1. TILING Wallpaper groups

2. Maths + Informatics + Art We created symmetrical artworks by using the program Kali. http://www.geometrygames.org/Kali/index.html Another tool we used was Paint (or Paintbrush), a component of Windows.

3. Menu Step by step A little bit of geometryA little bit of geometry Exercises Artwork gallery

4. Step by Step Draw by mouse

5. Press Print Screen Key (or Alt + PrintScreen) Open the program Paint Press Ctrl + V which will Paste the screenshot into Paint Crop the picture Use the Fill-With-Color tool and fill a closed area with the color Save your picture Step by Step

6. Here is the final artwork Main Menu

7. A little bit of geometry What is tiling of the plane ? It is a collection of plane figures that fills the plane with no overlaps and no gaps. Mathematicians say that there are 17 wallpaper groups.

8. The Theory of Wallpaper Groups is too complicated, but everyone can discover some interesting things. A symmetry of a pattern is a way of transforming the pattern so that the pattern looks exactly the same after the transformation.

9. Most of the Transformations are well known: translation rotation reflection (mirror)

10. Glide Reflection combines a reflection with a translation along the direction of the mirror line

11. What geometric transformation are found in wallpaper patterns? It is different for each group. the only one (e.g. translation) a combination of two or three ones multiple using (e.g. two rotation centres or two reflexion axes and so on) both combination and multiple using

12. Enough of Theory. Visit our gallery and have a look at our works. If you are interested in geometry, you may try exercises. Main Menu

13. EXERCISES FOR YOU

14. Which transformation was used?

15. Which transformation was used? Translations

16. Which transformation was used?

17. Which transformation was used? Glide reflection

18. Which transformation was used?

19. Which transformation was used? Two perpendicular axes + rotation (center )

20. Which two patterns belong to the same group? ABCABC

21. ACAC

22. ABCABC

23. BC BC

24. ABCABC

25. A CA C

26. ABCABC

27. BC

28. ARE YOU INTERESTED? For more explanation visit http://www.scienceu.com/geometry/articles/tiling/index.html Main Menu

29. ARTWORK GALLERY

30. Barbora

31. Aneta

32. Nikola

33. Andrea

34. Jana

35. Eliška

36. Tatiana

38. Kristýna

39. Sonia

40. Eva

41. Michaela Main Menu

42. The End Gymnázium a Střední odborná škola pedagogická Znojmo, CZ