main page, file list (478), single page HTML, source, report, wiki last updated on 09/22/23


{ I made a simple tangram game in SAF, look it up if you want to play some tangram. ~drummyfish }

Tangram is a simple, yet greatly amusing old puzzle game in which the player tries to compose a given shape (of which only silhouette is seen) out of given basic geometric shapes such as triangles and squares. It is a rearrangement puzzle. Many thousands of shapes can be created from just a few geometric shapes, some looking like animals, people and man made objects. This kind of puzzles have been known for a long time -- the oldest recorded tangram is Archimedes' box (square divided into 14 pieces), over 2000 years old. In general any such puzzle is called tangram, i.e. it is seen as a family of puzzle games, however tangram may also stand for modern tangram, a one with 7 polygons which comes from 18th century China and which then became very popular also in the west and even caused a so called "tangram craze" around the year 1818. Unless mentioned otherwise, we will talk about this modern version from now on.

|\_     big     _/|
|  \_   tri   _/  |
|tri_\_     _/    |
| _/   \_ _/  big |
|<_ sqr _X_   tri |
|  \_ _/tri\_     |
|mid \_______\_   |
| tri  \_ para \_ |

Divide square like this to get the 7 tangram pieces. Note that the parallelogram is allowed to be flipped when creating shapes as it has no mirror symmetry (while all other shapes do).

LRS considers tangram to be one of the best games as it is extremely simple to make and learn, it has practically no dependencies (computers, electricity, ... one probably doesn't even have to have the sense of sight), yet it offers countless hours of fun and allows deep insight, there is art in coming up with new shapes, math in counting possibilities, good exercise in trying to program the game etc.

Tangram usually comes as a box with the 7 pieces and a number of cards with shapes for the player to solve. Each card has on its back side a solution. Some shape are easy to solve, some are very difficult.

         /  |                           _/|\_
        |\_ |                          /  |  \_
        |  \|                         |   |    \_
        | _/                      _   |   |______\
        |/ \_  ________         _/ \_ | _/ \_
       /     \/       /       _/     \|/     \
       \_   _/_______/      _/         \_   _/
         \_/|              /_____________\_/   
        _/  |                  |         _/
      _/    |                  |       _/
    _/      |                  |     _/
  _/        |                  |   _/
 /__________|                  | _/
 \_         |                  |/|
   \_       |                 /  |
     \_     |                 \_ | 
     _/\_   |                  |\|
   _/    \_ |                  |  \_
  /________\|                  |____\            

Two tangram shapes: bunny and stork (from 1917 book Amusements in Mathematics).

{ I found tangram to be a nice practice for letting go of ideas -- sometimes you've got an almost complete solution that looks just beautiful, it looks like THE only one that just has to be it, but you can't quite fir the last pieces. I learned that many times I just have to let go of it, destroy it and start over, usually there is a different, even more beautiful solution. This experience may carry over to practical life, e.g. programming. ~drummyfish }

Can tangram shapes be copyrighted? As always nothing is 100% clear in law, but it seems many tangram shapes are so simple to not pass the threshold of originality for copyright. Furthermore tangram is old and many shapes have been published centuries ago, making them public domain, i.e. if you find some old, public domain book (e.g. the book The Fashionable Chinese Puzzle, Amusement in Mathematics or Ch'i ch'iao hsin p'u: ch'i chiao t'u chieh) with the shape you want to use, you're most definitely safe to use it. HOWEVER watch out, a collection of shapes, their ordering and/or shapes including combinations of colors etc. may be considered non-trivial enough to spawn copyright (just as collections of colors may be copyrightable despite individual colors not being copyrightable), so do NOT copy whole shape collections.

Tangram paradoxes are an interesting discovery of this game -- a paradox is a shape that looks like another shape with added or substracted piece(s), despite both being composed of the same pieces. Of course geometrically this isn't possible, the missing/extra area is always compensated somewhere, but to a human eye this may be hard to spot (see also infinite chocolate). New players get confused when they encounter a paradox for the first time, they think they solved the problem but are missing a piece, or have an extra one, while in fact they just made a wrong shape. TODO: example

Tips for solving:

TODO: some PD shapes, math, stats, ...

All content available under CC0 1.0 (public domain). Send comments and corrections to drummyfish at disroot dot org.