The Arts of Ornamental Geometry

A Persian Compendium on Similar and Complementary Interlocking Figures. A Volume Commemorating Alpay Özdural


Volume Editor:
This collective study focuses on a unique anonymous medieval document on ornamental geometry featuring geometrical constructions and textual instructions in Persian. Selections from the unpublished work of Alpay Özdural (d. 2003) on this subject have been updated with original contributions by Jan P. Hogendijk, Elaheh Kheirandish, Gülru Necipoğlu, and Wheeler M. Thackston. The chapters interpreting this fascinating document are followed, for the first time, by a facsimile, transcription, and translation, as well as drawings of incised construction lines invisible in the photographed facsimile.

This publication intersects with the current interest in Islamic geometrical patterning as an inspiration for tessellation and parametrically derived forms in contemporary architecture and the arts. It aims to make this celebrated source more accessible, given its multifaceted relevance to historians of art, architecture, and science, as well as mathematicians, physicists, artists, and architects.

For those who wish to obtain a copy of the full, unedited original book manuscript of Alpay Özdural, where he discusses the mathematical properties of all geometrical constructions in the Anonymous Compendium as well as the step-by-step method for drawing each one, his work is available online at

Prices from (excl. shipping):

Add to Cart
Gülru Necipoğlu (Ph.D. Harvard 1986) is the Aga Khan Professor of Islamic Art and Director of the Aga Khan Program at Harvard University. Her books include The Topkapı Scroll: Geometry and Ornament in Islamic Architecture and The Age of Sinan: Architectural Culture in the Ottoman Empire
Winner of 26th World Award for Book of the Year in Iran 2019.

"The scholarly value of the edited volume lies in bringing diverse perspectives to bear on its interpretation. The resulting work is amajor contribution to scholarship and worthy of close and careful reading, despite its complex organizational structure and layout. Overall, it is a welcome tribute to the published and unpublished work of Alpay Özdural, extending his legacy and broadening its impact. It is hoped that this multi-disciplinary volume can now serve as a solid basis for future research, yielding advances in our understanding of just exactly why and when the histories of art, mathematics and science intersected, and how individuals interacted in the production of knowledge that yielded architectural monuments of cultural significance to this day." - Carol Bier, Center for Islamic Studies, Graduate Theological Union , in: Journal of Mathematics and the Arts 13:3 (2019)

"In the medieval era, Persia stood at the crossroads of great empires, a place where ancient learning, and new, coalesced to create new forms and perspectives. Although we may never fully grasp it firmly, Necipoğlu offers the most detailed description of its contours and the most compelling explanation of how one of the world’s great geometric traditions took shape. Fascinating and well researched, The Arts of Ornamental Geometry is full of previously unknown details and would be a great pedagogical introduction to this topic. It stands as a thorough work that will definitely be useful for historians of Persian architecture and mathematics." - Abdullah Drury, University of Waikato, New Zealand, in The Muslim World Book Review (2018)
GÜLRU NECİPOĞLU, In Memory of Alpay Özdural and His Unrealized Book Project

GÜLRU NECİPOĞLU, Ornamental Geometries: A Persian Compendium at the Intersection of the Visual Arts and Mathematical Sciences

ELAHEH KHEIRANDISH, An Early Tradition in Practical Geometry: The Telling Lines of Unique Arabic and Persian Sources

JAN P. HOGENDIJK, A Mathematical Classification of the Contents of an Anonymous Persian Compendium on Decorative Patterns

ALPAY ÖZDURAL, Preliminaries (first chapter of Alpay Özdural’s unpublished book)

An English translation by Alpay Özdural of Fī tadākhul al-ashkāl al-mutashābiha aw al-mutawāfiqa(On Similar and Complementary Interlocking Figures), edited and revised by Wheeler M. Thackston, with contributions by the other authors
Accompanied by Wheeler M. Thackston’s transcription of the Persian text and Alpay Özdural’s drawings, with commentaries by Gülru Necipoğlu (based on “Analyses,” the second chapter in Alpay Özdural’s unpublished book)

A reduced-scale reproduction of Fī tadākhul al-ashkāl al-mutashābiha aw al-mutawāfiqa (Bibliothèque nationale de France, Ms. Persan 169, fols. 180r–199r)

This book is of interest to historians of art, architecture, and science, as well as to mathematicians, physicists, artists, and architects.
  • Collapse
  • Expand