Individual Presentation or Panel Title
Applications of Abstract Algebra: Symmetry in Spanish Arab Tile Patterns
Abstract
There are precisely 17 two-dimensional groups of symmetry, or wallpaper patterns, which can be generated by rotating, reflecting, or glide reflecting a base image. In this project we investigate these patterns in the tiling of Spanish-Arab structures such as the Alhambra in Córdoba and the Real Alcázar in Seville, Spain. First we will show the characteristics of each pattern, and then make a table to represent how we can travel from one cell of the pattern to another. Next we define each pattern according to its point group and create a diagram to represent the elements of each group. We examine through abstract algebra the similarities between patterns with equivalent point groups, yet distinct characteristics, and why they can both be interpreted as the same group. Finally we use this information to create our own tile patterns using GeoGebra (free software for geometry and more). Through this process we will describe the connections among distinct wallpaper patterns and communicate the beauty of visual mathematics to nonspecialists.
Location
Glass Dining Room
Start Date
11-4-2015 3:30 PM
End Date
11-4-2015 4:20 PM
Applications of Abstract Algebra: Symmetry in Spanish Arab Tile Patterns
Glass Dining Room
There are precisely 17 two-dimensional groups of symmetry, or wallpaper patterns, which can be generated by rotating, reflecting, or glide reflecting a base image. In this project we investigate these patterns in the tiling of Spanish-Arab structures such as the Alhambra in Córdoba and the Real Alcázar in Seville, Spain. First we will show the characteristics of each pattern, and then make a table to represent how we can travel from one cell of the pattern to another. Next we define each pattern according to its point group and create a diagram to represent the elements of each group. We examine through abstract algebra the similarities between patterns with equivalent point groups, yet distinct characteristics, and why they can both be interpreted as the same group. Finally we use this information to create our own tile patterns using GeoGebra (free software for geometry and more). Through this process we will describe the connections among distinct wallpaper patterns and communicate the beauty of visual mathematics to nonspecialists.