tangram

A tangram is a dissection puzzle that uses seven flat pieces, called tans, which can be rearranged to form a wide variety of shapes. The objective is to use all seven pieces to reproduce a specified outline without overlaps or gaps. The shapes can be rotated or flipped and rearranged to create new forms, from simple silhouettes to complex figures.

The seven tans come from a square cut into five triangles, one square, and one parallelogram: two large right triangles, one medium right triangle, two small right triangles, one square, and one parallelogram. The standard set is typically uniform in size and can be rearranged to form numerous shapes.

Origins and history are somewhat unclear. Tangrams are commonly associated with China and are believed to date from the 18th or 19th century, after which they spread widely to Europe and the Americas in the 19th century. The exact details of their origin remain a topic of traditional lore and scholarly debate.

Gameplay and varieties: for a given target shape, the puzzle requires placing all seven pieces within the outline without overlaps, with pieces allowed to be rotated and flipped. There are many possible solutions for each shape, and catalogs of standard tangram figures—ranging from animals to objects to letters—are widely published. Digital versions extend the range of puzzles and provide interactive tools for constructing solutions.

Educational and cultural significance: tangrams are used to develop spatial reasoning, geometry understanding (triangles, squares, symmetry, similarity), and problem-solving skills. They are employed in classrooms and homes around the world and remain a popular example of a simple yet versatile geometric puzzle.