Analysis and Synthesis of Islamic Geometric Designs

We have been working on the web site www.tilinqsearch.org for the past five years or so, and one of our aims has been to provide documentation on as many of the classical Islamic patterns as we can discover, from many sources (we already have over 1200 of these, and we think there may be at least 2000). For each pattern, part of the documentation consists of the results of sequences of trigonometrical formulae relating to the edge lengths of individual polygons within the pattern, to enable our computer software to build up a complete two-dimensional design. As a preliminary to working out the formulae, we attempt an analysis of the patterns along mathematical lines - as far as this is possible - and here we encounter one of the major difficulties in treating all Islamic patterns as though they were complicated diagrams in a geometry textbook.