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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