escher exhibition: art and maths. presentation (4º eso)
TRANSCRIPT
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
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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
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Escher's Artwork
© Belén Pena y Luis M. Rodríguez
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Escher's Artwork
Escher´sartwork
Art(technique, poetry,
beauty) Perceptions of reality as
constructions
Geometry & Mathematics
© Belén Pena y Luis M. Rodríguez
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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.
© Belén Pena y Luis M. Rodríguez
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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.
© Belén Pena y Luis M. Rodríguez
8/3/2019 Escher Exhibition: Art and Maths. Presentation (4º ESO)
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8/3/2019 Escher Exhibition: Art and Maths. Presentation (4º ESO)
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© Belén Pena
© Belén Pena y Luis M. Rodríguez
8/3/2019 Escher Exhibition: Art and Maths. Presentation (4º ESO)
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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
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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)
© Belén Pena y Luis M. Rodríguez
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Escher's Techniques
PrintmakingMethods
Relief Printing
Woodcut
Wood Engraving
Linocut
Intaglio Mezzotint
Planographic Lithography
Stencilling
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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.
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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.
© Belén Pena y Luis M. Rodríguez
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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.
© Belén Pena y Luis M. Rodríguez
8/3/2019 Escher Exhibition: Art and Maths. Presentation (4º ESO)
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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.
© Belén Pena y Luis M. Rodríguez
8/3/2019 Escher Exhibition: Art and Maths. Presentation (4º ESO)
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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).
© Belén Pena y Luis M. Rodríguez
8/3/2019 Escher Exhibition: Art and Maths. Presentation (4º ESO)
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• 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
8/3/2019 Escher Exhibition: Art and Maths. Presentation (4º ESO)
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• 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
© Belén Pena y Luis M. Rodríguez
8/3/2019 Escher Exhibition: Art and Maths. Presentation (4º ESO)
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• 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?
© Belén Pena y Luis M. Rodríguez
8/3/2019 Escher Exhibition: Art and Maths. Presentation (4º ESO)
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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
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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
8/3/2019 Escher Exhibition: Art and Maths. Presentation (4º ESO)
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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
© Belén Pena y Luis M. Rodríguez
8/3/2019 Escher Exhibition: Art and Maths. Presentation (4º ESO)
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• 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
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© 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 ( 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
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© Belén Pena
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© Belén Pena
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