Last week I visited the Metro Show in New York. This is an art and antiques fair where 35 dealers display a wide range of items including folk art, outsider art, and ethnic antiquities. I did not necessarily expect to find Mathematical Art in this venue. Much to my surprise the first thing that caught my eye, as I walked into the exhibition hall was a Peruvian textile in the William Siegal Gallery  area, made by weavers from the Nasca Culture (sometimes spelled “Nazka”) from the Southern coast of Peru. It was made somewhere between 200-600 AD from camelid wool and natural dyes. This Stepped Mantle has interesting symmetrical properties. If you only look at shapes and ignore the colors, this is a great example of order 2 rotational symmetry, also called a “point symmetry”. Rotating at any point where all four colors meet you can rotate the four rectangles 180 degrees and still have the same pattern (disregarding colors):

Nasca Culture (200-600 AD) – Stepped Mantle – Camelid Wool and Natural Dyes

On another wall in the booth of the William Siegal Gallery there was a Stepped Cushma (one piece dress) also Nasca 200-600 AD. This textile demonstrates reflection symmetry,  also referred to as “mirror symmetry”. There are 7 vertical lines of symmetry that can be drawn through this example. If you consider each on the four columns of V-shaped chevron patterns, they have lines of symmetry through the center. Then, each of the two pairs of adjacent columns have a line of symmetry between them. Finally, the complete textile has a line of symmetry down the middle:

Nasca Culture – Stepped Cushma – Camelid Wool and Natural Dyes

The moral of this blog is to keep your eyes out for Mathematical Art everywhere. The connections between Mathematics and Art can be found in unexpected places.

– FibonacciSusan