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):
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:
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.