M.C. Escher ~ Tessellations: Mathematics or Art? Introduction

1. M.C. Escher ~ Tessellations: Mathematics or Art? Introduction Maurits Cornelis Escher (or simply M.C. Escher) was born in Leeuwarden, Holland in 1898. He was never a good student during his childhood days. The whole of his school days was a nightmare, the only saving grace was his weekly 2 hour art lessons. Although he was considered by his art teacher for having a more than average talent for art, Escher scored a lowly seven. His art was not highly thought of by the examiners. Little did they know that Escher would eventually become a famous artist for creating highly imaginative artwork that marries the world of art and mathematics. In his later years, he recalled his childhood days and wrote: At high school in Arnhem, I was extremely poor at arithmetic and algebra because I had, and still have, great difficulty with the abstractions of numbers and letters. When, later, in stereometry [solid geometry], an appeal was made to my imagination, it went a bit better, but in school I never excelled in that subject. But our path through life can take strange turns.~~ Despite having no formal training in mathematics, Escher created artwork that followed certain mathematical principles. His works included exploration of the 3 dimensional world, perspective, abstract mathematical solids, approaches to infinity and also – the art of creating tessellations.

2. 1943 Reptiles Untitled (Reducing Lizards)

3. 1936 Strong Men 1938 Swallows 1936 China Boy

4. What are tessellations? Tessellations are arrangements of closed shapes that completely cover the plane or surface without overlapping and leaving gaps.Escher was fascinated by all types of tessellations, regular and irregular, and he himself questioned the domain in which tessellations fell under: mathematics or art?Mathematics has shown that there are only three regular shapes that can be used for a tiling. Escher exploited these basic patterns in his tessellations, and applied principles of translations, glide reflections and rotations to obtain a wide variety of patterns. The effects of his tessellations are usually both astounding and beautiful. Lizard 1946 Horseman 1956 Smaller and Smaller

5. Modern Day Tessellations • wallpaper designs

6. soccer balls • bathroom floors • patio designs & • more

7. How to make a tessellation 1 2 3 4

9. Escher's sketch of the tessellations in Alhambra, Spain

10. “For me it remains an open question whether [this work]pertains to the realm of mathematics or to that of art.” 1939 Development II 1964 Fish 1958 Circle Limit III Task: Learn more about M.C. Escher and see animated transformations by going to… www.cawthrapark.com  Teacher Web  Ms. Brady  Links  Principals of Tessellations Read through the content on the following pages and see how animation helps you to understand Escher and the principals of tessellations. • Principals of Tessellations • Mathematics in Escher’s work • Our original Tessellations

11. The Alhambra ~ Escher's Inspiration The Alhambrais comprised of royal residential quarters, court complexes flanked by official chambers, a bath, and a mosque—was begun in the thirteenth century by Ibn al-Ahmar, founder of the Nasrid dynasty, and was continued by his successors in the fourteenth century. Its most celebrated portions—a series of courtyards surrounded by rooms—present a varied repertoire of Moorish arched, columnar, and domical forms. The romantic imagination of centuries of visitors has been captivated by the special combination of the slender columnar arcades, fountains, and light-reflecting water basins found in those courtyards—the Lion Court in particular; this combination is understood from inscriptions to be a physical realization of descriptions of paradise in Islamic poetry.

12. Map of Spain

13. On a hill overlooking Granada, the Alhambra – a sprawling palace citadel. The greatest monument to Islamic mathematical art on Earth.

14. Because the Qur'an (def: n. the sacred text of Islam, considered by Muslims to contain the revelations of God to Muhammad)considers the depiction of living beings in religious settings blasphemous, Islamic artists created intricate patterns to symbolize the wonders of creation: the repetitive nature of these complex geometric designs suggested the limitless power of God. The citadel boasts a remarkable array of mosaics with tiles arranged in intricate patterns. view of Grenada from the Alhambra decorative arch with mosaic tiling, Alhambra door & wall detail, Alhambra tile detail, Alhambra

15. The Alhambra tiling are periodic; in other words, they consist of some basic unit that is repeated in all directions to fill up the available space.