Translation and analysis of words by ChatGPT artificial intelligence
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What (who) is equiangular spiral - definition
![A section of the [[Mandelbrot set]] following a logarithmic spiral](https://commons.wikimedia.org/wiki/Special:FilePath/Mandel zoom 04 seehorse tail.jpg?width=200 "A section of the [[Mandelbrot set]] following a logarithmic spiral")
![Cutaway of a [[nautilus]] shell showing the chambers arranged in an approximately logarithmic spiral. The plotted spiral (dashed blue curve) is based on growth rate parameter <math>b = 0.1759</math>, resulting in a pitch of <math>\arctan b \approx 10^\circ</math>.](https://commons.wikimedia.org/wiki/Special:FilePath/Nautilus Cutaway with Logarithmic Spiral.png?width=200 "Cutaway of a [[nautilus]] shell showing the chambers arranged in an approximately logarithmic spiral. The plotted spiral (dashed blue curve) is based on growth rate parameter <math>b = 0.1759</math>, resulting in a pitch of <math>\arctan b \approx 10^\circ</math>.")
![Albulabahn]]](https://commons.wikimedia.org/wiki/Special:FilePath/Albulabahn01.jpg?width=200 "Albulabahn]]")
![Dduallt]] on the [[Ffestiniog Railway]], Wales.](https://commons.wikimedia.org/wiki/Special:FilePath/Dduallt spiral simkins.jpg?width=200 "Dduallt]] on the [[Ffestiniog Railway]], Wales.")
![Geumdae 2nd Tunnel in [[Jungang Line]], [[South Korea]]](https://commons.wikimedia.org/wiki/Special:FilePath/Jungang Line - Geumdae 2nd Tunnel 060606.JPG?width=200 "Geumdae 2nd Tunnel in [[Jungang Line]], [[South Korea]]")
![zig zag]] in [[Hisatsu Line]], Japan](https://commons.wikimedia.org/wiki/Special:FilePath/Okoba spiral and zig zag aerial photography 1976-001.jpg?width=200 "zig zag]] in [[Hisatsu Line]], Japan")
![1903 view of Riflesight Notch loop, near [[Rollins Pass]] in Colorado](https://commons.wikimedia.org/wiki/Special:FilePath/Riflesight Notch 1903.PNG?width=200 "1903 view of Riflesight Notch loop, near [[Rollins Pass]] in Colorado")
![Myanmar]]](https://commons.wikimedia.org/wiki/Special:FilePath/Taunggyi line, Myanmar (Burma).jpg?width=200 "Myanmar]]")
![[[Tehachapi Loop]], on the [[Union Pacific Railroad]], California, United States, viewed from the air.](https://commons.wikimedia.org/wiki/Special:FilePath/Tehachapi Loop USGS closeup.jpg?width=200 "[[Tehachapi Loop]], on the [[Union Pacific Railroad]], California, United States, viewed from the air.")
![Guanjiao Spiral on [[Qinghai–Tibet Railway]] at night, it was replaced by a 32-km long tunnel in 2014](https://commons.wikimedia.org/wiki/Special:FilePath/巡道工出品 photo by Xundaogong——关角B门 - panoramio.jpg?width=200 "Guanjiao Spiral on [[Qinghai–Tibet Railway]] at night, it was replaced by a 32-km long tunnel in 2014")
![Animation depicting evolution of a Cornu spiral with the tangential circle with the same radius of curvature as at its tip, also known as an [[osculating circle]].](https://commons.wikimedia.org/wiki/Special:FilePath/CornuSpiralAnimation.gif?width=200 "Animation depicting evolution of a Cornu spiral with the tangential circle with the same radius of curvature as at its tip, also known as an [[osculating circle]].")
![[[NGC 1300]] in [[infrared]] light.](https://commons.wikimedia.org/wiki/Special:FilePath/HAWK-I NGC 1300.jpg?width=200 "[[NGC 1300]] in [[infrared]] light.")
![Tuning-fork-style diagram of the [[Hubble sequence]]](https://commons.wikimedia.org/wiki/Special:FilePath/HubbleTuningFork.jpg?width=200 "Tuning-fork-style diagram of the [[Hubble sequence]]")
![Spiral galaxy [[NGC 1345]]](https://commons.wikimedia.org/wiki/Special:FilePath/NGC 1345 HST.jpg?width=200 "Spiral galaxy [[NGC 1345]]")
![The bright galaxy [[NGC 3810]] demonstrates classical spiral structure in this very detailed image from Hubble. Credit: ESA/Hubble and NASA.](https://commons.wikimedia.org/wiki/Special:FilePath/NGC 3810 (captured by the Hubble Space Telescope).jpg?width=200 "The bright galaxy [[NGC 3810]] demonstrates classical spiral structure in this very detailed image from Hubble. Credit: ESA/Hubble and NASA.")
![Spiral galaxy [[NGC 6384]] taken by [[Hubble Space Telescope]].](https://commons.wikimedia.org/wiki/Special:FilePath/NGC 6384 HST.jpg?width=200 "Spiral galaxy [[NGC 6384]] taken by [[Hubble Space Telescope]].")
![WISE]] data](https://commons.wikimedia.org/wiki/Special:FilePath/PIA19341-MilkyWayGalaxy-SpiralArmsData-WISE-20150603.jpg?width=200 "WISE]] data")
![[[Barred spiral galaxy]] [[UGC 12158]].](https://commons.wikimedia.org/wiki/Special:FilePath/UGC 12158.jpg?width=200 "[[Barred spiral galaxy]] [[UGC 12158]].")
Wikipedia
A logarithmic spiral, equiangular spiral, or growth spiral is a 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"). More than a century later, the curve was discussed by Descartes (1638), and later extensively investigated by Jacob Bernoulli, who called it Spira mirabilis, "the marvelous spiral".
The logarithmic spiral can be distinguished from the Archimedean spiral by the fact that the distances between the turnings of a logarithmic spiral increase in geometric progression, while in an Archimedean spiral these distances are constant.
