Definition:Epicycloid/Generator/Epicycle

Definition

Let an epicycloid be generated by rolling a circle $C_1$ around the outside of another circle $C_2$.

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

Also known as

An epicycle of an epicycloid is also known as a rotor.

The term has been taken by $\mathsf{Pr} \infty \mathsf{fWiki}$ from the children's toy Spirograph, which itself was taken from the term rotor as applied to the moving (rotating) part of a rotary machine.

Also see

• Definition:Deferent of Epicycloid

• Results about epicycloids can be found here.

Linguistic Note

The term epicycle in this context was used by Apollonius of Perga in his exposition on epicycloids.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): epicycloid
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): epicycle
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): epicycloid
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): epicycle
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): epicycloid