Re: [ATM] Off-Topic: String Theory

[David Weinshenker <daze39@earthlink.net>]

Jim Burrows wrote:
> 
> At 2007-09-09 16:36 -0700, Richard Schwartz wrote:
> 
> >My friend George has a problem.   He plans to build a hinged frame
> >A-B-C-D with diagonals AC and BD. The sides will be one meter.
> >Obviously the frame will be  "floppy" and will not hold its desired
> >square shape.   To stabilize the frame, George plans to run a single
> >string A-C-B-D, anchored at A and D, and with frictionless slides at B
> >and C so that all of the wire is under the same tension.
> >
> >George thinks this is a great idea because all you have to do to
> >stiffen the whole frame is use a single tensioner like a guitar head.
> >There is no need to mess with separate tensioners for separate
> >strings.
> 
> A neat problem (should be part of the SAT math test <g>).  Turns out
> the square is unstable!  The length of string with the square square
> (the second one is an adjective) is 2*sqrt(2) + 1.  If the square
> goes out of square by a small angle, whose sine we'll call s, by
> expanding the square roots in a power series, it turns out the length
> shortens by sqr(s)/sqrt(8), so the slightest nudge on the square will
> make it collapse, even faster if the string is a rubber band.

So an interesting question would then be whether there are any shapes that 
would work... what we need is a 3-d cable-braced strut assembly that 
stiffens when one last crosswise string is connected and tensioned, 
but goes floppy and folds conveniently when that one is loosened...
bonus points if a fabric web can serve also as part of a light shroud.
Is there anything in the structure of tents, sails, etc. that might apply?

I don't have any specific solutions to offer, but I highly admire the
problem!

-dave w
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