1. Math-Art from Germany

2. There is a lot of art without math and a lot of math without art.

3. What is the intersection of both - math and art
What is the intersection of both - math and art? That's very often a combination of repetition and variation.

4. Repetition alone is boring.

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6. Variation makes it interesting.

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8. The deviation is an eye-catcher.

9. Both are not from Germany.
We did research on a lot of artists who experimented with geometrical forms. We decided to combine two of them to create a new “never have seen” kind of art. ESCHER and VASARELY
Both are not from Germany.

10. Maurits Cornelis Escher (1898  – 1972) was a Dutch graphic artist who made mathematically-inspired pictures. He took a geometrical form like a triangle or a square, cut things of and glued it to another side until he designed a form that could be used as a tile.

11. A tile is a form with which you can fill areas completely, so that no gaps remain free.

12. You understand?
The red tail is cut out and glued on again as a green tail.
The white mouth is cut out and glued on again as a green mouth.
And so on. At the end you got a tile with which you can fill the paper completely.

13. Victor Vasarely (1906 – 1997) was a Hungarian-French artist, who is widely accepted as the "grandfather" of the OP ART movement. He created optical illusions by making two-dimensional shapes appear three-dimensional.

14. Often picture-puzzles arise
Often picture-puzzles arise. You can see inside a room or in the same image you can see a figure that seems to come out of the picture. Please concentrate on one or the other center point and you will understand what I mean.

16. We chose the rhombus (Borussia – our soccer team) as the basic form.

17. The rhombus has four equally long sides, but no right angles
The rhombus has four equally long sides, but no right angles. The angles we use are 60° and 120°, as you can see in the background picture.

18. and you see something different.
That's important because then you can put three rhombuses together to a hexagon (6 angles, 6 corners). But there is an interesting optical effect: You put together three flat (2-dimensional) rhombuses
and you see something different.

20. Do you see a 3-dimensional cube. No. Do you see anythimg else
Do you see a 3-dimensional cube. No? Do you see anythimg else? Yes, some of you don't see a cube they look into a 3-dimensional room with three walls. Fix the point in the middle with your eyes and let it change. It comes out and it goes in. Does it make CLICK to you? It's an optical illusion.

21. Back to Escher: He took a geometrical form, cut things of and glue it to another side. Letˋs take a hexagon.

22. Then we cut one piece off and put it to another place.
Now, we have a tile with which you can fill an area completely.

23. And it's shape is remindful of a V like the name of our school Volksgarten or to a heart © If you like it more emotional.

24. This is the tile,
you can see the
rhombuses inside.

25. Here you can
see how we
can fill up
the whole
floor with
the tiles.

26. Instructions! Step One:
Two of you get one shape each. And a lot of rhombuses in different colors. Then you can fill your form as you like. But keep to the following rules.
Vacancies may arise only on the edge,
but not in the interior of the form,
and nothing may overlap the edges

27. Step Two:
When you are satisfied with your artwork, glue the parts to the base.
Please work very carefully. That makes our artwork beautiful.

28. Step Three: Fix all the parts.
When you're done, come to the front and put all the pieces together to create a great work of art.
Fix all the parts.

29. Step Four: At the end you have to do what all artists do: Sign your work! If you like you can also post a personal motto like: I like Math, Math makes me happy.
I like Finland. I love Erasmus.
or what ever you want to tell us.

30. Are there any questions?

31. Now, you can start. May the exercise be successful.