## Monday, April 03, 2006

### Puzzling paper folding

Here's a nifty mathematical puzzle, which you can solve either by building it with paper, or by writing a computer program to work out the solution. (I discovered this puzzle over at Wolfram's MathWorld, a site a highly recommend.)

Take a piece of paper, 8 inches long, by two inches wide. Fold it into four squares, each 2 inches by two inches. Now, fold each square along both of its diagonals so that all of the diagonals of the squares are scored. Connect the two ends, so that you have a tube:

It's possible to turn the tube inside out, only folding along the scored lines.

Solution when I figure it out :-)

• Rot13 for spoilers:

Sbyq gur evat syng vagb n erpgnatyr.

Sbyq gjb pbearef hc ba gur fnzr fvqr bs gur erpgnatyr gb sbez n gevnatyr.

Chyy bhg gur zvqqyr sync bs gur gevnatyr. Guvf vaibyirf fbzr 3q znavchyngvba ohg pna or qbar hfvat bayl gur tvira sbyqf.

Lbh fubhyq abj or va n fgngr jurer vg'f sbyqrq vagb n fdhner, jvgu bar fvqr bs gur cncre sbezvat n cbpxrg ba bar fvqr bs gur fdhner naq gur bgure fvqr bs gur cncre sbezvat n cbpxrg ba gur bgure fvqr bs gur fdhner. Vg'f flzzrgevp jvgu erfcrpg gb erirefnyf bs fvqrf bs cncre...

Erirefr gur fgrcf nobir: chg gur bccbfvgr sync vagb vgf cbpxrg naq hasbyq.

By  D. Eppstein, at 10:34 PM

• This is hard, all I've got so far is a mildly mangled version of the thing I started with. I'll have to work on it tommorow when I'm not as sleepy

By  Tiax, at 2:14 AM

• I've had this migraine for there days, and eppstein's response looked like plain English there four a minute, oy

looks like a fun puzzle; 'Ill second tiax & save it for a nothere day

By  andrea, at 7:14 PM

• If you want to do this by physical manipulation (personally, I think writing a computer program to solve it is more interesting) I'd suggest reinforcing your creases with tape, or better, cutting out triangles of cardstock and fastening them together with Duck tape.
--
Dave Empey (dempey at cruzio dot com)

By  Anonymous, at 1:35 PM

• This is the same design that is used as a stenth to reinforce veins internally. A whole sheet (several parallel strips) of the suitable material is rolled into a pipe and folded down to a smaller "rod". It then is inserted into the vein through a small hole, and expanded in place to form a prosthetic tubular internal wall.

By  Anonymous, at 6:22 PM