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Note: I intentionally left the equation in the title in plain text instead of MathJax, so it is searchable.

Here is a spiral's equation in polar coordinates: $$\theta=L/r,$$ and in Cartesian coordinates: $$(x,y) = \left(r\cdot\cos\frac Lr,\, r\cdot\sin\frac Lr\right)$$ for $0 < r < \infty$ and some positive constant $L$.

It appeared here, at Math SE, as an answer to the Spiral equation question.

Does this curve have a name?

CiaPan
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    It is called an hyperbolic spiral. https://www.google.com/search?q=hyperbolic+spiral&sxsrf=ALeKk00i2NlA9X96PVCVcSsfIcwoZ9hOzg:1595490525924&source=lnms&tbm=isch&sa=X&ved=2ahUKEwin1aiw8eLqAhUOC-wKHZomALcQ_AUoAXoECBIQAw&biw=1920&bih=969 –  Jul 23 '20 at 07:49
  • @YvesDaoust Quick and precise. Thank you. :) I'd like you like to post it as an answer, so I can put a green tick on it. – CiaPan Jul 23 '20 at 07:54
  • @CiaPan You can also answer your own question and accept it. – Paul Frost Jul 23 '20 at 07:57
  • @PaulFrost Sure I can But I like to give a green tick to someone. Or is this question too simple for anybody to care...? :) – CiaPan Jul 23 '20 at 08:08
  • ...and ticked. :) – CiaPan Jul 23 '20 at 08:08
  • More generaly it is member of the family of so-called "archimedean spirals" (http://xahlee.info/SpecialPlaneCurves_dir/ArchimedeanSpiral_dir/archimedeanSpiral.html). – Jean Marie Jul 23 '20 at 08:13
  • Thanks for the proposal, I am not after ticks and Henry did the job. –  Jul 23 '20 at 08:13
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    @CiaPan Sometimes people do not have the time to give an official answer and simply write a short comment which nevertheless answers the question. And frequently that is all what is happening - the question is de facto answered, but it is not visible at first glance and the question remains forever in the "unanswered queue". Therefore I recommend to wait some time for an official answer. If you get one (as in the present case), it is okay. Otherwise answer your own question. – Paul Frost Jul 23 '20 at 08:19
  • @PaulFrost Thank you. I often comment, sometimes answer, almost never ask at StackExchange, so I have no big practice in answering my own questions – although there was one exception :) – CiaPan Jul 23 '20 at 08:25

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As @YvesDaoust said in a comment it is called a hyperbolic spiral, or a reciproke spiral as the circle inversion of an Archimedean spiral

Wikipedia has a couple of images, depending on whether you look at one or two arms of the hyperbola underlying $r=\frac a \varphi$

enter image description here

enter image description here

Henry
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  • May I ask you which (excellent !) drawing software you use ? – Jean Marie Jul 23 '20 at 08:14
  • @JeanMarie As Henry points out int he second paragraph, those are images from Wikipedia. More precisely, from Wikimedia Commons repository, Link1, Link2. You'd have to ask their author, a Wikipedian Ag2gaeh about a software. They seem to work mainly in German Wikipedia, here is a link to the user's talk page at German, and here at English Wikipedia.. – CiaPan Jul 23 '20 at 08:22
  • @CiaPan Thanks. I should have read more properly what Henry said. – Jean Marie Jul 23 '20 at 08:28