crafting & workshops • Laboratorio di giochi d'ingegno • Atelier
by Gianni A. Sarcone & Marie-Jo Waeber
game may have been given to Leonardo Pisano (Fibonacci)
by Chandlahuri his Indian servant when he was living
in Bougie (Algery) with his father. Leonardo renamed
this puzzle afterwards: "lo joco enimmatico del
brachiale torquato" (medieval italian, = the
puzzle of the twisted bracelet). Torquato puzzle
was inspired from the Chinese rings puzzle.
puzzle consists in 3 parts: 1 paper braid and a string
with 2 square cardboard pieces (one of them having a
hole in the middle).
To make your own Torquato puzzle, download first the PDF
file containing the 2 models shown below...
download, just click on the small PDF icon >>> )
the string from the puzzle without folding or tearing
up the square cardboard pieces or the braided paper puzzle...
Once you've freed the string, try to assemble the puzzle
a topological puzzle
is the study of geometric properties that are preserved
under deformation. Sometimes topology is referred to
as “rubber sheet geometry”, because it does
not distinguish between a circle and a square (a circle
made out of a rubber band can be stretched into a square)
but does distinguish between a circle and a figure eight
(you cannot stretch a figure eight into a circle without
Topology deals with the ways that surfaces can be twisted,
bent, pulled, or otherwise deformed from one shape to another
(without tearings!). A topologist is interested in the
properties that remain unchanged after all these transformations
have taken place. Topologically speaking there is no difference
between a doughnut and a coffee cup (see drawing below),
since either one can be deformed into the shape of the
other. Many string and wire puzzles, like Torquato puzzle,
are based on topological principles. Understanding a few
basic principles will help you analyze and solve these
is made of a ‘closed loop’ (the braid) interlaced
with an ‘open loop’ (the string), having
at one end a ‘locking loop’ (the cardboard
piece with the hole) and at the other end an ‘end
loop’ (the other cardboard piece). Since we can
free the string from the braid bracelet we can consider
the ‘closed’ and ‘open’ loops
as two unlinked rings.
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!