M.C. Escher: Art and Tilings June 17, 1898

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M.C. Escher Art and TilingsJune 17, 1898
March 27, 1971

• By Janine Keizer
• and
• Monica McVicar

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• I could fill an entire second life with working
  on my prints
• - M.C. Escher

Self Portrait, 1943
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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 1898. 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.

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Biography Cont

• His work went almost unnoticed until the 1950s.
• 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
  Penroses to develop many intriguing works of
  art.
• Eschers work encompasses two broad areas the
  geometry of space, and what we may call the logic
  of space.

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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 1936.
  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)
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Tessellation Cont
Reptiles (Lithograph, March 1943)
Regular Division of the Plane Drawing 21, 1938
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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)
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Polyhedra Cont
Order and Chaos
(Lithograph, 1950)
Gravitation (printed as a
black-and-white lithograph and then colored by
hand in watercolor, 1952)
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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.

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Space cont
Circle Limit III (Woodcut, 1958)
Circle Limit V
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Topology

• In addition to Euclidean and non-Euclidean
  geometries, Escher was very interested in visual
  aspects of Topology

Möbius Strip II (Woodcut, 1963)
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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)
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The Logic of Space Cont

• The Penrose triangle, also known as the tribar,
  is an impossible object first created by the
  Swedish artist Oscar Reutersvärd in 1934. The
  mathematician Roger Penrose independently devised
  and popularized it in the 1950s. It is featured
  prominently in the works of artist M.C. Escher.

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The Logic of Space Cont
Waterfall(lithograph, 1961)
Still Life and Street (Woodcut Print, 1937)
High and Low (Lithograph, 1947)
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Cool Prints
Relativity (Lithograph, 1953)
Ascending and Descending (Lithograph
print, March 1960)
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Conclusion

• Eschers 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.

Eschers Eye ( Lithograph, 1946)
Drawing Hands (Lithograph, 1948)
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Questions??
"I can't stop fooling around with our irrefutable
certainties. It is, for example, a pleasure
knowingly to mix up two- and three-dimensionalitie
s? 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)
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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.