Sunday, October 14, 2012

Tangram - I

The tangram ("seven boards of skill") is a dissection puzzle consists of seven flat shapes, called tans, which are put together to form other shapes. The objective of the puzzle is to form a specific shape (given only an outline) using all seven pieces, which may not overlap. It was originally invented in China at some unknown point in history, and then carried over to Europe by trading ships in the early 19th century. It became very popular in Europe for a time then, and then again during World War I. It is one of the most popular dissection puzzles in the world. 


Choosing a unit of measurement so that the seven shapes can be assembled to form a square of side one unit and having area one square unit, the seven shapes are: 

  •  2 large right triangles (Shape 1 and 2) 
  •  1 medium right triangle (Shape 3) 
  •  2 small right triangle (Shape 4 and 6) 
  •  1 square (Shape 5) 
  •  1 parallelogram (Shape 7)

 Of these seven shapes, the parallelogram is unique in that it has no reflection symmetry but only rotational symmetry, and so its mirror image can be obtained only by flipping it over. Thus, it is the only shape that may need to be flipped when forming certain shapes. This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to