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Puzzle crafting & workshops • Laboratorio di giochi d'ingegno • Atelier de puzzles
by Gianni A. Sarcone & Marie-Jo Waeber
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The Puzzle
Tangramagic title

  Puzzles with ‘vanish’ effects are a curious branch of geometric pattern puzzles (mechanical puzzles) which is useful for hands-on teaching purposes and as math-thinking motivator. A “vanish puzzle” is actually an optical illusion that can be used in mathematics classes to help students reason about geometrical figures. When the pieces of a vanish puzzle are rearranged, part of the original area seems to disappear, even though the outline of the puzzle shape remains apparently the same! For instance, you may form with the same pieces of a vanish puzzle a square both with and without a 1x1 hole in it (cf. 'Ghost hole').
  The game inventor, G. Sarcone, found that with a humble puzzle like the Tangram, it is possible to make geometrical miracles if 2 L-shaped pieces are added to it: in fact, 1 set of Tangram puzzle combined with these 2 L-shaped pieces form together a rectangle. But with these two extra pieces, it is possible, by rearranging the puzzle pieces, to recompose the initial rectangular configuration with 1 piece missing! (see below)

Vanishing area paradox
tangramagic beforeRemove the pieces from the frame, then replace them without the small square to fill the rectangular frame again without gaps!

Réarrangez les pièces du jeu dans l’espace rectangulaire en omettant la pièce carrée, et sans laisser d’espace vide!

Riordina i pezzi del puzzle nel contenitore rettangolare omettendo il pezzo quadrato, e senza lasciare spazi lacunari!



tangramagic afterThe dimensions of the puzzle seem the same - take a ruler and see for yourself! - Could you explain why this is so?

Les dimensions du puzzle semblent les mêmes, mesurez-les avant et après… Sauriez-vous expliquer pourquoi?

Stranamente, le dimensioni del rompicapo sembrano le stesse, con o senza quadratino! Sapresti spiegare perché?

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The Challenges
arrow Build your own TangraMagic
arrow Form figures both with and without a mystifying triangle!
arrow More brain teasing challenges
TangraMagic puzzle articles
arrow Where can I get the puzzle?
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Archimedes journal ARCHIMEDES journal is an interactive review devoted to entertaining & involving the readers with puzzles, recreational mathematics and visual creativity. This journal is published for an audience without a specific math background. Each issue covers a broad range of mental and hands-on activities for the reader to enjoy! Workshop image "How to focus attention? Encourage creative exploration?" Multicultural interactive puzzle activities & workshops for museums and institutions.
Related links
arrow A large selection of puzzles books.
arrow Puzzles for publishers and editors.

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A range of
puzzles for
you to make!

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tangramagic foam
Obtain your TangraMagic puzzle here!
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Large 3D TangraMagic puzzle ideal for exhibitions, classrooms and training classes...
Marie-Jo playing king size tangram
TangraMagic booklet gives designs for making your own TangraMagic puzzle...
Tangram book

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tangram figure
Visit our official Tangram website!

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