Definition:Reciprocal Spiral

Definition

The reciprocal spiral is the locus of the equation expressed in polar coordinates as:

$r = \dfrac a \theta$

For negative $r$, the figure appears as:

and when plotted both together:

Also known as

Some sources refer to the reciprocal spiral as the hyperbolic spiral.

Also see

• Asymptote of Reciprocal Spiral

• Results about the reciprocal spiral can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): hyperbolic spiral
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): spiral: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): reciprocal spiral
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): spiral
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): reciprocal spiral
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): spiral
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): hyperbolic spiral