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.

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Step by step A little bit of geometry Exercises Artwork gallery

Step by Step

Draw by mouse

Press Print Screen Key (or Alt + PrintScreen)

Open the program PaintPress Ctrl + V which will Paste the

screenshot into PaintCrop the pictureUse the Fill-With-Color tool and fill a

closed area with the colorSave your picture

Step by Step

Here is the final artwork

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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.

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. 

Most of the Transformations

are well known: translation

rotation

reflection (mirror)

Glide Reflection

combines a reflection with a translation along the direction of the mirror line

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

Enough of Theory.

Visit our gallery and have a look at our works.

If you are interested in geometry, you may try exercises.

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EXERCISES FOR YOU

Which transformation was used?

Which transformation was used? Translations

Which transformation was used?

Which transformation was used? Glide reflection

Which transformation was used?

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

Which two patterns belong to the same group?

A B C

Which two patterns belong to the same group?

A C

Which two patterns belong to the same group?

A B C

Which two patterns belong to the same group?

B C

Which two patterns belong to the same group?

A B C

Which two patterns belong to the same group?

A C

Which two patterns belong to the same group?

A B C

Which two patterns belong to the same group?

B C

ARE YOU INTERESTED?

For more explanation visithttp://www.scienceu.com/geometry/articles/tiling/index.html

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ARTWORK GALLERY

Barbora

Aneta

Nikola

Andrea

Jana

Eliška

Tatiana

Tatiana

Kristýna

Sonia

Eva

Michaela

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The End

Gymnázium a Střední odborná škola pedagogickáZnojmo, CZ