Re: [ATM] Off-Topic: String Theory

[Jim Burrows <burrjaw@earthlink.net>]

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.

         -- Jim Burrows
         -- http://home.earthlink.net/~burrjaw
         -- mailto:burrjaw@earthlink.net
         -- Seattle N47.4723 W122.3662 (WGS84)


_______________________________________________
ATM mailing list http://www.atmlist.net/