ART & MATHS : M.C. Escher “Although I am absolute innocent of training or knowledge in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists” M.C. Escher, 1967 © Belén Pena y Luis M. Rodríguez

Escher's Artwork During his lifetime made 448 lithographies, woodcuts and wood engravings 2000 drawings and sketches. He illustrated books, designed tapestries, postage stamps and murals. He published the illustrated book “The Regular Division of the Plane” (1958) During his lifetime made 448 lithographies, woodcuts and wood engravings 2000 drawings and sketches. He illustrated books, designed tapestries, postage stamps and murals. He published the illustrated book “The Regular Division of the Plane” (1958)  M.C. Escher ( ) is one of the world´s most famous graphic artists, although occasionally produced watercolours and sculptures.  Printmaking fascinated him for its beauty, technique and endless multiplications of his works  M.C. Escher ( ) is one of the world´s most famous graphic artists, although occasionally produced watercolours and sculptures.  Printmaking fascinated him for its beauty, technique and endless multiplications of his works © Belén Pena y Luis M. Rodríguez

Escher's Artwork © Belén Pena y Luis M. Rodríguez

Escher's Artwork Escher´s artwork Art (technique, poetry, beauty) Perceptions of reality as constructions Geometry & Mathematics © Belén Pena y Luis M. Rodríguez

M.C. Escher at the Alhambra R EGULAR D IVISION OF THE P LANE -T ESSELLATIONS - One major source of inspiration for Escher´s designs is the Alhambra. He became fascinated by the R EGULAR D IVISION OF THE P LANE and developed patterns -T ESSELLATIONS - filling the plane with regular geometric structures and no overlaps or gaps. © Belén Pena y Luis M. Rodríguez

ART & MATHS : M.C. Escher A BILINGUAL CROSS-CURRICULAR ACTIVITY - 4 ° ºESO - PLANNING THE ACTIVITY PLANNING THE ACTIVITY  Meeting MC Escher  Educational visit to INFINITE UNIVERSES, an Exibition about Escher´s artwork.  Studying the Escher´s world  Undertaking the study of the Escher´s artwork concerned with Art History and Maths.Several resources and a student´s workbook to carry out different assignments on Maths and History. © Belén Pena y Luis M. Rodríguez

© Belén Pena © Belén Pena y Luis M. Rodríguez

Biography & Chronological Periods  Early work from 1916 – 1922  Italian Period from 1922 – 1935  Switzerland and Belgium  Back in Holland 1941 – 1954  Recognition and Success  Early work from 1916 – 1922  Italian Period from 1922 – 1935  Switzerland and Belgium  Back in Holland 1941 – 1954  Recognition and Success © Belén Pena y Luis M. Rodríguez

Escher's Techniques  "What is really so fascinating about graphic processes? What is that strange power of attraction that keeps its hold on the graphic artist, which is the reason he specializes to such an extent that, as a rule, he does not engage in any other form of art? There are, I believe, three elements that are an inherent part of this fascination: 1. desire for multiplication, 2. beauty of the craft, 3. forced limitations resulting from the technique." (Escher, in Escher, 1989)  "What is really so fascinating about graphic processes? What is that strange power of attraction that keeps its hold on the graphic artist, which is the reason he specializes to such an extent that, as a rule, he does not engage in any other form of art? There are, I believe, three elements that are an inherent part of this fascination: 1. desire for multiplication, 2. beauty of the craft, 3. forced limitations resulting from the technique." (Escher, in Escher, 1989) © Belén Pena y Luis M. Rodríguez

Escher's Techniques Printmaking Methods Relief Printing WoodcutWood EngravingLinocut Intaglio Mezzotint Planographic Lithography Stencilling © Belén Pena y Luis M. Rodríguez

Printmaking Techniques Printmaking Techniques Basic Categories (According to Processes) Stencil ink or paint is pressed through a prepared screen screenprinting pochoir Planographic inked areas separated from noninked areas by chemical means lithography monotyping digital techniques Intaglio ink is applied beneath the original surface of the matrix engraving etching mezzotint aquatint Relief ink is applied to the original surface of the matrix woodcut / woodblock (for Asian forms) wood engraving linocut metalcut Many of these techniques can also be combined, especially within the same family Contemporary printmaking may include digital printing, photographic mediums, or a combination of digital, photographic, and traditional processes. © Belén Pena y Luis M. Rodríguez

Escher's Techniques Printmaking Methods - 1 Intaglio Mezzotint The entire surface of a copper plate is roughened over with a rocker. Using a scraper and burnisher to flatten and press the copper, the artist makes areas of the surface smooth again, so that they do not hold ink and therefore print white. The mezzotint tcreates images with soft and subtle gradations of tones from dark to light. © Belén Pena y Luis M. Rodríguez

Escher's Techniques Printmaking Methods - 2 Relief Printing WoodcutWood Engraving Woodcut Using various tools, the artist begins by cutting the grooves that form the design. Only the ungouged portion is inked. A roller is used to ink the surface, and thus the ink does not enter the hollow sections. The sheet of paper is placed on the inked block and pressure is applied to the back of the sheet. In woodcut, the wood used for printing is sawn along the length of the tree, which makes the surface relatively soft. The wood should ideally be worked in the direction of the grain to ensure a clean cut. Wood Engraving Unlike woodcut, in wood engraving the wood is sawn perpendicular to the trunk, producing an extremely hard surface. By gluing several pieces together, an uniform block of adequate dimensions may be produced. The hard surface allows the artist to attain various shades of grey by fine cross- hatching. The wood may be worked in any direction, but the technique requires great dexterity and attention to detail. © Belén Pena y Luis M. Rodríguez

Escher's Techniques Printmaking Methods - 2 Relief Printing Linocut Printing from linoleum has two advantages: it is inexpensive, and it allows cutting in every direction. Unlike wood, linoleum has virtually no grain, and so it gives the printed sections a uniform appearance. One slight disadvantage is that fine lines are more difficult to execute than in wood. © Belén Pena y Luis M. Rodríguez

Escher's Techniques Printmaking Methods – 3 Planographic Lithography Lithography 2 Lithography 1 Lithography 3 Lithography, which may appear somewhat mysterious at first, is based on the natural repulsion of oil and water. The technique may be summed up in five steps: 1. Using a crayon or a brush dipped in oily ink, the artist draws a design on a limestone slab. 2. The stone is then bathed in a solution of nitric acid and gum arabic. The solution allows the oil to thoroughly penetrate the stone and makes the unoiled portion even more sensitive to water and less sensitive to oil. 3. Before printing, water is generously applied to the stone. The water saturates the unoiled portions. 4. The stone is inked with a roller. The ink will adhere only to the oily areas; the water- soaked portions will repel the ink. 5. Printing is done on a lithographic press (equipped with a scraper). © Belén Pena y Luis M. Rodríguez

Landscapes Crossing Worlds Mathematical forms Space Structure Metamorphosis Cycles - Tessellations Infinite Universes Surface Structure Perspectives & Arquitectures Impossible Structures & Worlds Projecting 3dimensional space to the plane Escher's Themes © Belén Pena y Luis M. Rodríguez

Regular Polihedra or Platonic Solids Archimedean Solids Space Structure Regular Division of the plane: Reflections, Translations or glides and Rotations Topology: Möbius Strip Non-Euclidean Geometry and Fractal Geometry Surface Structure Perspective: Cylinder Perspective 3 Dimensional Representation Projecting 3dimensional space to the plane Escher's Themes: Mathematics in Escher ' s Artwork © Belén Pena y Luis M. Rodríguez

To represent the world, his world: continuous, dual, dialectic, relativist, cyclic, magic, staggering, bewildering. To represent the conflict between reality and imagination To represent the perception mystery. Maths as a tool: Processual Art “Mathematics laws are neither creations nor human inventions. They merely “are”, and they exist completely apart from the human spirit”. (Escher) Maths as magic structure under reality Despite having no formal training in mathematics, Escher’s artwork has been considered by some mathematicians as a way of visualizing difficult mathematics concepts. Maths as a concept we can visualized: Conceptual Art Escher's Themes: Why Mathematics? © Belén Pena y Luis M. Rodríguez

Escher's Themes I: Space Structure Landscapes, Crossing Worlds and Mathematical forms Platonic Solids or (Regular Polyhedra) Archimedean Solids Platonic Solids or (Regular Polyhedra) Archimedean Solids Tetrahedral Planetoid, woodcut 1954 Flatworms, lithograph 1959 Waterfall, lithograph, 1961 Stars, wood engraving, 1948 © Belén Pena y Luis M. Rodríguez

Escher's Themes II: Surface Structure Metamorphosis, Cycles – Tessellations and Infinite Universes Regular Division of the plane Transformational Geometry or Rigid Motion: Reflections, Translations (or Glides) and Rotations Cycle, lithograph, 1938 Horsemen, 1946 Metamorphosis, from his book “Regular Division of the Plane”, 1938 Metamorphosis © Belén Pena y Luis M. Rodríguez

Escher's Themes II: Surface Structure Metamorphosis, Cycles – Tessellations and Infinite Universes Topology: Möbius Strip and “rubber sheet geometry” Non-Euclidean Geometry Fractal Geometry Topology: Möbius Strip and “rubber sheet geometry” Non-Euclidean Geometry Fractal Geometry Print Gallery, lithograph, 1956 Balcony, lithograph, 1945 Circle limit III, woodcut, 1959 Square limit, woodcut, 1964 Möbius Strip I, wood engraving, 1961 Möbius Strip II, wood engraving, 1963 © Belén Pena y Luis M. Rodríguez

Perspective: Cylinder perspective 3 Dimensional Representation Perspective: Cylinder perspective 3 Dimensional Representation Escher's Themes III: Projecting 3dimensional space to the plane Belvedere (Detail), lithograph, 1958 Relativity, lithograph, 1953 Ascending and Descending, lithograph, 1960 Reptiles, lithograph, 1943 Up and Down, lithograph, 1947 © Belén Pena y Luis M. Rodríguez

Resources  On line (websites & videos)  See chapter Resources in your student´s workbook  Art Glossary  See on your student´s workbook Activities. Art Assignments.  PPT Presentation  To download from IES Albayzin website ( dpto-geografia-e-historia/396-4o-eso-art-a-maths-mc-escher ) dpto-geografia-e-historia/396-4o-eso-art-a-maths-mc-escher  MC Escher. Art & Maths. Art Assigments ∞ Resources.  One, Two and Three-point Perspective  La derisoire effervescence des comprimes by F. Boucq

© Belén Pena