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eureka!!!
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From the same authors of the article
Sarcone and Waeber
Big Book of Optical Illusions
Big Book of Optical Illusions, ISBN 0764135201
New Optical Illusions
New Optical Illusions, ISBN 1844423271
Fantastic Optical Illusions
Fantastic Optical Illusions, ISBN 184442295X
Dazzling Optical Illusions
Puzzillusions, ISBN 1844420647
MateMagica book
MateMagica, ISBN 8889197560
Almanach book
L'Almanach du mathématicien en herbe, ISBN 2844690254

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TangraMagic: the 'Paradoxical' Tangram

 
by Gianni A. Sarcone

Tangram logo



"In any quest for magic, in any search for sorcery, witchery, legedermain, first check the human heart"
Rod Serling


Puzzles with vanishing effects are a curious branch of geometry which are useful for hands-on teaching purposes and as math-thinking motivators. With a humble puzzle like the Tangram, the 7-piece 'chinese' puzzle, we can make geometrical miracle if we add to it 2 L-shaped pieces as shown below (fig. 1). By rearranging the puzzle pieces, you have to recompose the initial rectangular puzzle with 1 piece missing!
tangram making
Source: Big Book of Optical Illusions, Sarcone & Waeber, 2005

Take a Tangram puzzle (if you haven't one, cut the puzzle out of a chipboard sheet according to the diagram above with grey background, fig.1) and form with these 7 pieces the black figures below. Then, form their white counterparts. In both cases, you have to use all 7 pieces! Explain why a small triangular element is missing in the black figures.

tangram shapes
©1996 Gianni A. Sarcone
Source: Almanacco del Matematico, G. Sarcone, 2001

TangraMagic (Foam)
Tangramagic Foam
TangraMagic (Forex®)
Tangramagic Forex

Tangramagic Puzzle
Is an innovative version of the famous Tangram puzzle. First, the issue is to recompose the rectangular puzzle with 1 piece missing, then, to make an element of an assembled figure disappear (or appear). There are two puzzle models available: TangraMagic Foam and TangraMagic Forex® (hard plastic).
Price: $6.50 (T foam) | $13.00 (T forex) | Age: 8 +

1-click ordering (multiple ordering form here)
Select your TangraMagic puzzle(s): Foam Forex
...and buy now from

Tangram logo

The Tangram puzzle is said to come from China 200 years ago. Actually, its origin is uncertain. In Chinese, the Tangram puzzle is named "qi qiao ban" (pron. Ch'ee Ch'yao Pann) or "qi qiao tu", and even "yi zhi tu"... A lot of names for such a humble game!

qi qiao pan sinogram
tangram in Chinese

Visit our
Tangram
website!
tangram puzzle

Early tangram book
 Early book of the Tangram puzzle published around the XIX century
(other early book references)
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