# Reza Sarhangi

Professor
Department of Mathematics, Towson University
Towson, Maryland, USA

I am interested in Persian geometric art and its historical methods of construction, which I explore using the computer software Geometer's Sketchpad. I then create digital artworks from these geometric constructions primarily using the computer software PaintShopPro.

Metaphor III
16" X 20"
Digital Print
2008

In Metaphor III (December 2008) we see the same metamorphosis as Metaphor II but in a new way, where spirals are introduced to eliminate rigid lines and present a new harmony and balance.

Metaphor II
16" X 20"
Digital Print
2008

Metaphor II (December 2008) is a metamorphosis made from two different patterns: Cross–Octagram pattern, and Butterfly pattern. The far sides to the left and to the right of the artwork present the Cross–Octagram pattern but in opposite orders. The transition from left to right is achieved by some butterfly shaped elements. The blank space between four octagrams is a cross, and the four crosses make an octagram. So in some sense, we may say that the cross and the octagram are each other’s duals. An interesting observation about the butterfly shaped element is that the space between four of them could be either a cross or octagram, depending on their arrangements. Because of this property, the transition from Cross–Octagram to itself but in an opposite order is possible.

Kharragan I
16" X 20"
Digital print
2011

Kharragan I (January 2011) is an artwork based on a design on one of the 11th century twin tomb towers in Kharraqan, western Iran. The artwork demonstrates two different approaches that are assumed to have been utilized centuries ago to create the layout of the pattern, which is at the center of the artwork. From left to right, the artwork exhibits the construction of the design based on a compass and straightedge. From right to left, we see another approach, the Modularity method, to construct the same design using cutting and pasting of tiles in two colors. These two methods of constructions were presented at “A Workshop in Geometric Constructions of Mosaic Designs” during the 2010 Bridges Conference, Pécs, Hungary.