Author Topic: " It's not "math".... It's all cutting "  (Read 3248 times)

X1

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" It's not "math".... It's all cutting "
« on: February 05, 2013, 05:50:21 AM »
It's not "math"....  It's all cutting.

     :) :) :)
    How one can "cut" , with "scissors", a "pretzel" ...  :)   
   
   THE NON-COMMUTATIVE A-POLYNOMIAL OF (−2, 3, n) PRETZEL KNOTS
   Stavros Garoufalidis, Christoph Koutschan

  We study q-holonomic sequences that arise as the colored Jones polynomial of knots in 3-space.
  The minimal-order recurrence for such a sequence is called the (non-commutative) A-polynomial of a knot.
  Using the method of guessing, we obtain this polynomial explicitly for the Kp = (−2, 3, 3+2p) pretzel knots for p = −5, . . . , 5. This is a particularly interesting family since the pairs (Kp,−K−p) are geometrically similar (in particular, scissors congruent) with similar character varieties. Our computation of the non-commutative A-polynomial (a) complements the computation of the A-polynomial of the pretzel knots done by the first author and Mattman, (b) supports the AJ Conjecture for knots with reducible A-polynomial and (c) numerically computes the Kashaev invariant of pretzel knots in linear time. In a later publication, we will use the numerical computation of the Kashaev invariant to numerically verify the Volume Conjecture for the above mentioned pretzel knots.


   (arXiv:1101.2844v4 [math.GT] 11 Sep 2012)
http://arxiv.org/abs/1101.2844
https://docs.google.com/viewer?a=v&q=cache:GjMtvT6vEjwJ:arxiv.org/pdf/1101.2844+%22jones+polynomial%22+trefoil+knot+2012&hl=en&gl=uk&pid=bl&srcid=ADGEESiqyuw6M_oagu6mh5rAA5jIDBbqLCNlre7Y-YuG5SWtS1MiQQv4_tNI2E8QUzMuwEURLa-so-2TLUM9B0OPt64KO8uckDpP1dJs769Q7OGf28TgMyQO3AgM20eXfgIR7S4P7j7R&sig=AHIEtbSnplhJAgDXS60LebuWhUjPXwPN7Q

   To play with torus knots, a nice Java applet :
   http://www.javaview.de/vgp/tutor/torusknot/PaTorusKnot.html
   
   Keizo Ushio s Art, and Knots :
   https://docs.google.com/viewer?a=v&q=cache:2xHasNy-4UEJ:www.maths.ed.ac.uk/~aar/papers/keizo.pdf+Keiao+Ushio+sculptures+split+tori&hl=en&gl=uk&pid=bl&srcid=ADGEESgVj8pC-HPceLGSYCq1Py-BzyKOMhJczssDx8WiGWLHqecnP8EdjI7oFgfq6Q8Yn6yvGcJuI7ycYip0seCDdNoHI-GqYkQoAYKDHSrsVTeek_z3fcPsw_ZFXO0QkbfFbCHA0b7_&sig=AHIEtbT96rHHjCPHU9AvgM2XWc0mybd8uQ

   http://www.flickr.com/photos/m487396/2054796432/sizes/z/in/photostream/
« Last Edit: February 05, 2013, 06:25:58 AM by X1 »


X1

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Re: " It's not "math".... It's all cutting "
« Reply #2 on: February 05, 2013, 06:22:16 PM »
" ...using recycled copper coaxial cable to form part of a corset."
She uses the kern, the mantle, or both ?
 :)


struktor

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