty \mathsf{fWiki}$.

The term generator circle can sometimes be seen used for what $\mathsf{Pr} \infty \mathsf{fWiki}$ refers to as the epicycle.