mathadomicile.fr

Tans Generator & Solver

1. The default mode of the program is mode 'Research shapes' which is the
place to create shapes to be matched with the tanset in the 'Play' mode.
You may select here the number of triangles in your shapes (this number
should be equal to the tanset number of triangles for its ability to match
the shapes) and also the shape type : convex or not, with a center of symmetry
or an axis... When you validate your choice the program starts the research
wich could take some time if you are working with a great number of triangles
or sides. When the research ends, it displays the result by pages of 8 shapes.
These shapes are those you may try to match with your tanset if you press
the 'Record shapes' button.

2. In the 'Choose a tanset' mode, you may select the tans of your game
(tanset) to play with in the 'Play' mode. The total area of the tans should
fit the number of triangles of your recorded shapes. You may change the
color of each tan, erase a tan from the tanset or select a well-known tanset
(Tangram, Chie-no-ita, etc.). At this stage, you may also change the way
of computing the Z score. When your choice is done, you press the 'Choose'
button and then enter the 'Play' mode.

3. After shapes have been recorded and a tanset is selected, you may try to play with the tans, in order to match the recorded shapes in the 'Play' mode. The button 'Next recorded shape' give you the shapes one by one. It is also possible to create here free shapes to be matched (it is colored in yellow when area become equal to the tanset area and when the constitution of the shape obeys to the tans rules, in red if the area is ok but not the rules). The button 'Progressive Solution' starts the solving program and dispays the research of the solution step by step. You may try that way to match all the recorded shapes and all the free shapes you create (see above how to create a shape with a hole that is matched by the 'Chie-no-ita tanset'). If you want to see how many recorded shapes are matched with the tanset, press the 'Bilan tanset' button, you then reach the last mode. You may also play in a simple way, trying by yourself to match the shapes using all the different tans : each tan could be moved when you hold the zero point (coloring in a cyan cross when you come close to it) ; a right clic make it turn clokwise, middle clic turn counterclockwise, double clic make a flip.

4. The 'Find a better tanset' mode is the place to see the recorded shapes
that could be matched by the tanset (a solution is given if any). This mode
also computs the Z score of the tanset wich is suppose to measure the ability
of the tanset to match the shapes in an aesthetic and ludic fashion (maximum
differences between tans, minimum number of tans). You may read more about
this Z score in our old page about Tangram
family or, if you read french, in the recent
one. If you press here the
button you starts the research of a better tanset amongst the tansets of
analogous structure. You may look for a better tanset (better Z score) or
even look for the best one. In the java console window, you may follow the
research according the Z parameter you have settled. If you write Z=-1you
will have a faster research and also better for your computer (a delay of
10 s is added every 1000 tansets). You may choose to use only convex tans
(this has an effect on the treatment time...), you may also change the structure:
all the various structures of the same number of tans as your structure
are dispayed on a list. You just have to select one of these structures
-the tanset count is thus displayed- and validate this choice. Here again
you could choose to research a tanset that has a better Z score, or use
all the possible tansets (beware of their number that could be great!)

Using all these possibilities given by the program, we have founded this
square dissection in 9 tans counting 32 triangles which is able to match
33 convex shapes and have this Z score = 35. Compare with the Z = 12 of
the Tangram wich is only able to match 13convex shapes...
Here are two square dissections in 9 tans counting 50 triangles : the first
contains only convex tans, is able to match 45 convex shapes and is granted
with this Z score = 46!,
the second contains a not convex tan, is able to match 48 convex shapes
and is granted with this Z score = 49!
This last square dissection in 10 tans counting 64 triangles is able to
match 60 convex shapes and is granted with this Z score = 60!!

This program has been created for mathadomicile.fr with the help and ideas
and procedures of Eric Warsop and his excellent program Wintanxx describe
in this guide.
Regards to your work Eric!

A lot of good things also came from the reading, the use and contribution
to this wonderfull applet
of Sergio Antoy.
Thanks a lot for your encouragements!

This version (S6.0) is in validation mode, far from the perfection. Thanks
to your suggestions or remarks for a future
better version... You may look at the code
or run it directly (better display) or change it as you want.

For those who are interested in the coding, the different ways of digitization
of the tans, or how the program works, we wrote here some
explanations. Sorry for my bad english..

New feature for last versions : Different threads are used to comput the
shapes or solutions and for the dispay. So, a progress bar could be dispayed
and new shapes or new solutions may be viewed during the comput process.
Minor changes are also added : possible change of the Z codification.

PM