The Art of Geometry – Virtual Lesson with the Aga Khan Museum

The geometric inspirations from nature are apparent in this tile that features an eight-pointed star opening surrounded by scrollwork resembling palm leaves.

Symmetry is found throughout life. Bilateral symmetry or linear symmetry can be shown on this skull where the left side and the right-side match. 

This dish is another good example of the way patterns in nature influence the geometry of art.

There are many different types of symmetry. A pinecone can have bilateral symmetry, but it also has spiral symmetry or growth symmetry, where parts of the pinecone grow out of from a central point, similar to a Fibonacci spiral.

These tiles are part of a repeat-pattern composition, an example of which adorns the walls of the sixteenth-century Rüstem Pasha Mosque in Istanbul. Typical of tiles with repeat patterns, the underglaze-painted design would have been applied to the tile through the use of a stencil.

Symmetry comes in multiple forms. Radial or rotational symmetry can be observed on this sea star,  which has five matching arms radiating from a central point. 

This double-page frontispiece is from an intact manuscript of the Kitab-i Nigaristan by Ahmad Muhammad Ghaffari (1504–67/68). Completed in 1552, the Kitab-i Nigaristan is a collection of historical anecdotes and incidents, written in prose and focusing largely on peculiarities in Iranian history. 

Dated 1573, this manuscript in the Aga Khan Museum Collection was copied by the scribe Ahmad Shirazi. It contains 44 illustrations executed in the Shiraz style. 

Symmetry also has adaptational advantages for moving around. If a tarantula gets hurt on one leg on the right side, the left side leg can help compensate. 

This manuscript is a well-known copy of Firdausi’s Shahnameh (Book of Kings) produced in Shiraz, Iran. Completed ca. 1010 and dedicated to the Mahmud of Ghazni, then ruler of the region of eastern Iran and today’s Afghanistan, Firdausi’s epic is considered to be one of the world’s longest poems. This copy is composed of 554 pages and 53 illustrations, and it may have been made ca. 1457 for the governor of Shiraz, Pir Bundaq.

Moving around also includes flying! Insects like the dragonfly have a shape that’s adapted for flying, and having balance or symmetry can make that action easier.