Patterns of stars and polygons

This lesson asks you to find and describe the elements and operations that repeat in patterns, and to create patterns and show them in different ways: with shapes, numbers and tables. The museum offers one record on girih, which builds stars and polygons from interlacing bands and rests on girih tiles; the rules, tables and extensions are the class's own work. ¹

Look at a pattern of stars and polygons. Point to the part that comes back. Does it come back in the same place, or somewhere else?

Draw the pattern with shapes, then write it with numbers or in a table. Does each way show the same repeat?

See where one kind of ornament turns up. The Encyclopaedia of Islam's article on the arabesque is illustrated with a motif from the mosque of Amr at Fustat, a Qur'an manuscript made in Granada, Egyptian wood carving, a faience mosaic in a tomb at Konya, and a Persian stucco tile ^{2 3}. The article says the ornament is not tied to one material ⁴.

The same kind of ornament appears in wood, in stucco, in tile and in a book. If you wanted to find out what stays the same when it moves from one material to another, what would you look for, and why?

• The arabesque: the article's pictures, and where each one comes from.
• The mosque of Amr at Fustat: one of the places the article's pictures come from.
• Girih: geometric patterns of stars and polygons.

Read the record on girih. Choose a star you can draw, draw three repeats of it, and make a small table that counts the points at each step.