1. Provide a general definition of tessellation. Define what Escher meant by regular tessellation of the plane. Link to 5 examples of Escher’s regular tessellations.
- Tessellation - arrangement of polygons without any gaps or overlap in a repeated process.
- Escher's purposes of regular tessellation of the plane was to combine different shapes with one another that can only be applied through proper mathematics. With Escher's influence from his visits to the Alhambra, he became inspired to further his research towards the regular tessellation of the plane.
- Escher wrote two books that focused on the regular tessellation of the plane. His first book was titled, Regular Division of the Plane with Asymmetric Congruent Polygons. His first book focused on his research to further his knowledge in shapes and symmetry. Also, in 1958 Escher wrote another book titled Regular Division of the Plane, which primarily focused on how mathematics has opened many doors in the art world. Link (Final Exam --> Links --> Escher's Regular Tessellation of the Plane)
- George Polya's paper, Uber die Analogle des Kristallsymmetrie in der Ebene, helped Escher get a better understanding of tessellations he had experienced during his visits to the Alhambra. Polya classified the 17 Plane Symmetry groups which heavily influenced Escher's creation of his own regular tessellations of the plane.
- Polya's 17 symmetry groups influenced Escher's rotation and transformation tessellations. Polya discovered exactly what shapes you can and cannot tessellate and how you can tessellate those shapes symmetrically. Escher made hundreds of woodcuts and lithographs of tessellations with the application of rotation and transformation due to Polya's findings . Link (Final Exam --> Links --> Escher vs. Polya)
- Platonic solids are convex polyhedrons in a three-dimensional space. It is constructed by congruent regular polygonal faces with the same number of faces meeting at each vertex. The five solids are: Tetrahedron, Cube, Octahedron, Dodecahedron, and Icosahedron.
- Escher's Solid is a complexity of polygons when formed together, create platonic solids like dodecahedrons and ocrahedrons. Escher's Solid is perceived to be a star in space in some works like Stars (1948) and sculptures on top of already complex figures like Waterfall (1961).
- Link (Final Exam --> Links --> Platonic Solids)
- The telegraph wire effect is the effect that provides different views of perspective. Ernst states two important rules, "1.) Horizontal and vertical lines running parallel to the picture are to be depicted as horizontal and vertical lines, Like distances from these lines in reality are to be shown as like distances in the picture. 2.) Parallel lines that recede from us are to be depicted as lines passing through a single point, i.e., the vanishing point. Like distances along these lines are not to be depicted as like distances in the picture." (Ernst 2007. Page 46) Link (Final Exam --> Links --> Telegraph Wire Effect.)
- Iconographic Analysis - Iconographic analysis is used to establish the meaning of a particular work at a particular time
- Formal Analysis - An explanation of visual structure, of the ways in which certain visual elements have been arranged and function within a composition.
- Stylistic Analysis - describes the techniques and precise aspects applied into the art by the artist. Analyzing the style and technique the artists used.
- Historical Analysis - What matters is the way the context is described and what kinds of relationships are established between it and the work or works being studied. This type of analysis is richest when it creates a web of very specific connections.
- (http://writingaboutart.org)
- One particular kind of visual description is also the oldest type of writing about art in the West. Called ekphrasis, it was created by the Greeks. The goal of this literary form is to make the reader envision the thing described as if it were physically present. In many cases, however, the subject never actually existed, making the ekphrastic description a demonstration of both the creative imagination and the skill of the writer. (http://writingaboutart.org/pages/ekphrasis.html)
- Putting Escher's work into context is a difficult task due to the complexity in his works and lack of art criticism Escher received. As students, you must find a understanding point of Escher and his work to realize just what he implemented in his art. Understanding Escher's influences and research generates appreciation for his works. Escher's tessellations, hyperbolic geometries, and impossible figures are so complex and quite intriguing. These art styles are unique to Escher which makes the study of his works relate to Escher personally.
- M.C. Escher's work is so creative and unique compared to most artist during his time. Escher's creativity and imagination helped him succeed to create all of the mathematical pieces Escher created. Each piece Escher created, I felt obligated to appreciate his effort and knowledge he implemented into all of his artwork. Learning more about M.C. Escher's work, I have learned to appreciate such creativity others have and help understand how he came about the ideas he translated into artwork. All in all, this course on M.C. Escher helped me expand my imagination and appreciate works that hard work and effort were applied.
- M.C. Escher's work has been largely ignored by art critics due to the complexity, science, and mathematics to Escher's pieces. Art critics do not appreciate artwork that tends to be mathematical or scientific due to the lack of ideology and imagination. Art critics tend to appreciate artwork that gives viewers feelings of happiness, proper color schematics, and creativity of the idea behind the art work. Escher's pieces tend to be more mathematical and scientific rather than imaginative and creative. Which makes the viewers feel obligated to put forth effort to understand the piece's complexity. By doing so, this eliminates the certain attractiveness art critics look for. "Escher mainly received recognition from mathematicians, crystallographers and physicists. Anyone who was willing to approach his work without preconceived ideas will derive enjoyment from it, whereas those whose only approach is through commentaries provided by art historians will discover that these latter latter are no more than a hindrance," (Ernst 2007. Page 20)
- Thesis- a proposition stated or put forward for consideration, especially one to be discussed and proved or to be maintained against objections.
- Strengths - Strengths of my thesis are efficient sources and plenty of information on my topic. Optical illusions and Impossible Worlds is a very interesting and intriguing topic with great visual examples provided by M.C. Escher. I was able to defend and discuss my thesis thoroughly throughout my paper.
- Weaknesses - Some weaknesses of my thesis is perhaps a topic that is too broad. Also, found some difficulty explaining certain aspects of my research that held a lot of substance.
- Overall, I felt pretty good about my research paper on M.C. Escher's Optical Illusions and Impossible Worlds. My thesis was backed with sufficient information and sources on Escher's works. Also, I was able to defend and discuss my thesis efficiently with implementation of useful visual descriptions and art analysis.
- The student comments I received from William Ryan were much more useful than the comments and revision from the writing center. William provided more in-depth changes and was able to bring out more clarity in my paper. The student in the writing center made little changes to my paper, only a few grammatical mistakes and citation mistakes. Although the citation mistakes were very important, I did not receive the revisions i hoped to receive from the writing center. The revisions made by William improved my paper much more than the student from the writing center.
- William Ryan changes example: Before: “It may be that the appreciation of such visual paradoxes is one sign of that kind of creativity possessed by the best mathematicians, scientists and artists. M. C. Escher's artistic output included many illusion pictures and highly geometric pictures, which some might dismiss as `intellectual mathematical games' rather than art. But they hold a special fascination for mathematicians and scientists,” (Simanek 1996) Belvedere (1958) is a piece that Escher implemented impossible structures.
- After: “It may be that the appreciation of such visual paradoxes is one sign of that kind of creativity possessed by the best mathematicians, scientists and artists. M. C. Escher's artistic output included many illusion pictures and highly geometric pictures, which some might dismiss as `intellectual mathematical games' rather than art. But they hold a special fascination for mathematicians and scientists,” (Simanek 1996) Belvedere (1958) is a piece that has visually reasonable appearance, but a mathematically impossible construction. Creating an impossible figure and optical illusion all in one piece of art.
- Writing center citation example: Before: “The conventions of classical perspective are very effective at simulating such reality, permitting 'photographic' representation of nature. This representation is incomplete in several ways. It does not allow us to see the scene from different vantage points, to walk into it, or to view objects from all sides.” (Simanek 1996).
- After: “The conventions of classical perspective are very effective at simulating such reality, permitting 'photographic' representation of nature. This representation is incomplete in several ways. It does not allow us to see the scene from different vantage points, to walk into it, or to view objects from all sides,” (Simanek 1996)
- Link (Papers-->Student & Writing Center Comments)