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TILING

TILING. Wallpaper groups. 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. Menu. Step by step A l ittle b it of g eometry

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TILING

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  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 geometry • Exercises • Artwork gallery

  4. Step by Step Draw by mouse

  5. Step by Step • 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

  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 isa 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 transformationare found inwallpaper 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 foryou

  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? A B C

  21. Which two patterns belong to the same group? AC

  22. Which two patterns belong to the same group? A B C

  23. Which two patterns belong to the same group? B C

  24. Which two patterns belong to the same group? A B C

  25. Which two patterns belong to the same group? A C

  26. Which two patterns belong to the same group? A B C

  27. Which two patterns belong to the same group? B C

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

  29. Artworkgallery

  30. Barbora

  31. Aneta

  32. Nikola

  33. Andrea

  34. Jana

  35. Eliška

  36. Tatiana

  37. Tatiana

  38. Kristýna

  39. Sonia

  40. Eva

  41. Michaela Main Menu

  42. The End Gymnázium a Střední odborná škola pedagogickáZnojmo, CZ

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