Abstract

The Darb-i Imam is a 15th century Islamic Shrine Complex in modern day Iran that underwent significant renovation from 1505 -1702. In particular, a specific geometric style tiling, also known as a girih tiling on the left portal of the Darb-i Imam has been compared to an important mathematical tiling known as Penrose tiling. It was mathematical scholars Peter Lu and Paul Steinhardt who first made this argument that the left portal of the Drab-i Imam is in fact an instance of Penrose tiling. However, to make this argument they assume there must have been a defect in construction of the Darb-i Imam. The bigger question becomes evident: did the tileworkers and craftspeople know about this aperiodic tiling and purposely include it in the Darb-i Imam? Or is it simply coincidence that it looks very similar to the Penrose tiling? In this paper, we take a deep dive into tiling, aperiodicity, and Penrose tiling, as well as theorists in ethnomathematics to build the necessary framework to enter this conversation in mathematics. By examining a variety of papers on this topic, I criticize the projection of modern mathematics onto the Darb-i Imam. By combining a mathematical understanding of Penrose tiling and aperiodicity with theory from the larger movement of ethnomathematics, we are able to more critically understand what is going wrong in this discussion and how it can be reframed. This independent study combines geometry and theory to spark critical conversations within mathematics.

Advisor

Pierce, Pam

Second Advisor

Park, Chan Sok

Department

Mathematics; Religious Studies

Publication Date

2026

Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis

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© Copyright 2026 Elizabeth M. Haar