My primary interest involves the examination and analysis of the patterns and symmetry evident in geometric Islamic ornamentation found during various time periods and in different regions of the Islamic world. Using mathematical group theory, which provides a scientific means for classifying a geometric pattern according to the set of symmetries that exist in the design as a whole, I seek to ascertain which symmetry groups were preferred and intuitively recognized as being “right” by various Islamic cultures. Additionally, I enjoy the challenge of finding plausible Euclidean compass and straightedge constructions of these fascinating geometric patterns. For more information & papers on this Islamic pattern & various others, see my webpage.
This Islamic pattern is a reconstruction of a similar one that may be found today on a bronze door of the Masjid al-Sultan al-Nasir Hasan in Cairo, Egypt. Created in 1363, it is considered a Mamluk masterpiece. It may also be found as Plate 121 in Bourgoin's 1879 book entitled "Arabic Geometrical Pattern and Designs." This image, consisting mainly of curved regular 12-star polygons and curved nearly-regular 5-star and 9-star polygons, was created using only a compass and straightedge following Euclidean construction techniques (which preclude measurement of any kind). See the artist's webpage for a paper entitled "Curved Islamic Star Patterns of Medieval Egypt and Syria" for more information on this pattern (& various other constructions).
This Islamic pattern is a reconstruction of a similar one (Plate 181) illustrated in Jules Bourgoin's 1879 book, "Arabic Geometrical Pattern and Designs," which contains sketches of over 200 Islamic patterns found at the end of the 19th century on then extant historic monuments in Cairo and Damascus. This image, consisting almost entirely of curved regular 10-star polygons, was created using only a compass and straightedge following Euclidean construction techniques (which preclude measurement of any kind). See the artist's webpage for her paper entitled "Curved Islamic Star Patterns of Medieval Egypt and Syria" for more information on the construction of this pattern, as well as information on the constructions of various other patterns.
Curved Sixteen-Star with Linear Twelve- and Seven-Stars
This Islamic pattern is a reconstruction of a similar one that may be found today as a carved wooden panel on a minbar (pulpit) of the Masjid (mosque of) al-Amir Qijmas al-Ishaqi in Cairo, Egypt (& also as Plate 135 in Bourgoin's "Arabic Geometrical Pattern and Design.") The original panel, created in 1481, is considered a Mamluk masterpiece. This image consists mainly of four regular 12-star & eight nearly-regular 7-star polygons surrounding a single curved regular 16-star. It was created using only a compass & straightedge following Euclidean construction techniques (which preclude measurement of any kind). For more information, see the artist's webpage for her paper entitled "Curved Islamic Star Patterns of Medieval Egypt and Syria."
