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Abstract: Constructed geometric diagrams capture a dynamic relationship between text and image that played a central role in ancient science and mathematics. Euclid, Theodosius, Ptolemy, Archimedes and others constructed diagrams to geometrically model optics, astronomy, cartography, and hydrostatics. Each derived geometric properties from their models and interpreted their results with respect to the model's underlying semantics. Although diagram construction is a dynamic process, the media in which these works were published (manuscripts and books) forced scholars to either view a snapshot of that process (a static image) or manually perform the entire construction. Mainstream approaches to digitization represent constructed diagrams as they appear in print, as static images. Such representations fail to capture the dynamic nature of constructed diagrams and so we designed and implemented a computational framework for dynamically interacting with them. Our architecture for representing, retrieving, and interacting with diagrams has already been used to produce a publicly-available, archival-quality digital corpus of diagrams for the Archimedes Palimpsest Project, establishing our approach's viability in the real world. After using our system to study diagrams in Archimedes, we discuss the generality of our approach and its application to other domains including circuit design, software engineering, and patent databases.

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   Gabriel A. Weaver, "Semantic and Visual Encoding of Diagrams." Dartmouth Computer Science Technical Report TR2009-654, August 2009.

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