Presentation on theme: "Professor Emeritus of Mathematics"— Presentation transcript:
1 Professor Emeritus of Mathematics Using MAPLE to Construct Repeating Patterns and Several Tessellations Inspired by M. C. EscherElliot A. TanisProfessor Emeritus of MathematicsHope CollegeMarch 2, 2006
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8 A Computer Algebra System (CAS) such as MAPLE can be used to construct tessellations. The way in which tessellations are classified will be illustrated using examples from Chinese Lattice Designs, The Alhambra, Hungarian Needlework, and M. C. Escher's Tessellations. Some examples of the 17 plane symmetry groups will be shown.
9 A repeating pattern or a tessellation or a tiling of the plane is a covering of the plane by one or more figures with a repeating pattern of the figures that has no gaps and no overlapping of the figures.Examples:Equilateral trianglesSquaresRegular HexagonsRegularPolygons
10 Some examples of periodic or repeating patterns, sometimes called “wallpaper designs,” will be shown. There are 17 “plane symmetry groups” or types of patterns.
11 Examples of places where repeating patterns are found: Wallpaper DesignsChinese Lattice DesignsHungarian NeedleworkIslamic ArtThe AlhambraM. C. Escher’s Tessellations
29 Escher’s Drawings of Alhambra Repeating Patterns
30 Escher Sketches of designs in the Alhambra and La Mezquita (Cordoba)
31 Mathematical Reference: “The Plane Symmetry Groups: Their Recognition and Notation”by Doris Schattschneider,The Mathematical Monthly, June-July, 1978Artistic Source: Maurits C. Escher ( ) was a master at constructing tessellations
34 Rotations: plottools[rotate](M,Pi/2,[40,40]) A unit cell or “tile” is the smallest region in the plane having the property that the set of all of its images will fill the plane. These images may be obtained by:Translations: plottools[translate](tile,XD,YD)Rotations: plottools[rotate](M,Pi/2,[40,40])Reflections:plottools[reflect](M,[[0,0],[40,40]])Glide Reflections: translate & reflect