Editing Logarithmic spiral (section)

{{short description|Self-similar growth curve}}
{{Redirect|Spira mirabilis|the orchestra|Spira Mirabilis (orchestra)|the Italian film|Spira Mirabilis (film)}}
[[Image:Logarithmic Spiral Pylab.svg|thumb|Logarithmic spiral ([[Pitch angle of a spiral|pitch]] 10°)]]
[[File:Mandel zoom 04 seehorse tail.jpg|thumb|upright=0.6|A section of the [[Mandelbrot set]] following a logarithmic spiral]]

A '''logarithmic spiral''', '''equiangular spiral''', or '''growth spiral''' is a [[self-similarity|self-similar]] [[spiral]] [[curve]] that often appears in nature. The first to describe a logarithmic [[spiral]] was [[Albrecht Dürer]] (1525) who called it an "eternal line" ("ewige Linie").<ref>{{cite book | title = Underweysung der Messung, mit dem Zirckel und Richtscheyt, in Linien, Ebenen unnd gantzen corporen | author = Albrecht Dürer | year = 1525 | url = https://digital.slub-dresden.de/werkansicht/dlf/17139/1/0/ }}</ref><ref>{{cite book
 | last = Hammer | first = Øyvind
 | contribution = Dürer's dirty secret
 | doi = 10.1007/978-3-319-47373-4_41
 | pages = 173–175
 | publisher = Springer International Publishing
 | title = The Perfect Shape: Spiral Stories
 | year = 2016| isbn = 978-3-319-47372-7
 }}</ref> More than a century later, the curve was discussed by [[René Descartes|Descartes]] (1638), and later extensively investigated by [[Jacob Bernoulli]], who called it ''Spira mirabilis'', "the marvelous spiral". 

The logarithmic spiral is distinct from the [[Archimedean spiral]] in that the distances between the turnings of a logarithmic spiral increase in a [[geometric progression]], whereas for an Archimedean spiral these distances are constant.