MC Escher, Images of Mathematics...

by keenly confronting the enigmas that surround us and by considering and analyzing the observations that I have made I ended up in the domain of mathematics although I am absolutely without training in the exact sciences I often seem to have more in common with mathematicians than with my fellow artists MC Escher born June 17th 1898 was a Dutch graphic artist known worldwide for his mathematically inspired woodcuts lithographs and mezzo teens that feature impossible constructions exploration of infinity architecture and tessellations of the Euclidian and the hyperbolic plane many of his pieces were drawn from unusual perspectives thus creating an ik spatial effects in his graphic art he portrayed mathematical relationships among shapes figures and space he explored repeating patterns of interlocking motifs using black and white to enhance different dimensions integrated into his prints were mirror images of combs spheres cubes rings and spirals although Asher did not have any formal mathematical training his understanding of mathematics was largely visual and intuitive MC Escher became fascinated with the regular division of the plane by employing a repeated tiling called tessellation a tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps throughout the Second World War he vigorously pursued his hobby by drawing 62 of the 137 regular division drawings he would make in his lifetime Asher's work had a strong mathematical component and more than a few of the worlds which he drew are built around impossible objects such as the Necker cube and the Penrose triangle a long time ago I chanced upon this domain of regular division of the plane in one of my wanderings however on the other side I landed in a wilderness I came to the open gate of mathematics sometimes I think I have covered the whole area and then I suddenly discover a new path and experience fresh delights around 1956 Asher's interests changed again taking regular division of the plane to the next level by representing infinity on a fixed two-dimensional plane he had put his designs onto a variety of 3-dimensional objects such as columns and spheres again in an attempt to impart an endless perspective to his work he later tried working with the concept of similarities using identical motifs of diminishing size arranged in a series of concentric circles Asher used the poincaré disk model of hyperbolic geometry for his circle limit patterns and these models Euclidian objects are used to represent objects in hyperbolic geometry the points of hyperbolic geometry in this model are just the Euclidean points within a Euclidean bounding circle in this way one creates as it were a universe a geometrical enclosure if the progressive reduction in size radiates in all directions at an equal rate then the limit becomes a circle the hyperbolic lines are represented by circular arcs orthogonal to the bounding circle the plunk or a disk model was appealing to Escher since an infinitely repeating pattern could be shown in a bounded area and shapes remain recognizable even for small copies of the motif Asher was more interested in the Euclidean properties of the disk model than the fact that it could be interpreted as hyperbolic geometry Asher's artwork is especially well liked by mathematicians and scientists who enjoy his use of polyhedra and geometric distortions he continued to develop and enhance this field and produced many more prints using both circles and squares as the frames for his works he also studied the mathematical concepts of topology and learned additional concepts of mathematics from the British mathematician Roger Penrose from this knowledge he created waterfall and up and down featuring irregular perspectives similar to the concept of the mobius strip Asher's works covered a variety of subjects throughout his life over a hundred and fifty colorful and recognizable works testify to Escher's ingenuity and vision his art continues to amaze and Wonder millions of people all over the world in his work we recognize his keen observation of the world around us and the expressions of his own fantasies a world which is far away from our general perception of reality a world of mathematics a world of abstraction but then as always we can make connections between this abstract world and the real world MC Escher shows us that reality is wondrous comprehensible and fascinating you

Channel: Shawn Taylor

Views: 286,083

Keywords: mc, escher, mathematics, breezwood, hughes, drive, circle, limit

Id: t-Gcz9FIB4w

Length: 10min 51sec (651 seconds)

Published: Mon May 18 2009