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Magic
Triangles, or the Area Paradox


by
Gianni A. Sarcone



"La
sapienza è figliola della sperienza. Fuggi i precetti
di quelli speculatori, che le loro ragioni non son confermate
dalla isperienza"
Leonardo
da Vinci


Pages:
 1  2  3 
Cut
out a square of 12 units per side into 8 triangular pieces,
as shown below (fig.1). We can rearrange these 8 right triangles
together to form some square variants. Further below you
will find 4 possible configurations. The first configuration
is a real square (fig. 2.a); the second one (fig. 2.b), though
it seems to be a square is not a square at all! Can you say
why this is so? The last examples (fig. 2.c and 2.d) are
squares but with extra protruding triangular elements! Compare
them to the square of the fig. 2.a). What is wrong? 
fig.1
The
8 triangles of the Circea's Puzzle
The
4 possible configurations
(This
8piece puzzle, called Circea's puzzle and created
by G. Sarcone, is copyrighted: © 19922007)

solution +
more exciting vanishing area paradoxes 


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