Logarithmic spiral

A logarithmic spiral, equiangular spiral or growth spiral is a self-similar spiral curve which often appears in nature. The logarithmic spiral was first described by Descartes and later extensively investigated by Jacob Bernoulli, who called it Spira mirabilis, "the marvelous spiral".

In polar coordinates ${\displaystyle (r,\theta )}$ the logarithmic curve can be written as

or

with ${\displaystyle e}$ being the base of natural logarithms, and ${\displaystyle a}$ and ${\displaystyle b}$ being arbitrary positive real constants.

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