M.C. Escher
Maurits Cornelis Escher (Leeuwarden, June 17, 1898 – March
27, 1972 in Laren) was a Dutch mathematical artist known for his
woodcuts, lithographs and mezzotints which feature impossible constructions,
explorations of infinity, and tessellations.
Youth
Maurits Cornelis, or Mauk as he was to be nicknamed, was born in
Leeuwarden (Friesland), the Netherlands. He was the youngest son
of civil engineer George Arnold Escher and his second wife, Sarah
Gleichman. In 1903, the family moved to Arnhem where he took carpentry
and piano lessons until the age of thirteen.
From 1912 until 1918 he attended secondary school. Though he excelled
at drawing, his grades were generally poor, and he was required
to repeat the second form. In 1919 Escher attended the Haarlem School
of Architecture and Decorative Arts. He briefly studied architecture,
but switched to decorative arts and studied under Samuel Jesserun
de Mesquita, an artist with whom he would remain friends for years.
In 1922 Escher left the school, having gained experience in drawing
and particularly woodcutting. Sadly, de Mesquita, his wife and son
were murdered by the Nazis in early 1944.
Marriage and later life
Escher travelled to Italy regularly in the following years. It
was in Italy that he first met Jetta Umiker, the woman whom he married
in 1924. The young couple settled down in Rome and stayed there
until 1935, when the political climate under Mussolini became unbearable.
The family next moved to Châteaud'Oex, Switzerland where
they remained for two years.
Escher, who had been very fond of and inspired by the landscape
in Italy, was decidedly unhappy in Switzerland, so in 1937, the
family moved again, to Ukkel, a small town near Brussels, Belgium.
World War II forced them to move for the last time in January 1941,
this time to Baarn, the Netherlands, where Escher lived until 1970.
Most of Escher's betterknown pictures date from this period. The
sometimes cloudy, cold, wet weather of the Netherlands allowed him
to focus intently on his works, and only during 1962, when he endured
surgery, was there a time when no new images were created.
Escher moved to the RosaSpier house in Laren in the northern Netherlands
in 1970, a retirement home for artists where he could have a studio
of his own. He died at the home on the 27th of March 1972, he was
73 years of age. Escher and Umiker had three sons.
Works
Well known examples of his work include Drawing Hands, a work in
which two hands are shown drawing each other, Sky and Water, in
which light plays on shadow to morph fish in water into birds in
the sky, and Ascending and Descending, in which lines of people
ascend and descend stairs in an infinite loop, on a construction
which is impossible to build and possible to draw only by taking
advantage of quirks of perception and perspective.
Escher's work has a strong mathematical component, and many of
the worlds which he drew are built around impossible objects such
as the Necker cube and the Penrose triangle. Many of Escher's works
employed repeated tilings called Tessellations. Escher's artwork
is especially wellliked by mathematicians and scientists who enjoy
his use of polyhedra and geometric distortions. For example, in
Gravity, multicolored turtles poke their heads out of a stellated
dodecahedron.
One of his most notable works is the piece Metamorphosis III, which
is wide enough to cover all the walls in a room, and then loop back
onto itself.
He used lithographs and woodcuts as media. In his graphic art,
he portrayed mathematical relationships among shapes and figures
to space. Additionally, he explored interlocking figures using black
and white to enhance different dimensions. Integrated into his prints
were mirror images of cones, spheres, cubes, rings, and spirals.
This results in circular waterfalls and endless staircases. (Escher,
M. C. 357)
In addition to sketching landscape and nature in his early years,
he also sketched insects, which frequently appeared in his later
work. His first artistic work was completed in 1922, which featured
eight human heads divided in different planes. Later in about 1924,
he lost interest in “regular division” of planes, and
turned to sketching landscapes in Italy with irregular perspectives
that are impossible in natural form.
Mathematical influence in his work emerged in about 1936, when
he was journeying the Mediterranean with the Adria Shipping Company.
Specifically, he became interested with order and symmetry. Escher
described his journey through the Mediterranean as “the richest
source of inspiration I have ever tapped.”
After the journey, at the Alhambra Palace, Escher tried to improve
upon the art works of Moors and used his sketches as basic geometric
grid, which then he built on with additional designs, mainly animals
such as birds and lions.
His first study of mathematics, which would later lead to its incorporation
into his art works, began with George Pólya’s academic
paper on plane symmetry groups sent to him by his brother Berend.
This paper inspired him to learn the concept of the 17 plane symmetry
groups. Utilizing this mathematical concept, Escher created periodic
tiling with 43 colored drawings of different types of symmetry.
From this point on he developed a mathematical approach to expressions
of symmetry in his art works. For the years following 1937 he created
woodcuts using the concept of the 17 plane symmetry groups.
In 1941 Escher wrote his first notebook, now publicly recognized,
called Regular Division of the Plane with Asymmetric Congruent Polygons,
which detailed his mathematical approach to artwork creation. His
intention in writing this was to aid himself in progressing the
integration of mathematics into art. Escher is considered a research
mathematician of his time because of his documentation with this
notebook. In this notebook, he studied color based division, and
developed a system of categorizing combinations of shape, color,
and symmetrical properties. By studying these areas, he explored
an area that later mathematicians labeled crystallography, an area
of mathematics.
Around 1956 Escher explored the concept of representing infinity
on a twodimensional plane. Discussions with Canadian mathematician
H.S.M. Coxeter inspired Escher’s interest in hyperbolic tessellations,
which are regular tilings of the hyperbolic plane. Escher’s
work Circle Limit I demonstrates this concept. In 1995, Coxeter
verified that Escher had achieved mathematical perfection in his
etchings in a published paper. Coxeter wrote, "[Escher] got
it absolutely right to the millimetre."
Escher later completed Circle Limit II, III and IV. These works
continued to demonstrate his ability to create perfectly consistent
mathematical designs. His works gained him fame: He was awarded
the Knighthood of the Oranje Nassau award in 1955. Subsequently
he regularly designed art for dignitaries around the world.
In 1958 he published a paper called Regular Division of the Plane,
in which he described the systematic buildup of mathematical designs
in his artworks. He emphasized, "[Mathematicians] have opened
the gate leading to an extensive domain."
Overall, his early love of Roman and Italian landscapes and of
nature led to his interest in regular division of a plane. He used
the media woodcuts, lithographs, and mezzotints. In his lifetime
he created over 150 colored works utilizing the concept of regular
division of a plane. Other mathematical principals evidenced in
his works include hyperbolic plane on a fixed 2dimensional plane,
and application threedimensional objects such as spheres, columns,
and cubes into his works. For example, in a print called "Reptiles,"
he combined two and threedimensional images. In one of his papers,
Escher emphasized the importance of dimensionality to him and described
himself as "irritated" by flat shapes: "I make them
come out of the plane."
Topology is another mathematical concept he studied in his life.
Topology is the study of properties that are left unchanged by continuous
deformation. Topology is the founding concept for its branches general
(pointset) topology, algebraic topology, and differential topology.
Escher learned additional concepts in mathematics from British mathematician
Roger Penrose. From the new knowledge he created Waterfall and Up
and Down, featuring irregular perspectives similar to the concept
of the Möbius strip; Möbius being a mathematician who
studied topology.
Escher printed Metamorphosis I in 1933, which was a beginning part
of a series of designs that told a story through the use of pictures.
These works demonstrated a columniation of Escher’s skills
to incorporate mathematics into art. In Metamorphosis I, he transformed
convex polygons into regular patterns in a plane to form a human
motif. This effect symbolizes his life change of interest from landscape
and nature to regular division of a plane.
After 1953 Escher was a lecturer to many organizations. A planned
series of lectures in North America in 1964 was cancelled due to
illness, but the illustrations and text for the lectures, written
out in full by Escher, was later published as part of the book Escher
on Escher. In July of 1969, he finished his last work before his
death, a woodcut called Snakes. It features etchings of patterns
that fade to infinity both to the center and the edge of a circle.
Snakes transverse the circle and the patterns in it, with their
heads sticking out of the circle.
During his life time he painted the selfportraits Reflection in
a Glass Ball and Rind, which combined a selfportrait integrated
with irregular perspectives. (O'Connor )
