Assignment asked us to review a book about math and history. After completing assignment we were asked to participate in a group discussion in regards what we have read, learned etc…
Discussion Expectations
As with all discussions, you are expected to initiate topics and provide substantive response the peers work A substantive response will move our understanding forward through comments, questions or new resources.
Student wrote:
“I chose the book M.C. Escher: Visions of Symmetry by Doris Schattschneider (2004) for my book review. The book was a biography of Escher’s life and detailed exploration of how his works were created.
The author’s thesis states “The urge to fill the plane with pieces, fitted snugly next to one another so as to leave no unoccupied space, seems to have been with Escher longer than even he could remember (p. 2).” I think the essence of this book was better captured in the forward by Douglas Hofstadter who states the book is “…about one man’s obsessed exploration of a magical space of potentialities that he discovered on his own when quite young, and then worked for four decades in a frustratingly isolated manner, bewildered by the fact that no one else seemed to see anything like what he saw (p. vii).” Escher created work that was not only unique in the artistic realm but in the world of mathematics and he spent painstaking hours developing rules and systems to govern this work.
The biggest educational piece in this book was the basis of Escher’s work: regular division of the plane. Defined by Escher, himself, regular division of the plane is “The various ways in which the individual pieces in these simple geometric tilings can be related to adjacent congruent pieces by geometric motions are the only ways that motifs with complicated shapes can relate to adjacent copies of themselves in any regular division of the plane (p. 31).” More simply stated, Escher’s works were “arrangements of closed shapes that completely cover the plane without overlapping (Smith, 2015).” His tessellations were not simple, as most could imagine and they were governed by rules set forth by Escher regarding symmetry, specific geometric shapes and color and contrast schemes to name a few. He developed extensive systems and diagrams to create his work and carefully studied calculations and geometry that would be applied to it. He would record his work so precisely thus making his works available for extensive study (Schattschneider, 2004).
Escher was primarily inspired by the field of crystallography which is the study of atomic and molecular structures. Crystallographers are scientists interested in how atoms are arranged and the relationship to its properties (American Crystallography Association, n.d.). Escher had exposure to one memorable professor in the field, George Polya with whom Escher would spend years as a pupil and ultimately as a friend. Escher would craft structures of artistic creations that crystallographers had never conceived of exploring. “By their very nature they [crystallographers] are more interested in the way in which the gate is opened than in the garden lying behind it (Schattschneider, 2004, p. 29).”
This was the first book I have ever read about mathematics but chose it because I have always been intrigued by the art of Escher. I would not say this book inspired me to read others about mathematics but it was definitely intriguing to learn about the precision Escher’s work. I would recommend this book to anyone who is interested in learning about art or mathematics history because the approach was primarily historic. Anyone wishing to learn about Escher’s work specifically from a mathematic or scientific perspective may consider studying Escher’s journals, lectures and educational posters as he did share his works over the years.
American Crystallography Association. (n.d.). Careers in Crystallography: Exploring the Structure of Matter. Retrieved from http://www.amercrystalassn.org/content/pages/main-careers
Schattschneider, Doris. (2004). M.C. Escher: Visions of Symmetry. New York, NY: Harry N. Abrams, Inc.
Smith, B. Sidney. (2015). The Mathematical Art of M.C. Escher. Retrieved from http://platonicrealms.com/minitexts/Mathematical-Art-Of-M-C-Escher/”
*Use U.S sources only
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