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Free
History Term
Paper - Mathematical Perspective in the Works of M.C. Escher
A resident of Leeuwarden, Holland,
and Maurits Cornelis Escher was born in 1898. He became
recognized because of his exclusive and captivating mathematical
creations in the works of art that explore and demonstrate a
broad array of mathematical thoughts. Against the will of his
family to turn into an architect, he had the talent for drawing
and design, which eventually led him to a career in the graphic
arts. His work was not much known till mid 50’s when in 1956 his
foremost important exhibition, was published in Time magazine,
which attained a universal repute. Mathematicians were one of
the leading admirers, who acknowledged his effort as an amazing
vision of mathematical ethics in spite of the fact that Escher
had no proper mathematics education except till secondary school
[Platonic Realm].
The more his works got matured, the more he got stimulated from
the already held mathematical ideas while understanding the
geometry of structures and eventually utilized the geometrical
principles in his master pieces. He looks enthralled with
impossibility of the figures, and produced some intriguing works
of art. M.C. Escher possessed exceptional visualization and
perceptions. A number of the Escher’s mathematical ideas are not
found somewhere else, specifically the interlocking shapes of
people, birds and fish and reptiles, which recur on an even
surface with no space in between.
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The Mathematical Art
When asked about his style by an interviewer, Escher had replied
about his aspiration to fill the space and his desire to fill a
restricted level of surface without gaps that stirred much of
his work [Biographical Sketches of Mathematical Giants]. His
desire was further enhanced when he visited the city of Granada
in 1922 where he happened to visit Alhambra palace, which had
been built in the fourteenth century as a house for the last of
the Moorish courts in Spain. He was fascinated by the designs of
the building specifically the walls and floors which were
wrapped with complex designs that were simple, yet at the same
time were very detailed. The regular divisions of the plane,
called “tessellations,” are arrangements of closed shapes that
completely cover the plane without overlapping and without
leaving gaps. These are the polygons or similar regular shapes,
such as the square tiles often used on floors. Escher, however,
was fascinated by every kind of tessellation, regular and
asymmetrical, and took special delight in what he called
“metamorphoses,” in which the shapes changed and interacted with
each other, and sometimes even broke free of the plane itself.
This had motivated him to fill a plane with repeated contiguous
shapes having no recognizable human or animal form and other
simple geometric shapes. Un aware of the mathematical principles
behind his work he continued working till until1940 he began his
work for depicting standard partition of a flat surface. The
work of Escher primarily contained a type of two-dimensional
crystallography, which at present has become a science dealing
with the formation and structure of crystals and rocks etcetera.
Having read works of other artists i.e. Polya, he used some
basic geometric motions to create regular division of a plane
including rotation, translation, reflection and
glide-reflection. He worked on the development of a total theory
for the regular division of a plane with a similar pattern of
shapes that were not convex polygons. Ultimately he could reach
his theory of "quadrilateral systems" in 1941, which was
published, in his book "Regular Division of the Plane with
Asymmetric Congruent Polygons." He also worked on the
creation of images that reduce in size until they became
considerably minute. To create these prints the geometric
principle of similarity is utilized in which the exact same
shape but decreased in size is obtained.
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It stands proved that of all the regular polygons, only the
triangle, square, and hexagon can be used for a tessellation.
Escher used these basic patterns in his tessellations; applying
what geometers would call reflections, glide reflections,
translations, and rotations .He also made these patterns by
“deforming ” the fundamental form to depict them into animals,
birds, and other figures. Escher's work also enclosed a
diversity of themes all through his life. His initial
descriptions, Roman and Italian landscapes and of nature,
finally led to expected partition of the plane. Many of his
mathematical works were obtained from extraordinary view
creating mysterious spatial special effects. Over 150 vibrant
and identifiable works confirm the Escher's originality and
curiosity in regular division of the plane. [Maurits Cornelius
Escher]
Conclusion
Escher throughout his life saw the
beauty in structure and infinity and forced the idea of
meaningful lines into the mathematical framework of regular
plane division. He liked to challenge the logic of seeing. One
can see the mathematical divisions in form of the white birds
and regard the black as background. The black and white horses
can be seen separately and the black fish can be regarded as the
white as background.
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