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is also called: chinese puzzle - gioco cinese,
or rompicapo cinese (it) - casse-tête
chinois (fr) - chinesisches Rätselspiel,
or japanesisches Legespiel (ger) - chineesch
raadsel (du) - 七巧板 qi-qiao
ban or 七巧圖 qi-qiao tu (chin)
- タングラム or chie-no-ita (jap)...
is the Tangram
The Tangram is nowadays the most popular dissection puzzle formed
from 7 polygons. The aim of the puzzle is to seamlessly arrange all the geometric
pieces to form problem figures (rules
of the game). More than 100 years ago, this game was as famous as
cube and has been played passionately by many as entertainment, educational
or mathematical tool, because it boosts shape recognition, problem solving, and
pattern design skills. It is said that the Pythagorean theorem was discovered
in the Orient with help of Tangram pieces...
The 7 polygons or 'tans' (see image further below)
that form the Tangram are:
• 5 right triangles:
2 small (hypotenuse of n/2 and sides of n/2√2); 1 medium
(hypotenuse of n/√2 and sides of n/2); 2 large (hypotenuse
of n and sides of n/√2). The large triangle is 4 times
the size of the small triangle, but curiously its perimeter is only 2 times as
• 1 square (side of n/2√2).
• 1 parallelogram/rhomboid (sides
of n/2 and n/2√2).
Of these 7 pieces, the parallelogram (or rhomboid) is the only piece
that may need to be flipped when forming certain shapes; in fact, it has no reflection
symmetry but only rotational symmetry, and so its mirror image
can only be obtained by flipping it over.
of the puzzle
object of the Tangram game is to put the seven geometric shapes
together so as to form a given outline/silhouette (rules
of the game). Sometimes there is more than one solution.
Alternative solutions are accepted as long as they have EXACTLY
the same outline of the matching figure. For instance, the two
pink figures opposite seem identical but are in fact NOT the
Print this page and cut out the 7 shapes below. Then, try with all
7 pieces to compose a perfect square (there are several solutions, this one is
7 'Tans' of the Tangram
Sarcone & Waeber, Genoa
you have tried that, see if you can form a larger square using
the above 'tans' and adding the extra shape 1)
below... Can you do the same using shape 2)?
or shape 3)?
on the shapes above to see solutions)
history of the Tangram
is known for certain about the origin of the Tangram. Even
the origin of the name is obscure! The earliest known book
was published in 1813 in China, but the publication date
is not reliable. Nevertheless, one Tangram-like puzzle first
appeared in a book published in Japan in 1742.
Scholars assume that Tangram began in the Orient before the 18th
century and then spread westward. Frankly, in my humble opinion, a lot of 'oriental'
games were first created in Europe and then readapted in Asia, like the "Chinese
checker", called tiao-qi in China (the "Chinese checker" was
actually invented in Germany in 1892 and is a descendant from the game Halma)...
In the past, the adjective 'Chinese' was commonly used to denote any odd, complicate
or contrived thing and not the origin! However, by 1817, Tangram publications
had appeared in the United States and in Europe. Whatever date the Tangram was
invented, you have to know that rearrangement puzzle roots can be traced back
to the 3rd century BC! Back in those days, Archimedes, a Greek mathematican,
designed a Tangram-like puzzle called Loculus
Archimedis or Ostomachion.
Toward the end of 19th century, Friedrich Ad. Richter, a German industrialist,
began to manufacture stone versions of Tangram along with other dissection puzzles
under the name of 'The
Anchor Puzzle' (Anker). The Anchor puzzles were so successful that
over 30 new designs of puzzle sets followed.
Chinese and Western Tangram books
illustration opposite comes from one of the earliest
books of Tangram problems “Nuovo Giuoco Chinese,
ossia Raccolta di 364 Figure Geometriche formate con
un Quadrato diviso in 7 pezzi” published by Agapito
Franzetti (Editor), 1817, Italy. One of the ‘Chinese’ puzzle
players is seen cutting his own Tangrams from cardboard,
while the two others try to solve a geometric problem.
First Tangram Books printed in Europe and in USA:
• “Nuovo dilettevole Giuoco Chinese”, Bertinazzi (Publisher),
• “Nuovo Giuoco Chinese”, Flli. Bettalli (Publisher), 1817,
• “The Fashionable Chinese Puzzle”, John Wallis (Publisher),
• “Enigmes Chinoises”, Grossin (Publisher), 1817, France.
• “Metamorfosi del Giuoco detto l'Enimma Chinese”, Landi (Publisher),
of the first books that talk of the Tangram puzzle
published in China around the first decades of the
The Tangram Legend.
A curious paradox
of the 'squares' below are made from the same 7 tangram
pieces. Why are 2 small triangles missing in the second one?
| Click here to
see more paradoxes like this!
are welcome to use whatever you want from this page, but
please CREDIT us! Please note that you can print and reproduce
the content of this page in unaltered form only for your
personal, non-commercial use. We would appreciate receiving
suggestions or corrections concerning our Tangram pages.
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