Overlapping Decagons on the Iranian Plateau: History of Architecture and the History of Mathematics

Carol Bier
Research Associate , The Textile Museum

Dan Shechtman received the Nobel Prize in Chemistry (2011) for discovery of a
crystalline structure in which five- and ten-fold symmetries are present in a way that is
“forbidden” according to the laws of symmetry as understood since the late nineteenth
century. Analysis of the three-dimensional structure yields a diffraction pattern that,
according to the Nobel award press release, resembles “medieval Islamic mosaics.”
Bier’s work strives to arrive at a methodology to interpret the meaning of geometry and is published in several articles that build one upon the other (Bridges conference proceedings [2002; 2011]; Iranian Studies 41/4 [2008]; Nexus: Architecture and Mathematics [Fall 2012]). Her conclusions establish a new paradigm that relates these patterns in pre-Mongol Iran to then contemporary philosophical discourse and the history of mathematics.