GeoGebra Classroom

# pattern and tiles

In next applet you can see the decorative line pattern and the girih tiles of the mausoleum in Maragha. Due to the great freedom in matching the tiles a line pattern can be created that looks random. The pattern runs continuously over the edges of the monument. These edges are marked with a dotted line.

## How to find the underlaying girih pattern?

You can find the underlaying girih pattern by constructing the bisectors of the intersecting decorative lines. Connecting these intersecting points mark the girh tiles.

## The mausoleum in Maragha

• Left you see a wall pannel colored with girih tiles.
• Right the yellow rectangle is zoomed in.
• Below you see the tiles used in the pattern.
The blue zigzagging lines are clearly marked in the pannel because they're sticking out of the wall surface. The white lines are just slightly sticking out of the wall and form another line pattern. On the pictures of the tiles you can see that the pattern of white lines is symmetrical horizontally and vertically in the tiles. So two types of symmetry, not compatible with each other, are mixed. The white lines are continued over matched tiles, but the 2 fold symmetry isn't. To create such a tall not regular tiling with so many lines is quite impossible with ruler and compass. It's a strong argument for the theory of Lu that another method was used. And indeed, just matching girh tiles is an easy alternative for it. Next applet shows the two pattern levels. The thick main lines are generated by the lines on the girih tiles. They define a serie of figures: pentagons, hexagons octagons and a bottle shaped decagon. All of them have got their own symmetries, followed by a 2nd line pattern. Also these lines continue over the boundaries of the figures, but most axes of symmetry don’t. Centuries later hierarchic dual layer patterns are created in which the lines on both level match with girih polygons of the same family each. Not just the wall panels are interesting. Carol Bier pays lot of attention to the tympan and the spandrels above the wall panels.