Chem Lecture Notes Ionic Solids

Chem Lecture Notes - Mathematical Art of M.C Escher Platonic Realms MiniText http/www.mathacademy.com/pr/minitext/escher/index.asp INTRODUCTION THE

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Mathematical Art of M.C. Escher -- Platonic Realms MiniText http://www.mathacademy.com/pr/minitext/escher/index.asp 1 of 10 4/28/04 9:19 AM Self Portrait (36k) INTRODUCTION TESSELLATIONS POLYHEDRA THE SHAPE OF SPACE THE LOGIC OF SPACE SELF-REFERENCE For me it remains an open question whether [this work] pertains to the realm of mathematics or to that of art. – M.C. Escher Click on any Escher thumbnail image to view the larger version. Valued Sponsors All M.C. Escher works and images copyright © Cordon Art B.V., PO Box 101, 3740 AC The Netherlands. Used by permission. M.C. Escher (TM) is a Trademark of Cordon Art B.V. No M.C. Escher image may be produced, reproduced, INTRODUCTION aurits Cornelis Escher, who was born in Leeuwarden, Holland in 1898, created unique and fascinating works of art that explore and exhibit a wide range of mathematical ideas. While he was still in school his family planned for him to follow his father's career of architecture, but poor grades and an aptitude for drawing and design eventually led him to a career in the graphic arts. His work went almost unnoticed until the 1950’s, but by 1956 he had given his first important exhibition, was written up in Time magazine, and acquired a world-wide reputation. Among his greatest admirers were mathematicians, who recognized in his work an extraordinary visualization of mathematical principles. This was the more remarkable in that Escher had no formal mathematics training beyond secondary school. As his work developed, he drew great inspiration from the mathematical ideas he read about, often working directly from structures in plane and projective geometry, and eventually capturing the essence of non-Euclidean geometries, as we will see below. He was
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Mathematical Art of M.C. Escher -- Platonic Realms MiniText http://www.mathacademy.com/pr/minitext/escher/index.asp 2 of 10 4/28/04 9:19 AM Alhambra sketch (62k) stored in a retrieval system, or transmitted in any form or by any means – electronic, mechanical, photocopying, recording, or otherwise – without the written permission of the copyright owner. Visit the official Escher site at www.mcescher.com . You can make your own models of the regular polyhedra, using Platonic Solids Model Paper available in Downloadables . also fascinated with paradox and "impossible" figures, and used an idea of Roger Penrose’s to develop many intriguing works of art. Thus, for the student of mathematics, Escher’s work encompasses two broad areas: the geometry of space, and what we may call the logic of space. TESSELLATIONS egular divisions of the plane, called “tessellations,” are arrangements of closed shapes that completely cover the plane without overlapping and without leaving gaps. Typically, the shapes making up a tessellation are 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 irregular – and took special delight in what he called
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This note was uploaded on 05/26/2010 for the course CHEM 416 taught by Professor Staff during the Fall '08 term at University of Washington.

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Chem Lecture Notes - Mathematical Art of M.C Escher Platonic Realms MiniText http/www.mathacademy.com/pr/minitext/escher/index.asp INTRODUCTION THE

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