View source for Math and the Art of M. C. Escher

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[[EscherMath:About|About This Book]]
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{{toc-part|Part One|Euclidean and Non-Euclidean Geometry}}
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{{toc-chapter|Introduction to Mathematics and M.C. Escher}}
{{toc-section|M.C. Escher|Self-portrait-1929-square.jpg|A brief overview of Escher's life and work.}}
{{toc-section|Escher on Display|Escher_Den_Haag_075-square.jpg|A tour of Escher's work in public and in museums.}}
{{toc-section|Fundamental Concepts|Malevich-Suprematism-square.jpg|Classifications. Plane Geometry.}}
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{{toc-section|The Alhambra and The Alcazar (Spain)|Alhambrasquare.jpg|A tour of Spain's palaces which inspired Escher.}}
{{toc-section|The Geometry of Antoni Gaudi|Alhambrasquare.jpg|The architect Gaudi used a variety of geometric concepts in his designs.}}
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{{toc-chapter|Symmetry and Isometries}}
{{toc-section|Introduction to Symmetry|Fish-vignette.jpg|Reflections, rotations, and rosette patterns. Color symmetry.}}
{{toc-section|Frieze Patterns|Borderpattern-square.jpg|Translations, glide reflections, and frieze patterns.}}
{{toc-section|Wallpaper Patterns| Wallpaper group-p2-3.jpg |Translations, glide reflections, and frieze patterns.}}
{{toc-section|Isometry Groups|Pfm-reptiles.jpg|Isometries. Composition. Multiplication tables. Groups of isometries.}}
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{{toc-chapter|Tessellations}}
{{toc-section|Introduction to Tessellations|Eight-heads-square.jpg| }}
{{toc-section|Tessellations by Polygons|Cristallo03.png|Regular tessellations. Triangle tessellations. Quadrilateral tessellations. Convex polygon tessellations}}
{{toc-section|Tessellations by Recognizable Figures|Reptiles-square.jpg|Escher's polygon systems. Techniques for tessellation. }}
{{toc-section|Aperiodic Tessellations|Cristallo04.png|Random tessellations and Penrose tessellations.}}
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{{toc-chapter|Non-Euclidean Geometry}}
{{toc-section|Introduction to Non-Euclidean Geometry|Uniform tiling 73-t012.png|General introduction.}}
{{toc-section|Spherical Geometry|Sphere-square.jpg|Geodesics. Angle sum and area. Tessellations. Platonic solids. Duality. Euler characteristic.}}
{{toc-section|Hyperbolic Geometry|Circle-Limit-III.jpg|The Poincaré Disk. Hyperbolic tessellations.}}
{{toc-section|The Three Geometries|Toroidal coordinates.png|The classification of regular tessellations. Axioms in geometry. The shape of the universe.}}
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{{toc-chapter|Activities<br>For Part One}}
{{toc-section|Seeking Symmetry|Fieldtrip-1.jpg|Field trip.}}
{{toc-section|Symmetric Art Project|Project.jpg|Art Project.}}
{{toc-section|Tessellation Art Project|Project.jpg|Art Project.}}
{{toc-section|Non-Euclidean Art Project|Project.jpg|Art Project.}}
{{toc-part-end}}
<!-- ****  Part Two **** -->
{{toc-part|Part Two|Topics in Geometry and Mathematics}}
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{{toc-chapter|Similarity and Fractals}}
{{toc-section|Similarity Transformations|Development-II-v2.jpg|Similarity. Dilation. Iteration.}}
{{toc-section|Fractals|Droste-square.jpg|Self-similarity. Fractals.}}
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{{toc-chapter|Art and Perception}}
{{toc-section|Depth and Perspective|Welder-square.jpg|Depth in art. Linear Perspective. 2D vs. 3D. Impossible Figures.}}
{{toc-section|The Fourth Dimension|Salvador-Dali-Profile-of-Time.jpg|Dimension. 4D as space. 4D as time. Fourth dimension in art and literature.}}
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{{toc-chapter|Topology}}
{{toc-section|The Mobius Band and Other Surfaces|Mobius-strip-I-square.jpg}}
{{toc-section|Knot Theory|Knot-Norse-broach.png}}
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{{toc-chapter|Egyptian Mathematics}}
{{toc-section|History and Numbers|Eye-of-Horus.svg|A discussion of the history of mathematics as well as an explanation of the Egyptian number system.}}
{{toc-section|The Mathematical Papyri|PapyrusTOC.jpg|Includes an overview of some of the geometry contained in the Rhind mathematical papyrus and the Moscow papyrus.}}
{{toc-section|The Pyramids|Cheops pyramid-square.jpg|The development of the Egyptian pyramids, with a discussion of the seqed.}}
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{{toc-chapter|Activities<br>For Part Two}}
{{toc-section|The Saint Louis Art Museum|Fieldtrip-1.jpg|Field trip.}}
{{toc-section|Flatland and the Fourth Dimension|Project.jpg|Creative Project.}}
{{toc-section|Visual Deception Project|Project.jpg|Art Project.}}
{{toc-section|Art and Mathematics Project|Project.jpg|Art Project.}}
{{toc-part-end}}
<!-- ****  Appendix **** -->
{{toc-part|Other|K-12 Geometry}}
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{{toc-chapter|High School Materials}}
{{toc-section|High School Materials|No-three-in-line.png|High school level geometry materials - introductory level}}
{{toc-section|Math at the Art Museum|Saint-louis-art-museum.jpg|Lesson plans}}
{{toc-part-end}}

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[[EscherMath:Resources|Instructor Resources]] &emsp; &emsp; &emsp;  [[EscherMath:Copyrights|Copyrights]]
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