The main purpose of this article is to substantiate the proposition that mathematicians and architect-artisans had collaborated through special meetings, called conversazioni in the text, for the application of geometry to architecture in the Islamic world. A meeting reportedly attended by Omar Khayyam furnishes convincing evidence for this proposition. The study expands on the untitled treatise written by Omar Khayyam as a response to a question raised at this meeting. The treatise is about a problem that concerns an ornamental pattern, the story of which can be traced in two other works on geometry: Abu ‘l-Wafa’ al-Buzajani’s book, What the Artisan Requires of Geometric Constructions, and an anonymous Persian treatise on ornamental geometry, On Interlocking Similar or Corresponding Figures. While these three works are analyzed in the article, the wider implications of the collaboration between mathematicians and artisans concerning the field of architecture are discussed.