Difference between revisions of "Math and the Art of M. C. Escher"
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| − | ** [[ | + | ** [[The Mathematical Papyri]] |
| − | ** [[ | + | ** [[The Pyramids]] |
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Revision as of 10:38, 23 January 2009
Math and the Art of M.C. Escher
| About This Book | Authors | Copyright |
Euclidean and Non-Euclidean Geometry
- Introduction to Mathematics and M.C. Escher
- M.C. Escher: Life. Work.
- Escher on Display A collection of photographs of Escher art that can be found in the Netherlands. The art represented ranges from items in the Escher museum to pillars, facades, etc in buildings
- Fundamental Concepts: Classifications. Plane Geometry.
- Symmetry and Isometries
- Introduction to Symmetry: Reflections, rotations, and rosette patterns. Color symmetry.
- Frieze Patterns: Translations, glide reflections, and frieze patterns.
- Wallpaper Patterns: Lattices. The 17 groups. Classification flow chart. Escher's use of symmetry.
- Isometry Groups: Isometries. Composition. Multiplication tables. Groups of isometries.
- Fieldtrip: Seeking Symmetry
- Tessellations
- Introduction to Tessellations
- Tessellations by Polygons: Regular tessellations. Triangle tessellations. Quadrilateral tessellations. Convex polygon tessellations.
- Tessellations by Recognizable Figures: Escher's polygon systems. Techniques for tessellation.
- Aperiodic Tessellations Random tessellations and Penrose tessellations.
- Project: Tessellation Art Project
- Non-Euclidean Geometry
- Introduction to Non-Euclidean Geometry
- Spherical Geometry: Geodesics. Angle sum and area. Tessellations. Platonic solids. Duality. Euler characteristic.
- Hyperbolic Geometry: The Poincaré Disk. Hyperbolic tessellations.
- The Three Geometries: The classification of regular tessellations. Axioms in geometry. The shape of the universe.
- Project: Non-Euclidean Geometry Project
Further topics in Geometry and Mathematics
- Similarity and Fractals
- Similarity Transformations: Similarity. Dilation. Iteration.
- Fractals: Self-similarity. Fractals.
- Art and Perception
- Depth and Perspective: Depth in art. Linear Perspective. 2D vs. 3D. Impossible Figures.
- The Fourth Dimension: Dimension. 4D as space. 4D as time. Fourth dimension in art and literature.
- Project: Flatland and the Fourth Dimension
- Project: Art and Mathematics Project
- Fieldtrip: The Saint Louis Art Museum
- History of Egyptian Mathematics
- History and Numbers A discussion of the history of mathematics as well as an explanation of the Egyptian number system.
- The Mathematical Papyri
- The Pyramids
