A present arrives topped with a 3 dimensional mechanical doughnut made from cardboard. It’s sort of a gear which continuously folds into itself. Open a flap and discover the words: “To Sara, Merry Christmas”.

Actually, the story of this chapter occurs many years before, when I was young, attending my first year of college as a freshman of engineering. My girlfriend at that time very much enjoyed all puzzles of all variation. (Or maybe, out of courtesy, she humored with great disguise, my wonderful love for puzzles). More than puzzles, Sara enjoyed optical illusions. She was the one who introduced me to the art of Echer and his endless Mobius Strip. Sara, that year, was the perfect victim for “The Mad Wrapper!”

The challenge here was more mine than hers. My goal that year was to put into her hands a three dimensional optical illusion. I suppose I could have composed my message onto a simple-to-construct Mobius Strip (something I was guilty of doing in another year). She would have appreciated this but I wanted to give her more than this. Triangles attached into a snake loop twist inside out around and around.

The diagram below gives a cutout pattern which you can use to make the loop. Simply print the figure and resize it to your desired size, with scissors, cut out the pattern. Standard printer paper should work fine for most situations but some people may decide to retrace the paper onto thin cardboard or a stiffer paper. Once cut, fold all the edges along the lines as shown and glue the tabs into place until it looks like the picture given below. I wrote my message blah blah. You don’t need to write a message if you want to simply use it as a toy.

(Sorry, I seem to have lost the pictures.  If I find them I will post them.)

– Snake Loop Picture: 2d cutout –

 

– Snake Loop Picture: 3d finished –

 

An alternative: put your message on the outside so it is read as the “doughnut” twists within itself.