Definition:Hypocycloid

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Definition

Let a circle $C_1$ roll around the inside of another (larger) circle $C_2$.

The locus of a given point on the circumference of $C_1$ is known as a hypocycloid.


Hypocycloid.png


Generator

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.


Cusp

A cusp of the hypocycloid is defined as a point where the hypocycloid meets the larger circle.


Arc

An arc of the hypocycloid is defined as one of the curves between two of the cusps of the hypocycloid.


Also known as

A hypocycloid is also seen referred to as a common hypocycloid, to distinguish it from the extended hypocycloid and contracted hypocycloid.

The latter two concepts are referred to on $\mathsf{Pr} \infty \mathsf{fWiki}$ as the prolate hypotrochoid and curtate hypotrochoid respectively.


Also see

  • Results about hypocycloids can be found here.


Linguistic Note

The hypo- prefix in the term hypocycloid comes from the Greek word meaning under or beneath.

The prefix can be seen in other common words, for example hypodermic, which literally means under the skin.


Sources

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