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'Carpenters Ruler' Problem Solved

Posted by timothy on from the what-about-the-twisted-knot-of-my-soul? dept.

An unnamed correspondent writes: "Three mathematicians just solved the 'carpenters ruler' problem. The carpenters ruler problem is given a chain of linked rods (a carpenters ruler) in two dimensions, can it always be unwound? As it turns out, it can, check here. You might be saying 'so what', but this has potential applications in anything from protein folding to robotic arm movement. Check here for some animations of the carpenters rule in action."

4 of 80 comments (clear)

  1. Answer: Surprisingly simple. by rjh · · Score: 5

    It just so happens that I have a paper napkin right here at my desk, leftover from lunch. I put it down on my desk: lo and behold, it's a plane.

    I then unfolded the paper napkin--and keep in mind that unfolding is really just folding in reverse. Lo and behold, it was four layers of thin paper atop each other; unfolded, it had a substantially larger perimeter.

    So the simple answer: unfold the damn napkin. :)

    (Extra credit will be given to those who figure out a way to increase the perimeter of an already unfolded napkin!)

  2. Carpenter's Crack by sean@thingsihate.org · · Score: 5

    Now if they can only do something about carpenter's crack (also applicable to plumbers).

    I swear, I've gone through so many quarters that way.

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    One of the many things I hate. thingsihate.org
  3. Oh, yeah? by cra · · Score: 5

    Unlike a two-dimensional chain, this knotted, three-dimensional "knitting needle" chain in space can't be untangled.

    Really? So how was it tangled in the first place, then . . . ;-)


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  4. fun problem in the same vein by e_lehman · · Score: 5

    Here's a vaguely-related problem that is fun to contemplate over dinner. You've got a square napkin. You can fold it however you want provided that the resulting shape lies in a plane. For example, you could fold a corner over, which reduces the perimeter, and then fold a "sub-corner" back (as students do with homeworks when they don't have a stapler. :-) ), which increases the perimeter again. The question is, can the perimeter of the shape you form by folding ever exceed the perimeter of the original napkin?

    The answer turns out to be... Oh! Look at the time! Gotta get going! :-)