@article(abanadesetal2016, author = {Miguel Ab\'anades and Francisco Botana and Zoltan Kov\'acs and S\'olyom-Gecse, Csilla}, year = {2016}, title = {Development of automatic reasoning tools in GeoGebra}, journal = {ACM Communications in Computer Algebra}, volume = {50}, number = {3}, pages = {85--88}, doi = {10.1145/3015306.3015309}, ) @incollection(cocoalib, author = {John Abbott and Anna M. Bigatti}, year = {2010}, title = {{CoCoALib}: A C++ Library for Computations in Commutative Algebra... and Beyond}, editor = {Hoeven K. and Joswig J.v.d. and Takayama and M.}, booktitle = {Mathematical Software {\textendash} {ICMS} 2010}, volume = {6327}, publisher = {Springer}, address = {Berlin, Heidelberg}, pages = {73--76}, doi = {10.1007/978-3-642-15582-6\_15}, ) @article(artigue, author = {Mich\`ele Artigue}, year = {2002}, title = {Learning Mathematics in a CAS Environment: The Genesis of a Reflection about Instrumentation and the Dialectics between Technical and Conceptual Work}, journal = {International Journal of Computers for Mathematical Learning}, volume = {7}, pages = {245--274}, doi = {10.1023/A:1022103903080}, ) @article(artiguetrouche2021, author = {Mich\`ele Artigue and Luc Trouche}, year = {2021}, title = {Revisiting the French Didactic Tradition through Technological Lenses}, journal = {Mathematics}, volume = {9(6)}, pages = {629}, doi = {10.3390/math9060629}, ) @article(MathTrails, author = {Anna Barbosa and Isabel Vale and Simona Jablonski and Matthias Ludwig}, year = {2022}, title = {Walking through Algebraic Thinking with Theme-Based (Mobile) Math Trails}, journal = {Education Sciences}, volume = {12}, number = {5}, pages = {346}, doi = {10.3390/educsci12050346}, ) @incollection(MathCityTrails, author = {Simon Barlovits and Baumann-Wehner, Morritz and Matthias Ludwig}, year = {2020}, title = {Curricular learning with MathCityMap: Creating theme-based math trails}, booktitle = {Mathematics Education in the Digital Age (MEDA) --- Proceedings}, publisher = {Linz, Austria}, address = {Johannes Kepler University}, pages = {143--150}, ) @book(berger, author = {M. Berger}, year = {2009}, title = {Geometry}, publisher = {2e}, address = {Springer}, ) @article(locusblazek, author = {Jiri Blazek and Pavel Pech}, year = {2017}, title = {Searching for loci using GeoGebra}, journal = {International Journal for Technology in Mathematics Education}, volume = {27}, pages = {143--147}, doi = {10.1564/tme\_v24.3.06}, ) @book(botanaloci, author = {Francisco Botana}, year = {2003}, title = {Automatic Determination of Algebraic Surfaces as Loci of Points}, publisher = {Springer Berlin Heidelberg}, doi = {10.1007/3-540-44860-8\_91}, ) @article(botana-abanades2014, author = {Francisco Botana and Miguel Ab\'anades}, year = {2014}, title = {Automatic Deduction in (Dynamic) Geometry: Loci Computation}, journal = {Computational Geometry}, volume = {47}, number = {1}, pages = {75--89}, doi = {10.1016/j.comgeo.2013.07.001}, ) @incollection(botana-abanades2011, author = {Francisco Botana and Miguel A. Ab{\'{a}}nades}, year = {2012}, title = {Automatic Deduction in Dynamic Geometry using Sage}, booktitle = {ThEdu'11, EPTCS}, volume = {79}, publisher = {Open Publishing Association}, pages = {49--62}, doi = {10.4204/EPTCS.79.3}, ) @article(automatedoutdoor, author = {Francisco Botana and Zoltan Kov\'acs and Tom\'as Recio}, year = {2018}, title = {Towards an automated geometer}, journal = {Lecture Notes in Computer Science}, volume = {11110}, pages = {215--220}, doi = {10.13140/RG.2.2.36788.71042}, ) @article(botanarecioAMAI, author = {Francisco Botana and Tom\'as Recio}, year = {2017}, title = {Computing envelopes in dynamic geometry environments}, journal = {AMAI (Annals of Mathematics and Artificial Intelligence)}, volume = {80}, number = {1}, pages = {3--20}, doi = {10.1007/s10472-016-9500-3}, ) @article(botanarecioJSSC, author = {Francisco Botana and Tom{\'{a}}s Recio}, year = {2019}, title = {A Proposal for the Automatic Computation of Envelopes of Families of Plane Curves}, journal = {Journal of Systems Science and Complexity}, volume = {32}, number = {1}, pages = {150--157}, doi = {10.1007/s11424-019-8341-7}, ) @article(botana-valcarce2, author = {Francisco Botana and Jos\'e L. Valcarce}, year = {2004}, title = {Automatic determination of envelopes and other derived curves within a graphic environment}, journal = {Mathematics and Computers in Simulation}, volume = {67}, number = {1-2}, pages = {3--13}, doi = {10.1016/j.matcom.2004.05.004}, ) @book(brousseau1997, author = {Guy Brousseau}, year = {1997}, title = {The theory of didactical situations in mathematics}, publisher = {Kluwer}, address = {Dordrecht}, ) @incollection(brousseau-warfield, author = {Guy Brousseau and Virginia Warfield}, year = {2014}, title = {Didactic Situations in Mathematics Education}, editor = {S Lerman}, booktitle = {Encyclopedia of Mathematics Education}, publisher = {Springer Netherlands}, address = {Dordrecht}, pages = {163--170}, doi = {10.1007/978-94-007-4978-8\_47}, ) @book(bruceandgiblin, author = {James W. Bruce and Peter J. Giblin}, year = {2012}, title = {Curves and Singularities}, publisher = {Cambridge University Press}, doi = {10.1017/CBO9781139172615}, ) @incollection(buchberger, author = {Bruno Buchberger}, year = {1985}, title = {Gr\"obner bases: an algorithmic method in polynomial ideal theory}, editor = {N. K. Bose}, booktitle = {Multidimensional Systems Theory}, publisher = {Springer Netherlands}, address = {Dordrecht, Netherlands}, pages = {184--232}, doi = {10.1007/978-94-009-5225-6\_6}, ) @misc(4Cs, author = {S. Chiruguru}, year = {2020}, title = {The Essential Skills of $21^{\textrm{st}}$ Century Classroom (4Cs)}, doi = {10.13140/RG.2.2.36190.59201}, ) @article(chou, author = {Shang Ching Chou}, year = {1988}, title = {Mechanical Geometry Theorem Proving}, journal = {D. Reidel Publishing Company, Dordrecht, Netherlands (}, volume = {1988}, ) @article(cieslak-miernowski-mozgawa1991, author = {Waldemar Cie\'slak and Andrzej Miernowski and Witold Mozgawa}, year = {1991}, title = {Isoptics of a closed strictly convex curve, global differential geometry and global analysis}, journal = {Lecture Notes in Mathematics}, volume = {1481}, pages = {28--35}, doi = {10.1007/BFb0083625}, ) @book(cox, author = {David A. Cox and John Little and Donal O'Shea}, year = {1992}, title = {Ideals, Varieties, and Algorithms}, publisher = {Springer New York}, address = {Springer Verlag, New York}, doi = {10.1007/978-1-4757-2181-2}, ) @article(dp-integrals, author = {Dana-Picard, Thierry}, year = {2005}, title = {Parametric integrals and symmetries of functions}, journal = {Mathematics and Computer Education}, volume = {39}, number = {1}, pages = {5--12}, ) @article(bypass, author = {Dana-Picard, Thierry}, year = {2005}, title = {Technology as a bypass for a lack of theoretical knowledge}, journal = {International Journal of Technology in Mathematics Education}, volume = {11}, number = {3}, pages = {101--109}, ) @article(DPCASproofsthms2006, author = {Dana-Picard, Thierry}, year = {2006}, title = {Some Reflections on CAS-assisted Proofs of Theorems}, journal = {International Journal for Technology in Mathematics Education}, volume = {12}, number = {4}, pages = {165--171}, ) @inproceedings(safety, author = {Dana-Picard, Thierry}, year = {2020}, title = {Safety zone in an entertainment park: Envelopes, offsets and a new construction of a Maltese Cross}, editor = {Electronic Proceedings}, booktitle = {Mathematics and Technology}, publisher = {of the Asian Conference on Technology in Mathematics ACTM 2020;}, address = {ISSN (online version}, pages = {1940--4204}, ) @article(talbot, author = {Dana-Picard, Thierry}, year = {2021}, title = {Envelopes and Offsets of Two Algebraic Plane Curves: Exploration of Their Similarities and Differences}, journal = {Mathematics in Computer Science}, volume = {15}, number = {4}, pages = {757--774}, doi = {10.1007/s11786-021-00504-5}, ) @article(open, author = {Dana-Picard, Thierry and Sara Hershkovitz}, year = {2020}, title = {{STEAM} Education: Technological Skills, Students' Cultural Background and Covid-19 Crisis}, journal = {Open Education Studies}, volume = {2}, number = {1}, pages = {171--179}, doi = {10.1515/edu-2020-0121}, ) @techreport(planetaryorbits, author = {Dana-Picard, Thierry and Sara Hershkovitz}, year = {2023}, title = {From Space to Maths And to Arts: Virtual Art in Space with Planetary Orbits}, type = {Technical Report}, institution = {Preprint, 2023}, ) @incollection(DPKdynamiccoloring, author = {Dana-Picard, Thierry and Zolt{\'{a}}n Kov{\'{a}}cs}, year = {2018}, title = {Automated determination of isoptics with dynamic geometry}, editor = {W. Farmer Rabe and G. Passmore and A. Youssef}, booktitle = {Lecture Notes in Computer Science}, publisher = {Springer International Publishing}, address = {Springer}, pages = {60--75}, doi = {10.1007/978-3-319-96812-4\_6}, ) @article(DPKdialog, author = {Dana-Picard, Thierry and Zoltan Kov\'acs}, year = {2021}, title = {Networking of technologies: a dialog between CAS and DGS}, journal = {The electronic Journal of Mathematics and Technology}, volume = {15}, number = {1}, pages = {43--59}, ) @article(DPK-cassini-5C, author = {Dana-Picard, Thierry and Zoltan Kov\'acs}, year = {2022}, title = {Offsets of Cassini ovals}, journal = {The Electronic Journal of Mathematics and Technology}, volume = {16}, number = {1}, pages = {25--39}, ) @article(DPK-dynamicalcoloring, author = {Dana-Picard, Thierry and Zolt{\'{a}}n Kov{\'{a}}cs}, year = {2023}, title = {Experimental study of isoptics of a plane curve using dynamical coloring}, journal = {Mathematics in Computer Science}, volume = {17}, number = {1}, doi = {10.1007/s11786-022-00555-2}, note = {261-280}, ) @article(DMZ-bisopticsofellipses, author = {Dana-Picard, Thierry and Giora Mann and Nurit Zehavi}, year = {2011}, title = {From conic intersections to toric intersections: the case of the isoptic curves of an ellipse}, journal = {The Montana Mathematical Enthusiast}, volume = {9}, number = {1}, pages = {59--76}, ) @article(dp-mozgawainner, author = {Dana-Picard, Thierry and Witold Mozgawa}, year = {2020}, title = {Automated exploration of inner isoptics of an ellipse}, journal = {Journal of Geometry}, volume = {111}, number = {2}, pages = {34}, doi = {10.1007/s00022-020-00546-3}, ) @article(isopticsfermat, author = {Dana-Picard, Thierry and Aharon Naiman and Witold Mozgawa and Waldemar Cie{\'{s}}lak}, year = {2019}, title = {Exploring the Isoptics of Fermat Curves in the Affine Plane Using {DGS} and {CAS}}, journal = {Mathematics in Computer Science}, volume = {14}, number = {1}, pages = {45--67}, doi = {10.1007/s11786-019-00419-2}, ) @book(dps1993, author = {Dana-Picard, Thierry and Malka Schaps}, year = {1993}, title = {A computer assisted project: Classification of Algebras}, series = {Computational algebraic geometry and commutative algebra (Cortona 1991)}, publisher = {Cambridge University Press}, address = {Cambridge}, note = {71--83}, ) @article(dps1996, author = {Dana-Picard, Thierry and Malka Schaps}, year = {1996}, title = {Classifying Generic Algebras: the Local Case}, journal = {Houston Journal of Mathematics}, volume = {22}, number = {4}, pages = {749--773}, ) @article(dpzrevival, author = {Dana-Picard, Thierry and Nurit Zehavi}, year = {2016}, title = {Revival of a classical topic in differential geometry: the exploration of envelopes in a computerized environment}, journal = {International Journal of Mathematical Education in Science and Technology}, volume = {47}, number = {6}, pages = {938--959}, doi = {10.1080/0020739X.2015.1133852}, ) @article(DMZ-bisopticsofhyperbolas, author = {Dana-Picard, Thierry and Nurit Zehavi and Giora Mann}, year = {2014}, title = {Bisoptic curves of hyperbolas}, journal = {International Journal of Mathematical Education in Science and Technology}, volume = {45}, number = {5}, pages = {762--781}, doi = {10.1080/0020739X.2013.877608}, ) @article(DPZ-soil, author = {Dana-Picard, Thierry and David Zeitoun}, year = {2016}, title = {Exploration of parametric integrals related to a question of soil mechanics}, journal = {International Journal of Mathematical Education in Science and Technology}, volume = {48}, number = {4}, pages = {617--630}, doi = {10.1080/0020739X.2016.1256445}, ) @article(parametric2012, author = {Dana-Picard, Thierry and David G. Zeitoun}, year = {2012}, title = {Parametric improper integrals, Wallis formula and Catalan numbers}, journal = {International Journal of Mathematical Education in Science and Technology}, volume = {43}, number = {4}, pages = {515--520}, doi = {10.1080/0020739X.2011.599877}, ) @article(DPZe2017, author = {Dana-Picard, Thierry and David G. Zeitoun}, year = {2017}, title = {A Framework for an {ICT}-Based Study of Parametric Integrals}, journal = {Mathematics in Computer Science}, volume = {11}, number = {3-4}, pages = {285--296}, doi = {10.1007/s11786-017-0299-z}, ) @book(debray, author = {R\'egis Debray}, year = {2001}, title = {D.ieu, un itin{\'e}raire}, publisher = {Editions Odile Jacob}, address = {Paris}, ) @article(drijvers1995, author = {Paul Drijvers}, year = {1995}, title = {White-box/black-box revisited}, journal = {The International Derive Journal}, volume = {2}, number = {1}, pages = {3--14}, ) @article(drijvers2000, author = {Paul Drijvers}, year = {2000}, title = {Students encountering obstacles using a CAS}, journal = {International Journal of Computers for Mathematical Learning}, volume = {5}, number = {3}, pages = {189--209}, doi = {10.1023/A:1009825629417}, ) @book(duval2017, author = {Raymond Duval}, year = {2017}, title = {Understanding the Mathematical Way of Thinking --- The Registers of Semiotic Representations}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-56910-9}, ) @incollection(gelernter, author = {Herbert Gelernter}, year = {1963}, title = {Realization of a geometry-theorem proving machine}, editor = {J. Feldman Feigenbaum}, booktitle = {Computers and thought}, publisher = {McGraw-Hill}, address = {New York}, pages = {134--152}, ) @article(kock, author = {Anders Kock}, year = {2007}, title = {Envelopes - notion and definiteness}, journal = {Beitr{\"a}ge zur Algebra und Geometrie (Contributions to Algebra and Geometry)}, volume = {48}, pages = {345--350}, ) @inproceedings(KDR2022, author = {Zoltan Kov\'acs and Dana-Picard, Thierry and Tom\'as Recio}, year = {2022}, title = {Inner isoptics of a parabola}, booktitle = {Conference: 5th Croatian Conference on Geometry and Graphics}, address = {Dubrovnik}, pages = {4--8}, ) @incollection(kovacs-parisse, author = {Zoltan Kov\'acs and Bernard Parisse}, year = {2015}, title = {Giac and GeoGebra --- improved Gr\"obner basis computations}, booktitle = {Lecture Notes in Computer Science}, publisher = {Springer}, pages = {126--138}, note = {Computer Algebra and Polynomials}, ) @book(KR2020, author = {Zoltan Kov\'acs and Tom\'as Recio}, year = {2020}, title = {Automatically Augmented Reality for Outdoor Mathematics}, publisher = {in Research on Outdoor STEM Education in the digiTal Age}, address = {WTM Verlag f{\"u}r wissenschaftliche Texte und Medien, M{\"u}nster, 2020}, doi = {10.37626/GA9783959871440.0}, ) @article(ecosystem, author = {Zolt{\'{a}}n Kov{\'{a}}cs and Tom{\'{a}}s Recio and Philippe R. Richard and Steven Van Vaerenbergh and M. Pilar V{\'{e}}lez}, year = {2020}, title = {Towards an ecosystem for computer-supported geometric reasoning}, journal = {International Journal of Mathematical Education in Science and Technology}, volume = {53}, number = {7}, pages = {1701--1710}, doi = {10.1080/0020739X.2020.1837400}, ) @article(mariotti2001, author = {Maria Alessandra Mariotti}, year = {2001}, title = {Justifying and Proving in the Cabri Environment}, journal = {International Journal of Computers for Mathematical Learning}, volume = {6}, number = {3}, pages = {257--281}, doi = {10.1023/A:1013357611987}, ) @article(miernowski-mozgawa1997, author = {Anfrzej Miernowski and Witold Mozgawa}, year = {1997}, title = {On some geometric condition for convexity of isoptics}, journal = {Rendiconti del Seminario Matematico Universit`a e Politecnico di Torino}, volume = {55}, ) @incollection(montes, author = {Antonio Montes}, year = {2018}, title = {I-Regular Functions on a Locally Closed Set}, booktitle = {The Gröbner Cover}, volume = {27}, publisher = {Springer International Publishing}, pages = {67--77}, doi = {10.1007/978-3-030-03904-2\_4}, note = {Algorithms and Computations in Mathematics}, ) @book(noss-hoyles, author = {Richard Noss and Celia Hoyles}, year = {1996}, title = {Windows on Mathematical Meanings}, publisher = {Springer Netherlands}, doi = {10.1007/978-94-009-1696-8}, ) @book(pechbook, author = {Pavel Pech}, year = {2007}, title = {Selected Topics in Geometry with Classical vs. Computer Proving}, publisher = {World Scientific Publishers}, doi = {10.1142/6556}, ) @inproceedings(pottmann-peternell, author = {Helmut Pottmann and Martin Peternell}, year = {2000}, title = {Envelopes-computational theory and applications}, booktitle = {Spring Conference on Computer Graphics}, publisher = {Comenius University}, address = {Bratislava}, pages = {3--23}, ) @article(quaresma2020, author = {Pedro Quaresma}, year = {2020}, title = {Automated Deduction and Knowledge Management in Geometry}, journal = {Mathematics in Computer Science}, volume = {14}, number = {4}, pages = {673--692}, doi = {10.1007/s11786-020-00489-7}, ) @article(inequalities2021, author = {Tom\'as Recio and Rafael Losada and Zoltan Kov{\'a}cs and Carlos Ueno}, year = {2021}, title = {Discovering Geometric Inequalities: The Concourse of {GeoGebra} Discovery, Dynamic Coloring and Maple Tools}, journal = {Mathematics}, volume = {9}, number = {20}, pages = {2548}, doi = {10.3390/math9202548}, ) @book(recioetalSI, author = {Tom\'as Recio and Rodr{\'\i}guez-Pi$\tilde{\text{n}}$ero, Piedad Tolmos and Cid-Cid, Ana and Rocio Guede-Cid (edts)}, year = {2021}, title = {STEAM Teacher Education: Problems and Proposals}, publisher = {Mathematics (Special Issue)}, url = {https://www.mdpi.com/journal/mathematics/special\_issues/STEAM\_Teacher\_Education}, ) @article(roanes2003, author = {Roanes-Lozano, E. and Roanes-Mac{\'{\i}}as, E. and Villar-Mena, M.}, year = {2003}, title = {A bridge between dynamic geometry and computer algebra}, journal = {Mathematical and Computer Modelling}, volume = {37}, number = {9-10}, pages = {1005--1028}, doi = {10.1016/S0895-7177(03)00115-8}, ) @incollection(roanes2020, author = {Roanes-Lozano, Eugenio}, year = {2002}, title = {Boosting the Geometrical Possibilities of Dynamic Geometry Systems and Computer Algebra Systems through Cooperation}, editor = {H. Kautschitsch Borovcnik}, booktitle = {Technology in Mathematics Teaching. Proceedings of ICTMT-5}, address = {Schrifrenreihe Didaktik der Mathematik \textbf{25}. \"obv \& hpt, Vienna (2002}, pages = {335--348}, ) @article(rovenski, author = {Vladimir Rovenski}, year = {2000}, title = {Geometry of Curves and Surfaces with MAPLE}, journal = {Birkh\"auser}, volume = {2000}, ) @article(schultz-juttler, author = {Tino Schultz and Bert J\"uttler}, year = {2011}, title = {Envelope computation in the plane by approximate implicitization}, journal = {Applicable Algebra in Engineering, Communication and Computing}, volume = {22}, number = {4}, pages = {265--288}, doi = {10.1007/s00200-011-0149-1}, ) @book(sendra, author = {Juan Refael Sendra and Franz Winkler and Perez-Diaz, Sonia}, year = {2008}, title = {Rational Algebraic Curves}, publisher = {Springer Berlin Heidelberg}, doi = {10.1007/978-3-540-73725-4}, ) @article(humanvscomputer, author = {Joseph Steiner and Dana-Picard, Thierry}, year = {2004}, title = {Classroom note: Teaching mathematical integration: human computational skills versus computer algebra}, journal = {International Journal of Mathematical Education in Science and Technology}, volume = {35}, number = {2}, pages = {249--258}, doi = {10.1080/00207390310001615570}, ) @article(szalkowski, author = {Sza\l, Dominik}, year = {2005}, title = {kowski (2005):\emph{Isoptics of open rosettes}}, journal = {Annales Universitatis Mariae Curie-Sk\l odowska}, volume = {Vol. LIX Section A}, pages = {119--128}, ) @article(thom, author = {Ren\'e Thom}, year = {1962}, title = {Sur la th\'eorie des enveloppes}, journal = {Journal de Math\'ematiques Pures et Appliqu{\'e}es}, volume = {XLI}, number = {2}, pages = {1962}, ) @incollection(trouche, author = {Luc Trouche}, year = {2005}, title = {Instrumental Genesis, Individual and Social Aspects}, editor = {Ruthven D. and Trouche and K.}, booktitle = {Mathematics Education Library}, publisher = {Springer-Verlag}, pages = {197--230}, doi = {10.1007/0-387-23435-7\_9}, ) @book(vygotsky1978, author = {Lev Vygotsky}, year = {1978}, title = {Mind in society: The development of higher psychological processes}, publisher = {Harvard University Press}, address = {Cambridge, MA}, ) @incollection(walker, author = {R. A. Walker}, year = {2010}, title = {Sociocultural Issues in Motivation}, booktitle = {International Encyclopedia of Education}, publisher = {Elsevier}, pages = {712--717}, doi = {10.1016/b978-0-08-044894-7.00629-1}, ) @article(wu2, author = {Wen-Tsun, Wu}, year = {1986}, title = {Basic principles of mechanical theorem proving in geometries}, journal = {Journal of Automated Reasoning}, volume = {2}, number = {3}, pages = {221--252}, doi = {10.1007/BF02328447}, ) @book(wu3, author = {Wen tsün Wu}, year = {1994}, title = {Mechanical Theorem Proving in Geometries}, publisher = {Springer Vienna}, doi = {10.1007/978-3-7091-6639-0}, ) @misc(wu1, author = {Wen-Ts\"u Wu}, year = {1984}, title = {Some Recent Advances in Mechanical Theorem-Proving of Geometries}, doi = {10.1090/conm/029/13}, note = {\emph{Contemporary Mathematics} \textbf{29}}, ) @article(ZeDP2010, author = {D. Zeitoun and Dana-Picard, Th.}, year = {2010}, title = {Accurate visualization of graphs of functions of two real variables}, journal = {International Journal of Computational and Mathematical Sciences}, volume = {4}, number = {1}, pages = {1--11}, url = {http://www.waset.org/journals/ijcms/v4/v4-1-1.pdf}, ) @book(ZeDP2017, author = {David Zeitoun and Dana-Picard, Thierry}, year = {2017}, title = {Zooming algorithms for accurate plotting of functions of two real variables}, series = {Proceedings in Mathematics \& Statistics (PROMS)}, volume = {198)}, publisher = {Springer}, note = {499--515}, )