Math Department (Thesis/2009-10)

Frieze and wallpaper patterns

Under the direction of: Paul Friedman

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A frieze, in design or architecture, is a decorative horizontal band, as along the upper part of a wall in a room, with repeating motif. It can be thought of as a pattern that repeats itself in one dimension. A wallpaper pattern can similarly be thought of as a pattern that repeats itself in two (not necessarily perpendicular) directions. This project will study the so-called Frieze Groups and the Wallpaper Groups, the symmetry groups of the respective patterns. Remarkably, there are only seven Frieze Groups and just 17 Wallpaper Groups.

A quote from Hermann Weyl's book "Symmetry": "Examples for all 17 groups of symmetry are found among the decorative patterns of antiquity, in particular among Egyptian ornaments. One can hardly overestimate the depth of geometric imagination and inventiveness reflected in these patterns. Their construction is far from being mathematically trivial. The art of ornament contains in implicit form the oldest piece of higher mathematics known to us."

This is a one-term thesis.

Prerequisite: Math 224 (as Transformation Geometry) and preferably 332, too.

Math Department web pages Created: 11 May 2009 Last modified: 11 May 2009 00:00:00 Comments to: math@union.edu

Thesis Topics - P. Friedman Thesis Topics for 2009-2010 Thesis Topics - J. Barbanel