@article(botana2015automated, author = {Francisco Botana and Markus Hohenwarter and Jani{\v{c}}i{\'c}, Predrag and Zolt{\'a}n Kov{\'a}cs and Ivan Petrovi{\'c} and Tom{\'a}s Recio and Simon Weitzhofer}, year = {2015}, title = {Automated theorem proving in GeoGebra: Current achievements}, journal = {Journal of Automated Reasoning}, volume = {55}, number = {1}, pages = {39--59}, doi = {10.1007/s10817-015-9326-4}, ) @article(braun2017synthetic, author = {Gabriel Braun and Julien Narboux}, year = {2017}, title = {A synthetic proof of Pappus\IeC{\textquoteright} theorem in Tarski\IeC{\textquoteright}s geometry}, journal = {Journal of Automated Reasoning}, volume = {58}, number = {2}, pages = {209--230}, doi = {10.1007/s10817-016-9374-4}, ) @book(brousseau1998theorie, author = {Guy Brousseau and Nicolas Balacheff}, year = {1998}, title = {Th{\'e}orie des situations didactiques: Didactique des math{\'e}matiques 1970-1990}, publisher = {La pens{\'e}e sauvage Grenoble}, ) @incollection(buchberger1988applications, author = {Bruno Buchberger}, year = {1988}, title = {Applications of Gr{\"o}bner bases in non-linear computational geometry}, booktitle = {Trends in computer algebra}, publisher = {Springer}, pages = {52--80}, doi = {10.1007/3-540-18928-9_5}, ) @article(chou1988introduction, author = {Shang-Ching Chou}, year = {1988}, title = {An introduction to Wu's method for mechanical theorem proving in geometry}, journal = {Journal of Automated Reasoning}, volume = {4}, number = {3}, pages = {237--267}, doi = {10.1007/BF00244942}, ) @book(chou1994machine, author = {Shang-Ching Chou and Xiao-Shan Gao and Jing-Zhong Zhang}, year = {1994}, title = {Machine proofs in geometry: Automated production of readable proofs for geometry theorems}, volume = {6}, publisher = {World Scientific}, doi = {10.1142/9789812798152_0002}, ) @article(Chou1996, author = {Shang-Ching Chou and Xiao-Shan Gao and Jing-Zhong Zhang}, year = {1996}, title = {Automated Generation of Readable Proofs with Geometric Invariants, {I}. Multiple and Shortest Proof Generation}, journal = {Journal of Automated Reasoning}, volume = {17}, pages = {325--347}, doi = {10.1007/BF00283134}, ) @book(duval1995semiosis, author = {Raymond Duval}, year = {1995}, title = {S{\'e}miosis et pens{\'e}e humaine: registres s{\'e}miotiques et apprentissages intellectuels}, publisher = {Peter Lang Berne}, ) @article(font2018, author = {Ludovic Font and Philippe~R Richard and Michel Gagnon}, year = {2018}, title = {Improving QED-Tutrix by Automating the generation of Proofs}, journal = {arXiv preprint arXiv:1803.01468}, ) @inproceedings(houdement2006paradigmes, author = {Catherine Houdement and Alain Kuzniak}, year = {2006}, title = {Paradigmes g{\'e}om{\'e}triques et enseignement de la g{\'e}om{\'e}trie}, booktitle = {Annales de didactique et de sciences cognitives}, volume = {11}, pages = {175--193}, ) @article(Janicic2012a, author = {Jani\v{c}i\'c, Predrag and Julien Narboux and Pedro Quaresma}, year = {2012}, title = {The {A}rea {M}ethod: a Recapitulation}, journal = {Journal of Automated Reasoning}, volume = {48}, number = {4}, pages = {489--532}, doi = {10.1007/s10817-010-9209-7}, ) @article(kapur1986using, author = {Deepak Kapur}, year = {1986}, title = {Using Gr{\"o}bner bases to reason about geometry problems}, journal = {Journal of Symbolic Computation}, volume = {2}, number = {4}, pages = {399--408}, doi = {10.1016/S0747-7171(86)80007-4}, ) @article(kuzniak2011espace, author = {Alain Kuzniak}, year = {2011}, title = {{L'espace de Travail Math{\'e}matique et ses gen{\`e}ses}}, journal = {{Annales de didactique et de sciences cognitives}}, volume = {16}, pages = {9--24}, url = {https://halshs.archives-ouvertes.fr/halshs-01060043}, ) @article(kuzniak2014espacios, author = {Alain Kuzniak and Philippe~R Richard}, year = {2014}, title = {Espacios de trabajo matem{\'a}tico. Puntos de vista y perspectivas}, journal = {Revista latinoamericana de investigaci{\'o}n en matem{\'a}tica educativa}, volume = {17}, number = {4}, doi = {10.12802/relime.13.1741a}, ) @phdthesis(Leduc2016, author = {N.~Leduc}, year = {2016}, title = {QED-Tutrix : syst\IeC{\`e}me tutoriel intelligent pour l\IeC{\textquoteright}accompagnement d\IeC{\textquoteright}\IeC{\'e}l\IeC{\`e}ves en situation de r\IeC{\'e}solution de probl\IeC{\`e}mes de d\IeC{\'e}monstration en g\IeC{\'e}om\IeC{\'e}trie plane}, school = {\IeC{\'E}cole polytechnique de Montr\IeC{\'e}al.}, ) @article(matsuda2004gramy, author = {Noboru Matsuda and Kurt Vanlehn}, year = {2004}, title = {Gramy: A geometry theorem prover capable of construction}, journal = {Journal of Automated Reasoning}, volume = {32}, number = {1}, pages = {3--33}, doi = {10.1023/B:JARS.0000021960.39761.b7}, ) @inproceedings(narboux2006mechanical, author = {Julien Narboux}, year = {2006}, title = {Mechanical theorem proving in Tarski\IeC{\textquoteright}s geometry}, booktitle = {International Workshop on Automated Deduction in Geometry}, organization = {Springer}, pages = {139--156}, doi = {10.1007/978-3-540-77356-6_9}, ) @inbook(Richard2019Issues, author = {Philippe~R. Richard and Fabienne Venant and Michel Gagnon}, year = {2019}, title = {Issues and challenges about instrumental proof}, publisher = {Springer}, address = {Suisse}, doi = {10.1007/978-3-030-28483-1_7}, ) @phdthesis(Tessier-Baillargeon2015, author = {M~Tessier-Baillargeon}, year = {2015}, title = {GeoGebraTUTOR : D\IeC{\'e}veloppement d\IeC{\textquoteright}un syst\IeC{\`e}me tutoriel autonome pour l\IeC{\textquoteright}accompagnement d\IeC{\textquoteright}\IeC{\'e}l\IeC{\`e}ves en situation de r\IeC{\'e}solution de probl\IeC{\`e}mes de d\IeC{\'e}monstration en g\IeC{\'e}om\IeC{\'e}trie plane et gen\IeC{\`e}se d\IeC{\textquoteright}un espace de travail g\IeC{\'e}om\IeC{\'e}trique idoine}, school = {Universit\IeC{\'e} de Montr\IeC{\'e}al.}, ) @inproceedings(wang2015automated, author = {Ke~Wang and Zhendong Su}, year = {2015}, title = {Automated geometry theorem proving for human-readable proofs}, booktitle = {Twenty-Fourth International Joint Conference on Artificial Intelligence}, ) @article(wu1979elementary, author = {H~Wu}, year = {1979}, title = {An elementary method in the study of nonnegative curvature}, journal = {Acta Mathematica}, volume = {142}, number = {1}, pages = {57--78}, doi = {10.1007/BF02395057}, ) @article(zhang1990parallel, author = {Jingzhong Zhang and Lu~Yang and Mike Deng}, year = {1990}, title = {The parallel numerical method of mechanical theorem proving}, journal = {Theoretical Computer Science}, volume = {74}, number = {3}, pages = {253--271}, doi = {10.1016/0304-3975(90)90077-U}, )