By Martin Gardner
"Gardner is usually the clown prince of technology. . . . His Mathematical video games column in Scientific American is without doubt one of the few bridges over C. P. Snow's recognized 'gulf of mutual incomprehension' that lies among the technical and literary cultures."—Time
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Additional resources for The Second Scientific American Book of Mathematical Puzzles and Diversions
Quantity the small squares on both sides of the strip a s indicated, fold either ends inward (8c) and subscribe to edges with a section of obvious tape ( eight d ) . Face 2 is now in f r o n t ; face 1 is in again. To flex the constitution, fold it again alongside the vertical middle line of face 2. Face 1 will fold into the flexagon's inside as face three flexes into view. FIG. eight . the right way to make a tri-tet~aflexagon. Stone and his pals weren't the 1st to find this attention-grabbing constitution; it's been used for hundreds of years as a double-action hinge. i've got on my table, for example, small photograph frames containing images. The frames 26 Tetrnflezagons a r e joined by means of tri-tetraflexagon hinges which enable the frames to flex ahead or backward with equivalent ease. a similar constitution is curious about numerous kid's toys, the main widely used of that's a series of flat wood or plastic blocks hinged including crossed tapes. If the toy is manipulated competently, one block turns out to tumble down the chain from best to backside. truly this can be a n optical phantasm created through the flexing of the tri-tetraflexagon hinges in serial order. The toy was once well known within the U. S. throughout the 1890's, while it was once referred to as Jacob's Ladder. ( an image and outline of the toy look in Albert A. Hopkins's Magic: degree Illusions and clinical Diversions, 1897. ) present versions promote lower than the exchange names Klik-Klak Blox and turn Flop Blocks. There are a t least six varieties of four-faced tetraflexagons, referred to as tetra-tetraflexagons. with the intention to make one is firstly an oblong piece of skinny cardboard governed into 12 squares. quantity the squares on either side a s depicted in determine nine (9a and 9b). minimize the rectangle alongside the damaged traces. S t a r t a s proven in 9a, then fold the 2 heart squares again and to the left. Fold again the column at the severe correct. the card may still now seem as proven in 9c. back fold again the column at the correct. the one sq. projecting at the left is now folded ahead and to the perfect. This brings all six of the "1" squares to front. Fasten jointly the perimeters of the 2 center squares with a section of obvious tape a s proven in 9d. you can find it an easy subject to flex faces 1, 2, and three into view, yet discovering face four may possibly take a section extra doing. evidently you need to now not tear the card. Higher-order tetraflexagons of this kind, in the event that they have a n even variety of faces, may be comprised of related oblong beginning styles; tetraflexagons with a wierd variety of faces demand styles analogous to the only used for the tri-tetraflexagon. truly rows of small squares are adequate for Tetraflexagons 27 d c F I G . nine. how one can make a tetra-tetraflexagon. making tetraflexagons of this kind, yet including one o r extra extra rows (which doesn't swap the fundamental constitution) makes the version more straightforward to govern. The tetra-tetraflexagon proven in determine nine has frequently been used a s a n advertisements novelty as the trouble of discovering its fourth face makes it a delightful puzzle.