Page:Popular Science Monthly Volume 90.djvu/139

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Puzzling Tricks with Paper

If you would like to indulge in some mental gymnastics, just try this with a slip of paper

��A RECTANGULAR piece of paper has two faces or surfaces and four edges. Can you fold such a piece, say I in. wide and 12 in. long, so that it will have only one surface and one edge? At first thought it seems to be an impossibility. Yet the solution of the problem is easy and leads up to

��Take a second strip of paper, place it fiat on the table, give one end a half turn and paste the two ends together. A twisted ring or band will be the result. How many surfaces has it? Begin at some marked point and follow the surface. Soon you will return to the starting point, having gone over the

���Various ways of cutting and pasting up a piece of paper to reduce the num- ber of surfaces and edges and to form links of a chain fastened together

��an interesting and fascinating study of paper folding and cutting.

As a preliminary exercise overlap the tvvo ends of a strip of paper and paste them together to form a cylindrical surface similar to a napkin ring. It has two surfaces now, an inner and an outer, but only two edges in place of four as in the first place. If the ring be cut in two pieces, lengthwise of the paper, two narrow and similar rings will be formed, each having the same circum- ference as the original.

��entire surface. It has but one surface. In a similar manner trace your way around the edge, and you will be astonished to find that it has one continuous edge. The problem is solved. Experiment with this twisted ring still further and see what remarkable results you can obtain. With a pair of scissors cut this ring in two parts as you did the plain ring, and, astonishing to relate, the result will be not two rings but, instead, one ring having twice the circumference of the original. From

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