Cultural and Mathematical Meanings of Regular Octagons in Mesopotamia: Examining Islamic Art Designs

Jeanam Park

doi:10.7596/taksad.v7i1.1354

Abstract

The most common regular polygon in Islamic art design is the octagon. Historical evidence of the use of an 8-star polygon and an 8-fold rosette dates back to Jemdet Nasr (3100-2900 B.C.) in Mesopotamia. Additionally, in ancient Egypt, octagons can be found in mathematical problem (Ahmose papyrus, Problem number 48), household goods (papyrus storage), architecture (granite columns) and decorations (palace decorations). The regular octagon which is a fundamentally important element of Islamic art design, is widely used as arithmetic objects in metric algebra along with other regular polygons in Mesopotamia. The 8-point star polygon has long been a symbol of the ancient Sumerian goddess Inanna and her East Semitic counterpart Ishtar. During the Neo-Assyrian period, the 8-fold rosette occasionally replaced the star as the symbol of Ishtar. In this paper, we discuss how octagonal design prevailed in the Islamic region since the late ninth century, and has existed in Mesopotamia from Jemdet Nasr to the end of third century B.C. We describe reasons why the geometric pattern of regular polygons, including regular octagons, developed in the Islamic world. Furthermore, we also discuss mathematical meanings of regular polygons.

Highlights

Regular octagons can be found in the works of Pierre Paulin (1927-2009), the ceiling of the Paris Opera House (19th century), and the facade of the UMS building, Tashkent (Fig. 1)
The 8-pont star or 8-fold rosette has long been a symbol of the goddess, Inanna/Ishtar, symbolized by Venus
The regular octagon is believed to have developed in the Islamic world by integrating art, mathematics, and religion

Summary

Introduction

Regular octagons can be found in the works of Pierre Paulin (1927-2009), the ceiling of the Paris Opera House (19th century), and the facade of the UMS building, Tashkent (Fig. 1). In Islamic art, these designs are called the 8fold rosette, 8-star polygon, and 8-point star, respectively (see Fig. 5). The regular polygon is a fundamentally important element in Islamic art design, and is commonly used as arithmetic objects in metric algebra in Mesopotamia.

Results

Conclusion