Seven pieces, one fixed area
A tangram divides a square into seven pieces, traditionally called tans: five right-isosceles triangles, one small square, and one parallelogram. The pieces come in three sizes of triangle—two large, one medium, and two small. Together they still cover exactly the area of the original square; rearranging them changes the outline, not the amount of space they occupy.
That fixed inventory is what makes the puzzle more than a drawing exercise. A solver must use every piece, fit edges together, and avoid overlap. The silhouette supplies only an outer boundary, so the internal arrangement has to be inferred.
Why the shapes can suggest so many things
The pieces share a geometric language: their angles are based on 45-degree turns. That lets triangles meet along edges or at points in many combinations, while the square and parallelogram add shapes that can fill or extend parts of an outline. Rotating and flipping pieces creates new arrangements without changing their size.
The result is a useful visual challenge: the same set can form silhouettes that look very different, even though the pieces themselves never change. A narrow neck, a pointed beak, or a sloping back may be made from several pieces whose boundaries disappear into the larger outline.
A puzzle built around inference
Tangrams became widely known outside China in the early nineteenth century, when the puzzle circulated in Europe and elsewhere. Its appeal rests on a simple constraint: a small, fixed set of shapes must be made to represent a much larger range of forms. Solving one means discovering not just what the silhouette resembles, but how seven unchanging pieces can account for every turn in its edge.
