M.C. Escher: Art or Math?
In Leeuwarden, Netherlands in 1898, Maurits Cornelis Escher was born. Later in his life, he tried to be an architect, but that didn't work out, so he decided to study graphic art at the School for Architecture and Decorative Arts. Escher is most famous for tessellations, but he also has made portraits, landscapes, and geometric designs. In 1922, when he went to Alhambra in Spain, Escher really liked the Moorish mosaics. They inspired him to create his own versions. Escher created many, many tessellations, most involving humans, dogs, birds, horses, crabs, insects, and fish.
Mathematical Side of Escher
The Mathematical Art Of M.C. Escher
There are several transformations that are used in tessellations. One is a rotation. Rotations are when the shape is rotated either clockwise or counterclockwise. Next there is a reflection. A reflection is basically a mirror image of the object. Then there is a translation. That is when the object is exactly the same just slid over a little.
If you start with the triangle farthest to the left, and do a clockwise rotation, you'll get the other triangle.
The blue line is the line that you reflect over to get the green triangle.
This translation moves the triangle over six units.