# The Center of Math Blog

DO the math, DON'T overpay. We make high quality, low-cost math resources a reality.

## Wednesday, June 15, 2016

### Fun Friday: World Tesselation Day

"The geometry of space translates to a reoccurring theme in my creations: the tessellation." - M.C Escher

M.C Fisher was one of the artists responsible for leading the art of tessellation. Today, June 17th, is M.C Escher's birthday. This served as the inspiration for Emily Grosvenor's push to create World Tessellation Day. Grosvenor is the author of a children's book about a girl named Tessa who sees patterns everywhere titled, Tessalation

What is a tessellation?
 Wikipedia
According to Escher, a tessellation is an arrangement of closed shapes that completely covers the plane without overlapping or leaving gaps. In mathematics, tessellations are broken down farther through descriptions. A tessellation with a repeating pattern is periodic, while a non-repeating pattern is called non-periodic. An edge to edge tiling is a polygonal tessellation where adjacent tiles only share one full side. The sides of the polygons and the edges of the tiles are one in the same. A monohedral tessellation contains tiles that are all congruent. The Hirschhorn tiling uses all irregular pentagons. There are many other types of tessellations whose labels are dependent on color, vertices, edges, shapes, or levels of symmetry. Tessellations can also be raised to a higher dimension.  For a complete list of tessellations, check out this Wikipedia Page.

Where can you find tessellations?

 Roman mosaic, Wikipedia
In simple terms, everywhere! Tessellations can be created as art, through manufacturing, or in nature.

Art: Tessellations are often featured in quilts, woven or stitched. In Ancient Rome and Islamic art, tessellations were used to decorate temples and as decorative pieces in buildings. M. C Escher was inspired by Spanish and Moorish symmetry on a visit in 1936. Tessellations are not limited to any particular mediums, and can be found in any genre of art.

Manufacturing: Tessellations are often used in manufacturing to reduce waste. An example of this is found in sheet metal, when the cutouts for various products are engraved and later cut out. Many products are also designed with tessellations. This is evident in the bottom of a Vans sneaker, certain chain link fences, or as designs on household goods.

 Honeycomb
Nature: While some tessellations are created by man, some are found naturally. The most common example is a honeycomb, which is filled with hexagons. Tessellation patterns can also take the shape of a checkered pattern, found in trees or certain flowers. Gilbert tessellations are random crack networks, that form non-periodic functions in nature.

How do you celebrate World Tessellation Day!?
 Image by: Pedrita

This is an easy one. You can celebrate by creating a tessellation! This can be as a doodle, an art project, or a math problem! Check out this Tessellation Tutorial. You could also read up on M.C Escher, or read Tessalation, which comes out today! Be on the look out for tessellation products, such as these cool water bottles!