Taxonomies of geometric problems. (March 2020) - Quaresma, Pedro; Santos, Vanda; Graziani, Pierluigi; Baeta, Nuno
Abstract: In the current Information Society the organisation of the information is key to ensure the information safekeeping and retrieval. It is of utmost importance that each and every user can find the information he/she is looking for, presented in such a way that best fit his/her needs. Geometry is no exception, the servers of geometric information should be easily and successfully searchable. By classifying the information contained in the servers of geometric information accordingly to several taxonomies, it will be possible to begin applying filters to the users' queries, adjusting them to the perceived user's needs. Having that in mind, the introduction of an adaptive filtering mechanisms into servers of geometric information is considered. Different taxonomies for different goals are presented. For educational purposes, a classification like Common Core Standards should be considered, but other considerations like the complexity of the construction, the provability, by a geometry automatic theorem prover, of a given conjecture and the readability of the resulting proof, should be taken into account. For research in automated deduction purposes, other issues must be considered, e.g. efficiency and applicability of the available automated provers. To validate the usefulness of these taxonomies it will be used, as a case study, their application to a server of geometric information. In particular, Thousands of Geometric problems for geometric Theorem Provers will be considered. TGTP is a Web-based repository of geometric problems being developed to support the testing and evaluation of geometric automated theorem proving systems. Using this system it will be analysed how the taxonomies could help to tailor the search for information adapted to each and every geometer.