How the pieces work
A standard Tangram set cuts one square into seven tans: five triangles, one square, and one parallelogram. The pieces keep their area, but rotation, reflection, and recombination let the outline change completely.
Eastern Puzzle ArchiveGeometry-dissection system sample / Tangram
Seven pieces make area visible.
Tangram is the geometry-dissection system sample in this maker-run resource. It anchors the first shelf of shape, sequence, and search: seven tans make area visible while the same pieces become squares, animals, letters, and visual proofs.
Seven tansDissection geometryPlayable now
Read the system
Start with the cut square before the silhouette.
Tangram feels playful because the pieces invite making. It becomes mathematically useful because every figure uses the same seven pieces, so the changing outline can be compared against a stable area.
What the sources can support
The source material supports Tangram as a Chinese seven-piece dissection puzzle with a rich print and play culture. Many Tangram silhouettes depend on convention, drawing precision, or multiple valid arrangements, so the archive avoids claiming a single solution unless the source or a proof supports it.
What AI and visual reasoning can study
A Tangram figure can be treated as a shape search problem: match pieces to an outline, test rotations and reflections, compare near misses, and explain why the same area can become many silhouettes.
Try the workbench
Rebuild the square from scattered tans.
Drag, rotate, snap, and ask for a hint when the geometry gets stubborn. The current workbench teaches the square target first because it is the clearest way to see how seven fixed pieces can become one exact area again.
ShapeAreaSearch
Workbench 01 / Tangram
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Hidden mathematics
The same area becomes many shapes.
The first lesson is not calculation. It is seeing that dissection, rotation, reflection, and recombination can preserve area while radically changing what a shape appears to be.
Geometry
See how equal areas survive rotation, reflection, and recombination.
State
Treat every valid position as a readable system state, not just a picture.
Tangram library
Read the geometry guide behind the workbench.
A Short History of the Tangram
A careful history of Tangram origins, circulation, printed puzzle culture, and its later role in recreational mathematics.
Source pages 25-36Read the geometry guideMaking a Tangram
A practical guide to Tangram construction that explains why the standard cuts matter for play and mathematics.
Source pages 37-41Read the geometry guideTangram Mathematics
A source-backed path into dissection geometry, topology, graph thinking, and area-preserving transformations.
Source pages 42-96Read the geometry guideTangram Games
A guide to Tangram as a playable activity: free construction, silhouette solving, challenge rules, and group formats.
Source pages 97-100Read the geometry guideUnusual Uses of the Tangram
A survey of Tangram beyond pastime: demonstrations, teaching aids, design prompts, and visual reasoning tools.
Source pages 101-118Read the geometry guideTangrams Outside China
A reception history of Tangram abroad and the broader family of dissection puzzles influenced by its spread.
Source pages 119-137Read the geometry guideFrom Plane Tangram to Solid Tangram
A guide to three-dimensional Tangram ideas, spatial reasoning, and the shift from area-preserving figures to volume-aware construction.
Source pages 138-161Read the geometry guideNext challenge library
Add beginner silhouettes with hint levels.
The next product layer should add a small challenge library: beginner silhouettes with hint levels, completion messages, and notes about whether a figure is unique, conventional, or one of several possible arrangements.