# Definition:Logarithmic Spiral

## Definition

The logarithmic spiral is the locus of the equation expressed in Polar coordinates as:

$r = a e^{b \theta}$

## Also presented as

The logarithmic spiral can also be presented in the form:

$\map \ln {\dfrac r a} = \theta \cot b$

or:

$r = a e^{\theta \cot b}$

## Also known as

Other names for the logarithmic spiral include:

equiangular spiral
exponential spiral
logistic spiral

## Historical Note

The logarithmic spiral was investigated in some depth by Jacob Bernoulli.

He directed that on his death a logarithmic spiral would be engraved on his tombstone, with the motto Eadem mutata resurgo (Though changed I arise the same).