# B Lynn Bodner

Professor
Mathematics Department, Monmouth University
West Long Branch, New Jersey

Geometric Islamic patterns, especially those consisting predominantly of star polygons, fascinate me. How did medieval artisans conceive and create them using only the geometer's tools - compass and straightedge - available at the time? Since no written explanations describing the processes they used are currently known to exist, I have set out to reconstruct (or "reverse engineer") to their exact design proportions as many intriguing and beautiful geometric Islamic patterns as possible, using only Euclidean construction techniques and symmetry transformations. Links to some of my step-by-step reconstructions, including the images displayed in this exhibit, may be found on my webpage at http://bluehawk.monmouth.edu/~bodner/papers/index.htm.

Eleven and Nine Stars
20 inches by 16 inches
Paper and Ink Computer-Generated Image
2013

This pattern was created using Euclidean construction techniques and the electronic equivalent of the compass and straightedge. It was based on a rectangular repeat unit sketch known as Catalog Number 42 (CN42) of the Topkapi Scroll, which contains 114 Islamic architectural and ornamental designs dating from the 15th or 16th century. CN42 has half 11-stars along its vertical edges and half 9-stars along its horizontal edges. To achieve a complete pattern, this repeat unit must be replicated by reflection across its edges. The image displayed here contains four colored copies of the CN42 repeat unit. Since CN42 is the only sketch in the Topkapi Scroll containing 11-pointed star polygons, it was one of the more challenging ones to recreate.

Thirteen and Sixteen Stars
20 x 20
Paper and Ink Computer-Generated Image
2013

This pattern was constructed using Euclidean techniques and the electronic equivalent of compass and straightedge. It was based on a square repeat unit known as Catalog Number 30 (CN30) of the Topkapi Scroll. CN30 has half 13-stars along both the right vertical and bottom edges, with a quarter of a 16-star centered on the upper left vertex of the square. To achieve this image, CN42 was replicated by reflection across its edges yielding a square of 16 colored copies of the repeat unit. This was then rotated 45 degrees and the half of the image outside a 2nd smaller square (formed by joining the midpoints of the 1st square) was erased. CN30 is the only 13-star pattern in the Topkapi Scroll, thus, it too was quite challenging to recreate.