Transcript ART & MATHS: MC Escher

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)
 M.C. Escher (1898-1972) 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
Art
(technique, poetry,
beauty)
Perceptions of
Geometry &
reality as
Mathematics
constructions
Escher´s
artwork
© Belén Pena y Luis M. Rodríguez
M.C. Escher at the Alhambra
One major source of inspiration for Escher´s designs is the
Alhambra. He became fascinated by the REGULAR DIVISION OF THE
PLANE and developed patterns -TESSELLATIONS- 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

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 y Luis M. Rodríguez
© Belén Pena
© Belén Pena y Luis M. Rodríguez
© Belén Pena y Luis M. Rodríguez
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
© 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)
© Belén Pena y Luis M. Rodríguez
Escher's Techniques
Intaglio
Mezzotint
Woodcut
Printmaking
Methods
Relief Printing
Wood Engraving
Linocut
Planographic
Lithography
Stencilling
© Belén Pena y Luis M. Rodríguez
Printmaking Techniques
Printmaking Techniques
Basic Categories (According to Processes)
Relief
Intaglio
ink is applied to the
original surface of
the matrix
ink is applied
beneath the original
surface of the
matrix
woodcut / woodblock
(for Asian forms)
engraving
wood engraving
linocut
metalcut
etching
mezzotint
aquatint
Planographic
Stencil
inked areas
separated from
noninked areas by
chemical means
ink or paint is
pressed through
a prepared
screen
lithography
monotyping
digital techniques
screenprinting
pochoir
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
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
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.
Woodcut
Wood Engraving
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 crosshatching. 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
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
Lithography 1
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.
© Belén Pena y Luis M. Rodríguez
Planographic
Lithography 2
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.
Lithography
Lithography 3
4. The stone is inked
with a roller. The ink
will adhere only to the
oily areas; the watersoaked portions will
repel the ink.
5. Printing is done on a
lithographic press
(equipped with a
scraper).
Escher's Themes
Space Structure
• Landscapes
• Crossing Worlds
• Mathematical forms
Surface Structure
• Metamorphosis
• Cycles - Tessellations
• Infinite Universes
Projecting
3dimensional space
to the plane
• Perspectives & Arquitectures
• Impossible Structures &
Worlds
© Belén Pena y Luis M. Rodríguez
Escher's Themes:
Mathematics in Escher 's Artwork
Space Structure
Surface Structure
Projecting
3dimensional space
to the plane
• Regular Polihedra or Platonic
Solids
• Archimedean Solids
• Regular Division of the plane: Reflections,
Translations or glides and Rotations
• Topology: Möbius Strip
• Non-Euclidean Geometry and Fractal
Geometry
• Perspective: Cylinder
Perspective
• 3 Dimensional Representation
© Belén Pena y Luis M. Rodríguez
Escher's Themes: Why Mathematics?
Maths as a tool:
Processual Art
Maths as magic
structure under
reality
Maths as a concept
we can visualized:
Conceptual Art
• 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.
• “Mathematics laws are neither creations
nor human inventions. They merely “are”,
and they exist completely apart from the
human spirit”. (Escher)
• Despite having no formal training in
mathematics, Escher’s artwork has
been considered by some
mathematicians as a way of visualizing
difficult mathematics concepts.
© 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
Flatworms, lithograph 1959
Stars, wood engraving, 1948
Waterfall, lithograph, 1961
© Belén Pena y Luis M. Rodríguez
Tetrahedral Planetoid, woodcut 1954
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
Horsemen,
1946
Metamorphosis, from his book
“Regular Division of the Plane”, 1938
Cycle, lithograph, 1938
Metamorphosis
© Belén Pena y Luis M. Rodríguez
Escher's Themes II: Surface Structure
Metamorphosis, Cycles – Tessellations and Infinite Universes
Print Gallery,
lithograph, 1956
•Topology: Möbius Strip and
“rubber sheet geometry”
•Non-Euclidean Geometry
•Fractal Geometry
Möbius Strip I, wood engraving, 1961
Balcony, lithograph, 1945
Möbius Strip II, wood engraving, 1963
Circle limit III,
woodcut, 1959
Square limit, woodcut, 1964
© Belén Pena y Luis M. Rodríguez
Escher's Themes III: Projecting
3dimensional space to the plane
Up and Down,
lithograph, 1947
• Perspective: Cylinder perspective
• 3 Dimensional Representation
Relativity, lithograph, 1953
Belvedere (Detail),
lithograph, 1958
Reptiles, lithograph, 1943
© Belén Pena y Luis M. Rodríguez
Ascending and
Descending,
lithograph,
1960
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/65dpto-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 y Luis M. Rodríguez
© Belén Pena
© Belén Pena