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These days, I bought number Tangent dedicated to Benoit Mandelbrot and fractals. I will address the consequences at first, and I thought that I had a lot of fun bending a few years ago.
sheet is folded in half, draw the diagonal, and it marks the middle of the fold. It draws a line perpendicular to the fold through this point and stopping on the diagonal.

this segment is cut and then folded staircase. One side of the rectangle should be on the top of the sheet.

After relaxed the trick is aène this rectangle inward and gives a kind of pavement "hollow".

The first step is completed.
can count different things:
is the time to introduce the notations. The number of
scissors needed at each step: a
The number of extra blocks at each step: vn
The total number of blocks at each step: wn
Considering that bends to 90 °, and that meets these pavers rights, the volume added at each stage sn
The total volume of the blocks obtained at each step: = 1 tn
u1, v1 = 1, w1 = 1, s1 and t1 depend on the dimensions of the sheet and are worth 1 / 32 L * l.
I asked to do the accounts after the seventh stage.
Step 2: Place the middle of each pleat is folded and staircase.

Then bend inward. a kind of mask appears.

u2 = 2, v2 = 3, w 2 = 4, s2 = 3 / 8 s1, t2 = t1 + 3 / 8 t1 (results found using the reduction ratio 1 / 2)

can continue folds. Step 3

u3 = 4, v3 = 9; w3 = 13; s3 = 9 / 64 * s1;
t 3 = t 2 + 9 / 64 * t1
Step 4

More assembly progresses, it is difficult to cut some bands, the number of folds each time making thicker the strip to be cut. It would also be interesting to count the layers at each position.
But it is more difficult to formalize with suites.

Step 5, I'll stop there fois_ci this, even if I think I already have obtained in Step 6 with an A3 sheet.

As the number of steps increases, one sees less of the blocks, but the structure resembles more the Sierpinski triangle.

is also a pleasure to draw this object in view.

The sequence u is geometric ratio 2, the sequence is geometric reason v 3, then s is geometric because 3 / 8. Students quickly find and use formulas to calculate the 7th term.
Other suites are series. Students find the results by calculating all the terms of the other suites but will check the results when we discuss the sum of the terms of a geometric sequence .