# Difference between revisions of "Math and the Art of M. C. Escher"

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* '''History of Egyptian Mathematics''' | * '''History of Egyptian Mathematics''' | ||

** [[History and Numbers]] A discussion of the history of mathematics as well as an explanation of the Egyptian number system. | ** [[History and Numbers]] A discussion of the history of mathematics as well as an explanation of the Egyptian number system. | ||

− | ** [[The Mathematical Papyri]] | + | ** [[The Mathematical Papyri]] Includes an overview of some of the geometry contained in the Rhind mathematical papyrus and the Moscow papyrus. |

− | ** [[The Pyramids]] | + | ** [[The Pyramids]] The development of the Egyptian pyramids, with a discussion of the seqed. |

[[AB test frontpage]] | [[AB test frontpage]] |

## Revision as of 10:41, 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 Includes an overview of some of the geometry contained in the Rhind mathematical papyrus and the Moscow papyrus.
- The Pyramids The development of the Egyptian pyramids, with a discussion of the seqed.