If this is not a Bernoulli spiral, what is it then?

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    Bernoulli Spiral
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Discussion Overview

The discussion revolves around identifying a specific spiral design seen on a tie, which the original poster, Arthur, believes does not resemble a Bernoulli spiral. Participants explore various possibilities for the spiral's identity, including geometric and mathematical spirals, while sharing links and personal insights.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Arthur describes a spiral design on a tie that he believes is not a Bernoulli spiral and seeks help in identifying it.
  • Some participants suggest it could be a Golden spiral, referencing a Wikipedia article.
  • Another participant proposes it might be an Equiangular spiral, providing a link for further exploration.
  • Arthur expresses doubt about the Golden and Equiangular spirals, noting the steepness of the slope in the design compared to these spirals.
  • One participant suggests it resembles an Archimedean spiral, providing a mathematical description and a link to a relevant article.
  • Another participant agrees that the design looks more like an Archimedean spiral, noting its starting point at the pole, which differentiates it from the Equiangular spiral.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the identity of the spiral. Multiple competing views are presented, with suggestions including the Golden spiral, Equiangular spiral, and Archimedean spiral, each with varying degrees of support and skepticism.

Contextual Notes

Participants express uncertainty regarding the accuracy of the embroidery and the implications it has on identifying the spiral. There are also references to the visual characteristics of the spirals that may not align perfectly with the design on the tie.

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I met this old nerd wearing a tie with a certain spiral, which does not look like a Bernoulli spiral to me. He actually told me, what it was, but I seem to have lost the note and time made me forget it. I wouldn´t be able to describe properly, so I have a photograph of the tie on my flickr:
http://flic.kr/p/b1Dt6P

Anyone happens to know, what it is?

Much obliged,
Arthur
 
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Welcome to PF, Arthur. I'm afraid that I can't help you out on this.
It's a damned cool design, though. If it turns out to mean something that I like, I wouldn't mind getting it as a tatoo.
 
Thanks for the comments! I just don´t really think it´s the Golden or Equiangular Spiral as the angle to the rightmost slope to the x-axis seems a bit too steep for it to truly match.
Sure, it´s an embroidery and geometric accuracy cannot be fully expected, but I remember the guy telling another story and one could embroider the equiangular spiral much more clear!
So I´m still thankful for more suggestions.
By the way, here is the guy, who came with it:
http://flic.kr/p/b1DsCc
This guy makes it look even cooler on a tie, than as a tattoo...
 
Looks like spiral of Archimedes, in polar coordinates:

r = a θ , θ starting at 0

but the logo appears rotated left 90°, which would be:

r = a (θ - π/2), θ starting at π/2

For the rotated image, imagine rotating the image from the wiki article 90° to the left (tilt your head 90° to the right) and note the first 360° of the spiral would look like the logo. Link to the wiki artilcle.

http://en.wikipedia.org/wiki/Archimedean_spiral
 
Last edited:
It really does look more like the archimedean spiral, than any other. In all drawings I found, the archimedean spiral starts at the pole, while the equiangular spiral never reaches the pole. In the logo on the tie, the spiral quite clearly starts at 0.
Thanks a lot rcgldr and the other for help!

Happy New Year!
 

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