escher exhibition: art and maths. presentation (4º eso)

8/3/2019 Escher Exhibition: Art and Maths. Presentation (4º ESO)

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ART & MATHS:

M.C. Escher“Although I am absolute innocent of training orknowledge in the exact sciences, I often seem tohave 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)

M.C. Escher (1898-1972) is one of the world´smost famous graphic artists, although occasionallyproduced 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




Escher's Artwork

Escher´sartwork

Art(technique, poetry,

beauty) Perceptions of reality as

constructions

Geometry & Mathematics




M.C. Escher at the Alhambra

One major source of inspiration for Escher´s designs is theAlhambra. He became fascinated by the R EGULAR DIVISION OF THE PLANE and developed patterns -TESSELLATIONS- filling the planewith regular geometric structures and no overlaps or gaps.




ART & MATHS: M.C. Escher

A BILINGUAL CROSS-CURRICULAR

ACTIVITY - 4 ºESO -

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 andMaths. Several resources and a student´s workbook to carryout different assignments on Maths and History.



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Biography & Chronological Periods

Early work from 1916 – 1922

Italian Period from 1922 –

1935

Switzerland and Belgium 1935-1941

Back in Holland 1941–

1954

Recognition and Success 1955-1972




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)




Escher's Techniques

PrintmakingMethods

Relief Printing

Woodcut

Wood Engraving

Linocut

Intaglio Mezzotint

Planographic Lithography

Stencilling




Printmaking Techniques

Printmaking Techniques Basic Categories (According to Processes)

Stencilink or paint is

pressed through

a preparedscreen

screenprinting

pochoir

Planographicinked areas

separated from

noninked areas bychemical means

lithography

monotyping

digital techniques

Intaglioink is applied

beneath the original

surface of thematrix

engraving

etching

mezzotint

aquatint

Relief ink is applied to the

original surface of the matrix

woodcut / woodblock( for Asian forms)

wood engraving

linocutmetalcut

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.




Escher's Techniques

PrintmakingMethods - 1 Intaglio Mezzotint

MezzotintThe 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.




Escher's Techniques

PrintmakingMethods - 2 Relief Printing

Woodcut

Wood Engraving

WoodcutUsing 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 onthe 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 EngravingUnlike woodcut, in wood engraving the

wood is sawn perpendicular to the trunk,

producing an extremely hard surface.

By gluing several pieces together, an uniformblock 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.




Escher's Techniques

PrintmakingMethods - 2

Relief Printing Linocut

LinocutPrinting 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.




Escher's Techniques

PrintmakingMethods – 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 maybe 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 unoiledportion 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).




• 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




• Regular Polihedra or PlatonicSolids

• Archimedean SolidsSpace 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




• To represent the world, his world:continuous, dual, dialectic, relativist, cyclic,magic, staggering, bewildering.

• To represent the conflict between realityand imagination

• To represent the perception mystery.

Maths as a tool:Processual Art

• “Mathematics laws are neither creationsnor human inventions. They merely “are”,and they exist completely apart from thehuman spirit”. (Escher)

Maths as magicstructure under

reality

• Despite having no formal training inmathematics, Escher’s artwork hasbeen considered by somemathematicians as a way of visualizingdifficult mathematics concepts.

Maths as a conceptwe can visualized:

Conceptual Art

Escher's Themes: Why Mathematics?




Escher's Themes I: Space Structure

Landscapes, Crossing Worlds and Mathematical forms

• Platonic Solids or (Regular Polyhedra)•Archimedean Solids

Tetrahedral Planetoid , woodcut 1954

Flatworms, lithograph 1959

Waterfall , lithograph, 1961

Stars, wood engraving, 1948




Escher's Themes II: Surface StructureMetamorphosis, 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 StructureMetamorphosis, Cycles – Tessellations and Infinite Universes

• 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




• 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,

1960Reptiles, lithograph, 1943

Up and Down,lithograph, 1947





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 ( http://www.iesalbayzin.org/index.php/departamentos-didacticos/65-

dpto-geografia-e-historia/396-4o-eso-art-a-maths-mc-escher )

MC Escher. Art & Maths. Art Assignments Resources.

One, Two and Three-point Perspective La derisoire effervescence des comprimes by F. Boucq

http://www.iesalbayzin.org/index.php/departamentos-didacticos/65-dpto-geografia-e-historia/396-4o-eso-art-a-maths-mc-escher




























escher exhibition: art and maths. presentation (4º eso)

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