Art and Mathematics have always been inextricably intertwined and artistic works can be said to employ mathematics in their execution. Any keen look at a piece of art will reveal how the intricacies of the work seem to rely on geometrical shapes and other mathematical concepts to achieve their overall look. Over the centuries many famous artists have used math as the basis of their works. One such artist, M.C. Escher, became interested in the using various forms of geometry, including the depiction of infinity and the use of tessellations and he was able to do this with great efficiency, achieving many masterpieces in the course of his work.Escher was able to createworks of art that were unique and fascinating. His works explored and exhibited many different mathematical ideas.
MauritsCornelis Escher was born in 1898 on the Seventeenth of June, in Leeuwarden, the Netherlands (“Maurits Cornelius Escher,” 2000) and is regarded as “the father” of modern tessellations because of the way he pushed the boundaries of the field. His father was an architect and it was expected that he would follow in the same career. When he was still young, Escher moved to Arnhem with his family, grew up and went to high school there.While in high school, his liking for pen and ink drawings caught his art teacher’s eye who then taught him how to make linocuts. Escher was good at it prompting him to be sent to Roland Holtz who was the best graphic artist around. Holtz was impressed by Escher, suggesting that he switch to wood.
However, Escher failed his exams and Holtz suggested he become an architect. He joined a school in Haarlem, the School for Architecture and Decorative Arts in 1918 and was there until 1922. Mesquita, one the teachers at the school, recognized Escher’s ability and had him change courses which enabled him quickly develop his skills in woodcutting and produced great work in the process (Tessellations.org 2014). Escher took up graphic arts as a career eventually. His areas of specialization were in lithographs, woodcuts and mezzotints. (Smith, 2014). M.C. Escher produced many works of art during his lifetime including hundreds of 448 woodcuts, wood engravings and Lithographs. He also produced more than 2000 drawings and sketches. M.C. Escher was left handed and this is comparable to other great artists that came before him like da Vinci, Holbein, Dürer and Michelangelo (Schattschneider, 2010).
In 1922, M.C. Escher travelled to Spain and Italy, where he began his love for using regular divisions of the plane in his designs. His first work, using this form of geometry, was named Eight Heads (fig. A). Escher read about mathematical ideas like non-Euclidean geometry and was inspired by these ideas as his work continued to develop. In 1936, Escher’s’ true fascination with tessellation and infinity began when he traveled again to Spain and viewed the tile patterns used in the Alhambra (fig. B), a Moorish castle in Granada built in the 14th Century, remarking that it “was the richest source of inspiration that I have ever tapped.”(Smith 2014).He became very interested in the regular Division of the Plane after this visit. After this trip most of Escher’s artwork relied on tessellation. His main goal was to give the viewer a suggestion of the infinite in which the joining motifs could continue in all directions for eternity. He applied a wide variety of mathematical and artistic techniques to capture infinity on the printed page.
Tessellations are regular divisions of the plane. They are usually made of closed shapes arranged to cover a plane completely leaving any gaps or overlapping. Tessellations are typically made of shapes like polygons or other regular shapes like the square floor tiles found in many buildings. Escher, while he was fascinated by all kinds of tessellations, set out to create a new kind. He created what came to be known as “metamorphoses,” a kind of tessellation where the shapes changed while interacting with each other and even went against the common rule by allowing his shapes to break free of the plane itself (Smith, 2014).
In 1957 Escher wrote an article about tessellations. He wrote that:
“In mathematical quarters, the regular division of the plane has been considered theoretically… Does this mean that it is an exclusively mathematical question? In my opinion, it does not.
[Mathematicians] have opened the gate leading to an extensive domain, but they have not entered this domain themselves. By their very nature thay (sic) are more interested in the way in which the gate is opened than in the garden lying behind it.”(Smith, 2014).
Though this can be seen as being unfair to mathematicians and their work, the truth is that upto this point, mathematicians had only shown that shapes such as the triangle, the square or hexagon can be employed in creating a tessellation.In further defence of Escher, there are many irregular polygons that tile the plane and therefore many tessellations employing irregular pentagons. Escher was able to usethese basic patterns in making tessellations and used what in geometry is called are called rotations, translations, reflections and glide reflections to create varieties of patterns and distorted shapes to turn them into other figures like birds and animals (Fig C). In order to preserve the tessellation, Escher made the distortions obey different symmetries of the underlying patterns including the three, four, or six-fold symmetry and in the process produced great works of art.
Escher produced groundbreaking work in the field of tessellation that still inspire other artists in the field today. His work is still as relevant today as it was decades ago and Escher was a genius who, in spite of having no formal mathematics training was able to create artwork that based mathematical principles. His ability to create works that explored perspective, abstract mathematical solids the 3 dimensional world and approaches to infinity indeed prove his genius in the field of tessellation.
