M.C. Escher: Art and Tilings June 17, 1898 – March 27, 1971 By Janine Keizer and Monica McVicar

“I could fill an entire second life with working on my prints” - M.C. Escher Self Portrait, 1943

Biography Dutch graphic artist –Known for mathematically inspired woodcuts, lithographs and mezzotints which feature impossible constructions, explorations of infinity, architecture, and tessellations Maurits Cornelis, was born in Leeuwarden (Friesland), the Netherlands in He was the youngest son of civil engineer George Arnold Escher and his second wife, Sara Gleichman. From 1903 until 1918 he attended primary and secondary school. He excelled at drawing, but his grades were poor, and sometimes he was required to repeat courses twice. In 1919, Escher attended the Haarlem School of Architecture and Decorative Arts where he briefly studied architecture, but switched to decorative arts. In 1922 Escher left the school, having gained experience in drawing and making woodcuts.

Biography Con’t His work went almost unnoticed until the 1950’s. In 1956 he had given his first important exhibition and acquired a world-wide reputation. Among his greatest admirers were mathematicians. As his work developed, he drew great inspiration from the mathematical ideas he read about. He was also fascinated with paradox and "impossible" figures, and used an idea of Roger Penrose’s to develop many intriguing works of art. Escher’s work encompasses two broad areas: the geometry of space, and what we may call the logic of space.

Tessellations A tessellation, or tiling, is a collection of 2, 3, or n dimensional closed figures that fill a surface with no overlaps and no gaps. Richest source of inspiration that he had ever tapped. Regular Division of the Plane is a series of drawings by the Dutch artist which began in These images are based on the principle of tessellation, irregular shapes or combinations of shapes that interlock completely to cover a surface or plane. Sky and Water I (Woodcut print, 1938)

Tessellation Con’t Regular Division of the Plane Drawing # 21, 1938 Reptiles (Lithograph, March 1943)

Polyhedra A polyhedron is a solid bounded by a finite number of plane faces, each of which is a polygon. He made them the subject of many of his works and included them as secondary elements in a great many more. He used the regular polyhedra quite often because there were many interesting solids that could be obtained by intersecting them or stellating them. Stars (Wood engraved print, 1948)

Polyhedra Con’t Order and Chaos (Lithograph, 1950) Gravitation (printed as a black-and-white lithograph and then colored by hand in watercolor, 1952)

Space Among the most important of Escher's works from a mathematical point of view were those dealing with the nature of space. Geometry is the mathematics of shape and space. It's about the properties of objects (their angles and surfaces, for instance) and the consequences of how these objects are positioned (where their shadows fall, how people must move around them). Escher created many beautiful representations of Hyperbolic space Often used the Poincaré model to illustrate infinity.

Space con’t Circle Limit V Circle Limit III (Woodcut, 1958)

Topology In addition to Euclidean and non-Euclidean geometries, Escher was very interested in visual aspects of Topology Möbius Strip II (Woodcut, 1963)

The Logic of Space Attempted to challenge the traditional views of the geometry of space with his many representations of “impossible” objects. Created optical illusions by violating the necessary laws of spatial relations among physical objects. Print Gallery (Lithograph, 1956)

The Logic of Space Con’t The Penrose triangle, also known as the tribar, is an impossible object first created by the Swedish artist Oscar Reutersvärd in The mathematician Roger Penrose independently devised and popularized it in the 1950’s. It is featured prominently in the works of artist M.C. Escher.

The Logic of Space Con’t Waterfall (lithograph, 1961) High and Low (Lithograph, 1947) Still Life and Street (Woodcut Print, 1937)

Cool Prints Relativity (Lithograph, 1953) Ascending and Descending (Lithograph print, March 1960)

Conclusion Drawing Hands (Lithograph, 1948) Escher’s Eye ( Lithograph, 1946)  Escher’s work encompasses two broad areas: the geometry of space, and what we may call the logic of space.  He has drawn for us among the world of imagination, the world of mathematics, and the world of our waking life.  He has taken the worlds of art and mathematics and joined them together as one.

"I can't stop fooling around with our irrefutable certainties. It is, for example, a pleasure knowingly to mix up two- and three-dimensionalities? to make fun of gravity? Are you really sure that a floor can't also be a ceiling? Are you definitely convinced that you will be on a higher plane when you walk up a staircase? Is it a fact as far as you are concerned that half an egg isn't also half an empty shell?" - M. C. Escher Hand With Reflecting Sphere (Lithograph, 1935) Questions??

Exam Question What is regular division of the plane, when did Escher begin applying this to his works. Name one of his works that use this technique.