This book presents a selection of papers from the International Conference Geometrias17, which was hosted by the Department of Architecture at the University of Coimbra from 16 to 18 June 2017. The Geometrias conferences, organized by Aproged (the Portuguese Geometry and Drawing Teachers Association), foster debate and exchange on practical and theoretical research in mathematics, architecture, the arts, engineering, and related fields.

Geometrias17, with the leitmotif Thinking, Drawing, Modelling, brought together a group of recognized experts to discuss the importance of geometric literacy and the science of representation for the development of scientific and technological research and professional practices. The 12 peer-reviewed papers gathered here show how geometry, drawing, stereotomy, and the science of representation are still at the core of every act leading to the conception and materialization of form, and highlight their continuing relevance for scholars andprofessionals in the fields of architecture, engineering, and applied mathematics.

João Pedro Xavier is an Architect and Full Professor at the Faculty of Architecture,University of Porto (FAUP), where he received his initialdegree in 1985 and his Ph.D. in Architecture in 2005. From 1986 to 1999, he worked in Álvaro Sizas office. At the same time, he established his own practice as an Architect. Xavier is a member of the CEAU research teams Architecture: Theory, Project, History (ATPH) and Digital Fabrication Laboratory (DFL). The relationship between architecture and mathematics, especially perspective, is his main research interest. He is the author of the books Perspectiva, perspectivaacelerada e contraperspectiva (Perspective, accelerated perspective and counter-perspective) and Sobre as origens da perspectivaem Portugal (On the origins of perspective in Portugal). He is a Correspondent Editor of the Nexus Network Journal and a Council Member atthe European Association for Architectural Education (EAAE). 

Vitor Murtinho is an Architect and Full Professor at the Department of Architecture,University of Coimbra (UC), Portugal. A Senior Researcher at UCs Center for Social Studies, his research interests include Renaissance theory, architectonics of form, and geometry. As the UCs Vice-Rector (March 2011 to February 2019), he was responsible for heritage, buildings, and sustainability. He is the author or co-author of more than one hundred publications (books, book chapters, and papers in journals and conference proceedings). A detailed list of his publications can be found at http://ces.uc.pt/en/ces/pessoas/investigadoras-es/vitor-murtinho/publicacoes. 

Vera Viana has been the Director of Aproged (the Portuguese Geometry and Drawing Teachers Association) since 2009 and organizes, among other events, the International Conferences Geometrias. She is Editor-in-Chief of the Geometrias Conference Proceedings and Aprogeds Bulletins, and serves on the scientific committees of several international conferences. As a Researcher at the University of PortosCentre for Studies of Architecture and Urbanism, her work focuses on the connections between architecture and mathematics. Since 2001, she has been engaged in the development of educational resources, particularly on polyhedral geometry with three-dimensional modelling and algorithmic modelling software, and has released a Ph.D. thesis, papers, and presentations on the subject.

M. Barberio, Prototyping Stereotomic Assemblies: Stone Polysphere.- L. Cabezas, Geometry and Art.- A. Castro, Geometry and Digital Technologies in Herzog& De Meuron Architecture.- M. Colella, The Dome as Minimal Housing Unit: Ghibli and D-Home Prototypes.- S. Genin, The Vaults of Arronches Nossa Senhora da Assunção and Misericordia Churches. Geometric and Constructive Comparison with the Nave and Refectory Vaults of Jerónimos Monastery.- C. Leopold, Perspective Transformations for Architectural Design.- J. Maia and V. Murtinho, Ordered Creativity: The Sense of Proportion in the Architecture of João Álvaro Rocha.- A. Martín-Pastor and A. Lopez Martínez, Developable Ruled Surfaces from a Cylindrical Helix and their Application as an Architectural Surface.- H. Müller, C. Nething, A. Schalk, D. Kovaleva, O. Gericke and W. Sobek, Porous Spatial Concrete Structures Generated Using Frozen Sand Formwork .- J. Pedro Sousa, Calculated Geometries. From Manual to Robotic Experiments in Architectural.- M. Sroka-Bizo, How to Construct Red Sea?.- J. Tofil, How to Improve the Education of Engineers Visualization of String Construction Bridges.