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Magic
Triangles, or the Area Paradox (solutions 2)


by
Gianni A. Sarcone


Pages:  1  2  3 
Reassembling triangular puzzle
pieces, induces always to paradoxical conclusions. The squares
of the fig. 2.c) and 2.d) have extra triangular elements. Is
then their area larger than the one in the fig. 2.a)? As before,
we have to consider the angles of each right triangle which
form these squares. By doing that, we will easily notice that
the hypotenuse slopes of the small and of the large right triangles
are slightly different (a difference of approx. 0.8 degrees,
visually unnoticeable). So, the 8 right triangles do not form
exactly a square and the sum of all these tiny fitting errors
(grey zones in the fig. 5) is equal to the area of the protruding
triangular elements. In short, space apparition is only illusion!
Paradoxical
missing square puzzle
(called 'FehlendesQuadratPuzzle', in German;
and 'wigparadox', in Dutch)
We can even enhance the 'vanishing
area paradox' effect by adding 4 squares of
6 units per side to the Circea's puzzle. When you rearrange the
puzzle pieces a square space appears or disappears (see examples
below).
Both
squares are formed with exactly the same 12 pieces.
The second one, however, needs an extra piece!
For
classrooms and amateur magicians
Our puzzles Quadrix and Geometrex are
based on the above vanishing area principle:
when several pieces of the puzzles are permuted, a small
square hole magically appears...
You can purchase these handson games, useful for classroom
demonstrations or for magic closeup shows, online.
A
lot of well known magic tricks, such as the Winston
Freer Tile Puzzle or the Paul Curry's
Geometrical Paradox, are inspired by these basic
vanishing principles.
For
manufacturers or publishers
We are presently actively looking for manufacturers or
publishers interested to produce and market the vanish Quadrix magic
vanish puzzle under licence for specific countries on exclusive
or nonexclusive basis. Please contact
us if interested for details.

Back
to page 2
More vanish puzzles here


© 19922007 G.
Sarcone, www.archimedeslab.org
You can reuse content from Archimedes’ Lab on the ONLY condition
that you provide credit to the authors (© G.
Sarcone and/or M.J.
Waeber) and a link back to our site. You CANNOT reproduce the
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