Ceilings made of cells

This lesson asks you to build and take apart structures, and to name the flat shapes and solid objects you find in them. The museum offers one record on a ceiling made of cells; sorting and naming cubes, prisms, pyramids, cylinders and cones is the class's own work. ¹

Build a small structure from blocks, then take it apart. List the flat shapes and the solid objects you used. Did any piece count twice?

Look up at a muqarnas ceiling: it seems built of small hollows in steps. In the definition discussed by the study, a cell consists of two facets and a roof, and cells with bases in one horizontal plane form a tier ². In his measurement of muqarnas, al-Kashi selects a module, counts elements by shape, and adds the surfaces of facets, roofs and connecting pieces ³. The record says some visible pieces belong to cells and others fill gaps between them, and that counting hollows in a photograph is not enough to determine their exposed surface area ².

Some visible pieces of the ceiling are cells and others fill the gaps between them. Why does that make counting hollows in a photograph a poor way to find the surface of the ceiling?

• Al-Kashi's measurement of muqarnas: how the surfaces of the small parts were added.
• Muqarnas: the tiered cellular construction that articulates and decorates ceilings.
• Al-Kashi: the author of the Key to Arithmetic, where this measurement is set out.

Read the record on al-Kashi and the muqarnas. Look at a picture of a muqarnas ceiling and list the different shapes you can name.