Impossible Folding Puzzles and Other Mathematical Paradoxes by Gianni A. Sarcone & Marie-Jo Waeber

Author:Gianni A. Sarcone & Marie-Jo Waeber
Language: eng
Format: epub, mobi
Publisher: Dover Publications, Inc.
Published: 2013-02-21T16:00:00+00:00

Fig. 1

Fig. 2

Fig. 3

Any topologist, origami expert, or high school geometry teacher will tell you that cutting an interlaced strip of paper that forms a perfect trefoil knot from a flat single piece of paper is physically impossible, and has been known to be so for centuries. Yet, with this trick you can prove the contrary! Another way to form a trefoil in a piece of paper is to cut a ‘paradromic ring’ with three half-twist lengthwise (see “Paradromic rings” on page 29).

Reproduce the pattern in Fig. 1 on page 49 exactly on two A3-format color paper sheets. Then cut 6 slits with a utility knife into one of the paper sheets according to the red cut lines shown in Fig. 2. Turn the paper sheet over and lay it on a light table (or on a window pane) in order to see the outlines of the pattern on the back and carefully attach three paper patches of the same color as the sheet, as shown in Fig. 3. The patches are just elongated parallelograms of paper having the same width as the inner and outer borders of the triangles. As you can see, they must be placed perpendicularly to the cut lines. Make sure that the glue spots at the both ends of the patches don’t overlap the cut lines (slits). Let the glue dry and score the dotted lines of both color paper sheets. Fold and unfold them several times along the creases. You are now ready to perform this topological trick with a surprise ending for your friends and family!

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