Definition:Reciprocal Curve

Definition

Let $\CC$ be a curve embedded in a Cartesian plane whose general point $P$ is specified by $\tuple {x, y}$.

The reciprocal curve to $\CC$ is the curve generated from $\CC$ by replacing the ordinates of points $P$ by their reciprocals: $\tuple {x, \dfrac 1 y}$.

Examples

Arbitrary Example

Let $\CC$ be the curve described by the equation:

$y = 2 x$

The reciprocal curve of $\CC$ is the curve described by the equation:

$y = \dfrac 1 {2 x}$

and vice versa.

Also see

• Results about reciprocal curves can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): reciprocal curve
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): reciprocal curve