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Pedro Quaresma


Mathematics Department of the University of Coimbra


Coimbra, Portugal



GeoThms - Geometry Framework


Pedro Quaresma


I'm an assistant professor in the Mathematics Department of the University of Coimbra, Portugal. I have a PhD in Informatics, Foundations of Computer Science, by the University of Minho, Portugal.

Current Projects

My current projects in the area of Geometry are:

GeoThms: GeoThms is a web-based framework for exploring geometrical knowledge that integrates Dynamic Geometry Software (DGS), Automatic Theorem Provers (ATP), and a repository of geometrical constructions, figures and proofs.

An XML-suite is used as a mean of interchange constructions between the DGSs and the ATPs.

One if the ATPs used is an implementation of the Area Method, done in collaboration with Predrag Janicic (from the University of Belgrade).

EukleidesPT: the localization of Eukleides for the Portuguese Language (in collaboration with the author of Eukleides).

GeoTutor - Adaptative Learning Environment: a project submitted to FCT (Portuguese Science and Technology Foundation) The goal is to integrate the DGSs, the ATPs, and a repository of geometry problems, in a LMS, the student is able to explore the built-in knowledge but also to do new constructions, and new conjectures, allowing, in this way, a better understanding of the concepts presented in the e-course. With this project we intend to build a Adaptative Learning Environment for Geometry. A dynamic environment where the student can study the models and axiomatic theories of geometry, to understand the differences and connections between the two perspectives. An environment where the student should be challenged by new problems to be solved by the student.

This project is just starting and it will be done as part of a PhD thesis done under my supervision.


Pedro Quaresma and Predrag Janicic, "Framework for Constructive Geometry (Based on the Area Method)", CISUC Technical Report, TR2006/001, Coimbra, 2006.

Pedro Quaresma and Predrag Janicic, "GeoThms - Geometry Framework", CISUC Technical Report, Coimbra, TR2006/002, 2006.

Pedro Quaresma e Ana Pereira, "Visualização de Construções Geométricas", Gazeta de Matemática 151, SPM, Lisboa, Junho de 2006.

Pedro Quaresma and Predrag Janicic, "Integrating Dynamic Geometry Software, Deduction Systems, and Theorem Repositories", J.M. Borwein and W.M. Farmer. (Eds.): MKM 2006, LNAI 4108, pp. 280--294, Springer-Verlag Berlin Heidelberg 2006.

Predrag Janicic and Pedro Quaresma, "System Description: GCLCprover + GeoThms", U. Furbach and N. Shankar (Eds.): IJCAR 2006, LNAI 4130, pp. 145--150, 2006. Springer-Verlag Berlin Heidelberg 2006.

Pedro Quaresma and Predrag Janicic, "GeoThms --- a Web System for Euclidean Constructive Geometry", UITP06, ENTCS, Elsivier B.V., Amesterdam, 2006.

Predrag Janicic and Pedro Quaresma, "Automatic Verification of Regular Constructions in Dynamic Geometry Systems", ADG 2006, LNAI 4869, pp. 39-51, 2007, Springer-Verlag Berlin Heidelberg 2007.

Pedro Quaresma, Predrag Janicic, J. Tomasevic, M. V.-Janicic, and D. Tosic, "XML-based Format for Geometry", in Communicating Mathematics in the Digital Era, Edited by J.M. Borwein, E.M. Rocha and J.F. Rodrigues, pp 183-197, AK Peters lda, Wellesley, Massachusetts, USA, 2008.

Vanda Santos e Pedro Quaresma, e-Learning Course for Euclidean Geometry, in Proc. of the The 8th IEEE International Conference on Advanced Learning Technologies, pp 387-388, July 1-5, Santander, Spain, 2008.

Pedro Quaresma and Predrag Janicic, "The Area Method, Rigorous Proofs of Lemmas in Hilbert's Style Axiom System", CISUC Technical Report, TR2009/006, Coimbra, 2009.

Vanda Santos, Pedro Quaresma, "Adaptative Learning Environment for Geometry", in "Advances in Learning Processes", edited by: Mary Beth Rosson, Chapter 5, pp. 71-92, Itech Education and Publishing, Vienna, Austria, 2010.

Predrag Janicic, Julien Narboux, Pedro Quaresma "The Area Method: a Recapitulation", submitted to JAR in October 2009.