Logarithmic spiral

A logarithmic spiral, equiangular spiral, or growth spiral is a <a href="/facts/Self-similarity/9Nvo7edY">self-similar</a> <a href="/facts/Spiral/4R331aba">spiral</a> <a href="/facts/Curve/xBQ0pTBW">curve</a> that often appears in nature. The first to describe a logarithmic <a href="/facts/Spiral/4R331aba">spiral</a> was <a href="/facts/Albrecht_D%25C3%25BCrer/N38jX769">Albrecht Dürer</a> (1525) who called it an "eternal line" ("ewige Linie"). More than a century later, the curve was discussed by <a href="/facts/Ren%25C3%25A9_Descartes/ohqj6DMf">Descartes</a> (1638), and later extensively investigated by <a href="/facts/Jacob_Bernoulli/rUnwozsy">Jacob Bernoulli</a>, who called it Spira mirabilis, "the marvelous spiral". 
The logarithmic spiral is distinct from the <a href="/facts/Archimedean_spiral/wCW7WuyI">Archimedean spiral</a> in that the distances between the turnings of a logarithmic spiral increase in a <a href="/facts/Geometric_progression/SVrkRHDX">geometric progression</a>, whereas for an Archimedean spiral these distances are constant.

Logarithmic spiral open-in-new

Logarithmic spiral