Tangram
{ I made a simple tangram game in [1]SAF, look it up if you want to play
some tangram. ~drummyfish }
Tangram is a simple, yet greatly amusing old puzzle [2]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 [3]triangles and [4]squares.
It is a rearrangement puzzle, a 2D game that's in principle similar e.g.
to [5]Soma cube, a game in which, similarly, one makes shapes out of basic
parts, but in which the shapes are three dimensional. In Tangram 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).
[6]LRS considers tangram to be one of the best games as it is extremely
[7]simple to make and [8]learn, it has practically no [9]dependencies
(computers, electricity, ... one probably doesn't even have to have the
sense of sight), yet it offers countless hours of [10]fun and allows deep
insight, there is [11]art in coming up with new shapes, [12]math in
counting possibilities, good exercise in trying to [13]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 fit 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. [14]programming. ~drummyfish }
Can tangram shapes be [15]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, [16]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 [17]paradoxes are an [18]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 [19]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:
* Start by placing pieces you know for certain where they belong (small
details that can only be made with the smallest pieces, pieces you
deduce that HAVE to be somewhere etc.). This reduces the problem to
making a smaller shape from fewer pieces, making it much easier to
solve. But BEWARE: sometimes you wrongfully assume some piece in some
place because the silhouette "suggests" it, do not fall to this trap.
* At the beginning try to get a sense of scale, sometimes what in the
silhouette looks like the big triangle may actually be the middle
sized one etc.
* Learn some common patterns, e.g. you can make a rectangle out of the
two small triangles and parallelogram. This comes with just solving
more puzzles.
* If you have an "almost solution" and can't fit the last few pieces for
some time, just destroy it and start over. There are many nicely
looking blind paths.
* If in your partial solution you can replace some subshape composed of
smaller pieces with the same subshape composed of one larger piece, do
it. Having smaller pieces is preferable because you have more
flexibility.
* Be careful to make the exact shape you see, sometimes it is possible
to make a very similar looking shape that has just a tiny bit
different proportions e.g. by rotating the parallelogram.
* ...
TODO: some PD shapes, math, stats, ...
See Also
* [20]Soma cube
Links:
1. saf.md
2. game.md
3. triangle.md
4. square.md
5. soma_cube.md
6. lrs.md
7. kiss.md
8. easy_to_learn_hard_to_master.md
9. dependency.md
10. fun.md
11. art.md
12. math.md
13. programming.md
14. programming.md
15. copyright.md
16. public_domain.md
17. paradox.md
18. interesting.md
19. infinite_chocolate.md
20. soma_cube.md