Quadratum Cubicum

Quadratum Cubicum is a dissection puzzle.

A geometric dissection means that one or more figures are cut into parts

so that the pieces can be used to build other figures.

Thereby the emphasis is to use as few pieces as possible.

The two most famous dissection puzzles you should already know are:

* the Tangram:

two squares have to be rearranged to form one bigger square

* The Five Square Puzzle:


five squares of the same size have to be rearranged to build one big square.

The Quadratum Cubicum dealt extensively with square trisection:

thereby a square has to be cut into pieces in such a way

that they can be rearranged to form three identical squares.

One of the trisection used in the Quadratum Cubicum is well known in geometry,

because it has been used to illustrate the Pythagorean theorem, more than one thousand years ago.

Mathematicians continue to search for new solutions nowadays.

Christian Blanvillain and Janos Pach found one dissection in 2010 using only 6 = 2 * (3 different) parts.

It is worth mentioning that each part has the same area.

The Quadratum Cubicum provides a set of the nine historical most important solutions

founded for square trisection problem. The puzzle consist to check that those solution are correct,

thus to assemble three small squares in a bigger one!

This Quadratum Cubicum has one rare feature: it can be played at different level.

That makes this puzzle affordable for young children, and also be be really challenging for puzzle guy.

If you merge all the pieces of the nine puzzle, then you have a really challenging 68 pieces puzzle to solve!

With all the pieces you can create a huge 42cm square, that can be divided in three medium 24.2cm squares,

that can be again divided in three 14cm squares, that can finally be divided in three small 8.1cm squares!

The advantage is that every body in the house can play with this puzzle.

The three 24.2cm square and the twenty seven 8.1cm squares are easy to find.

The big 42cm square is really tricky and the nine 14cm squares have very different levels of difficulty :

Easy (for children):

Henry Perigal - 6 pieces - 1891

Abu Bakr Al-Khalil - 8 pieces - 14th

Christian Blanvillain - 6 pieces - 2010

Medium (for every body):

Greg N. Frederickson - 7 pieces - 2002

Colonel De Coatpont - 7 pieces - 1877

Abu Bakr Al-Khalil - 9 pieces - 14th

Abul Wafa - 9 pieces - 10th

Difficult (for puzzle guy):

Nobuyuki Yoshigahara - 9 pieces - 2004

Edouard Lucas - 7 pieces - 1883

I chose a mini QuCub with Christian Blanvillain trisection.

The puzzle looks very elegant and is relatively big (14 cm). From one side the puzzle is shining a bit.

This effect is due to satined plexiglas. I like the composition which is related to the logo very much.

You can recognize on first glance that a bigger square shall be arranged. As already mentioned,

the puzzle from Christian Blanvillain is easy and can be solved quickly (‹ 5 minutes).

For a puzzler who only wants to have only one puzzle in his collection,

I would recommend the more difficult puzzle by Edouard Lucas.

The online shop (see http://qucub.com) offers the puzzles in different sets.

Thus it is possible to purchase all nine puzzles, a set consisting of three puzzles or only a single puzzle.

To conclude, Quadratum Cubicum is well suited for adults as well as for children.

The problem is easy enough for children so that they can enhance their analytical skills.

But the puzzle is also a challenge for adults, especially if trying to build a big square of 68 single parts.

You can buy the Quadratum Cubicum on the official website.