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

  1. Dec 25, 2011 #1
    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:

    Anyone happens to know, what it is?

    Much obliged,
  2. jcsd
  3. Dec 25, 2011 #2


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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.
  4. Dec 25, 2011 #3
  5. Dec 25, 2011 #4


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  6. Dec 25, 2011 #5


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  7. Dec 26, 2011 #6
    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:
    This guy makes it look even cooler on a tie, than as a tattoo...
  8. Dec 26, 2011 #7


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    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.

    Last edited: Dec 26, 2011
  9. Dec 26, 2011 #8
    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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