Conchoid (mathematics)
In geometry, a conchoid is a curve derived from a fixed point O, another curve, and a length d. It was invented by the ancient Greek mathematician Nicomedes.
The conchoid is, therefore, the cissoid of the given curve and a circle of radius d and center O.
They are called conchoids because the shape of their outer branches resembles conch shells.
The simplest expression uses polar coordinates with O at the origin.
For instance, if the curve is the line x = a, then the line's polar form is r = a sec θ and therefore the conchoid can be expressed parametrically as A limaçon is a conchoid with a circle as the given curve.
Fixed point
O
Given curve
Each pair of coloured curves is length
d
from the intersection with the line that a ray through
O
makes.
d
>
distance of
O
from the line
d =
distance of
O
from the line
d
<
distance of
O
from the line
