# Definition:Epicycloid

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## Contents

## Definition

Let a circle $C_1$ roll around the outside of another circle $C_2$.

The locus of a given point on the circumference of $C_1$ is known as an **epicycloid**.

### Generator

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

### Stator

The circle $C_2$ can be referred to as the **stator** of the epicycloid.

### Rotor

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

### Cusp

A **cusp of the epicycloid** is defined as a point where the epicycloid meets the static circle, the stator.

### Arc

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

## Also see

- Results about
**epicycloids**can be found here.

## Linguistic Note

The **epi-** prefix in the term **epicycloid** comes from the Greek word meaning **on** or **above**.

The prefix can be seen in other common words, for example **epicenter**.

## Sources

- 1968: Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*... (previous) ... (next): $\S 11$: Special Plane Curves: Epicycloid: $11.18$ - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**epicycloid** - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {B}.21$: The Cycloid - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**epicycloid**