Definition:Epitrochoid
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Definition
Let a circle $C_1$ of radius $b$ roll around the outside of another circle $C_2$ of radius $a$.
Consider a point $P$ on the line of a radius of $C_1$ at a distance $d$ from the center of $C_1$.
The curve traced out by $P$ is called an epitrochoid.
Curtate
Let $d < b$.
The curve traced out by $P$ is called a curtate epitrochoid.
Graph
Prolate
Let $d > b$.
The curve traced out by $P$ is called a prolate epitrochoid.
Graph
Epicycloid
The special case where $d = b$ is usually treated separately:
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.
Also see
- Results about epitrochoids can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): epitrochoid
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): epitrochoid