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
Remove
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!
The
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?
Solution
The
Tangram portion of the fig. B below occupies a
space slightly less than the apparent 5 x 10 dimensions.
Its real area is in fact 4.95 x 9.9 units. The
discrepancy in the apparent vs. actual area is
1 square unit.
Dans
la fig. B, le Tangram semble occuper un espace
de 5 x 10 unités. En fait, il n’occupe
que 4,95 x 9,9 unités, c’est-à-dire
49 unités carrées. Cela ne se
voit pas à l’oeil nu, mais grâce
au calcul!
Il
rettangolo composto con i 7 pezzi del Tangram
in B sembra occupare uno spazio di 5 x 10; in
realtà, occupa uno spazio di 4,95 x 9,9
unità, cioè di 49 unità quadre.
A occhio, le differenze non si notano, bisogna
calcolarle!
You
will find more information and resources in the
booklet TangraMagic... Vous trouverez davantage d'informations
utiles dans le livret TangraMagic...
Troverai maggiori informazioni nel libretto TangraMagic...
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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!
"How
to focus attention? Encourage creative exploration?" Multicultural
interactive puzzle
activities & workshops for museums
and institutions.
Obtain
your TangraMagic puzzle here! Large 3DTangraMagic puzzle
ideal for exhibitions, classrooms and training classes... TangraMagic
booklet gives designs for making
your own TangraMagic puzzle...