Definition:Hypotrochoid/Curtate

Definition

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

Let $d < b$.

The curve traced out by $P$ is called a curtate hypotrochoid.

Graph

Also known as

A curtate hypotrochoid is also known as a contracted hypocycloid.

Also see

• Definition:Hypotrochoid
• Definition:Prolate Hypotrochoid

• Definition:Hypocycloid