×

zbMATH — the first resource for mathematics

New dynamics in dynamic geometry: dragging constructed points. (English) Zbl 1444.68277
Summary: Dynamic Geometry Software (DGS) is present for more than three decades: it found its way to classrooms worldwide and it is now an irreplaceable component of mathematical education. From the very beginning and still, DGS tools are built around one central scenario: the user chooses several (free) points and, using them, constructs some other points and other geometric objects. Then, the user can move (“drag”) a chosen free point and explore how the constructed points and other constructed objects change. In this paper we describe one new DGS scenario: the user can move the constructed points and explore how the free points and the constructed objects change accordingly. This scenario uses a solver for geometry construction problems. We implemented this DGS feature within our prototype tool Touch&Drag, developed for touch-based devices. The presented feature can be implemented in other DGS tools, too.
MSC:
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
68W30 Symbolic computation and algebraic computation
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Baran, I., KSEG (2007)
[2] Björck, A., Numerical Methods for Least Squares Problems (1996), SIAM · Zbl 0847.65023
[3] Botana, F.; Hohenwarter, M.; Janičić, P.; Kovács, Z.; Petrović, I.; Recio, T.; Weitzhofer, S., Automated theorem proving in GeoGebra: current achievements, J. Autom. Reason., 55, 1, 39-59 (2015) · Zbl 1356.68181
[4] Cheema, S.; Gulwani, S.; LaViola, J. J., Quickdraw: improving drawing experience for geometric diagrams, (Conference on Human Factors in Computing Systems, CHI ’12 (2012)), 1037-1064
[5] Chen, X.; Wang, D., Automated generation of geometric theorems from images of diagrams, Ann. Math. Artif. Intell., 74, 333-358 (2015) · Zbl 1330.68263
[6] Chou, S.-C.; Gao, X.-S.; Zhang, J.-Z., Machine Proofs in Geometry (1994), World Scientific: World Scientific Singapore
[7] Connelly, H., An extension of triangle constructions from located points, Forum Geom., 9, 109-112 (2009) · Zbl 1168.51302
[8] Ehmann, M.; Gerhäuser, M.; Miller, C.; Wassermann, A., Sketchometry and jsxgraph: dynamic geometry for mobile devices, South Bohemia Math. Lett., 21, 1, 1-7 (2013)
[9] Fernandes, H.; Ducasse, S.; Carron, T., DR. GEO II: adding interactivity planes in interactive dynamic geometry, (Fifth International Conference on Creating, Connecting and Collaborating through Computing \((C^5 2007) (2007)\), IEEE Computer Society: IEEE Computer Society Japan), 153-162
[10] Hohenwarter, M.; Fuchs, K., Combination of dynamic geometry, algebra and calculus in the software system geogebra, (Computer Algebra Systems and Dynamic Geometry Systems in Mathematics Teaching Conference 2004, Pecs, Hungary (2004)), 128-133
[11] Jackiw, N., The Geometer’s Sketchpad v4.0 (2001), Key Curriculum Press: Key Curriculum Press Emeryville
[12] Janičić, P., GCLC - a tool for constructive euclidean geometry and more than that, (Proceedings of International Congress of Mathematical Software (ICMS 2006). Proceedings of International Congress of Mathematical Software (ICMS 2006), Lecture Notes in Computer Science, vol. 4151 (2006), Springer-Verlag), 58-73 · Zbl 1230.51024
[13] Janičić, P., Geometry constructions language, J. Autom. Reason., 44, 1-2, 3-24 (2010) · Zbl 1185.68626
[14] Janičić, P.; Quaresma, P., System description: GCLCprover + GeoThms, (International Joint Conference on Automated Reasoning (IJCAR-2006). International Joint Conference on Automated Reasoning (IJCAR-2006), Lecture Notes in Artificial Intelligence, vol. 4130 (2006), Springer-Verlag), 145-150
[15] Kapur, D., Using Gröbner bases to reason about geometry problems, J. Symb. Comput., 2, 4, 399-408 (1986) · Zbl 0629.68087
[16] Kortenkamp, U., Foundations of Dynamic Geometry (1999), ETH Zurich, Ph.D. thesis
[17] Laborde, J.-M.; Strasser, R., Cabri-géométre: a microworld of geometry for guided discovery learning, Zent.bl. Didact. Mat., 22, 5, 171-177 (1990)
[18] Marić, F.; Petrović, I.; Petrović, D.; Janičić, P., Formalization and implementation of algebraic methods in geometry, (Proceedings First Workshop on CTP Components for Educational Software. Proceedings First Workshop on CTP Components for Educational Software, Electronic Proceedings in Theoretical Computer Science, vol. 79 (2012), Open Publishing Association), 63-81
[19] Marinković, V., On-line compendium of triangle construction problems with automatically generated solutions, Teach. Math., XVIII, 1, 29-44 (2015)
[20] Marinković, V., ArgoTriCS - automated triangle construction solver, J. Exp. Theor. Artif. Intell., 29, 2, 247-271 (2017)
[21] Marinković, V.; Janičić, P., Towards understanding triangle construction problems, (Intelligent Computer Mathematics — CICM 2012. Intelligent Computer Mathematics — CICM 2012, Lecture Notes in Computer Science, vol. 7362 (2012), Springer), 126-141 · Zbl 1359.68265
[22] Marinković, V.; Janičić, P.; Schreck, P., Computer theorem proving for verifiable solving of geometric construction problems, (Automated Deduction in Geometry (2015), Springer International Publishing), 72-93 · Zbl 1434.03032
[23] Obrecht, C., Eukleides (2010)
[24] Princen, J.; Illingworth, J.; Kittler, J., A formal definition of the Hough transform: properties and relationships, J. Math. Imaging Vis., 1, 2, 153-168 (1992)
[25] Richter-Gebert, J.; Kortenkamp, U., Cinderella — The Interactive Geometry Software (1999), Springer · Zbl 0926.51002
[26] Schreck, P.; Mathis, P., RC-constructibility of problems in Wernick’s list, (Proceedings of the 10th International Workshop on Automated Deduction in Geometry (ADG 2014) (2014)), 85-104, CISUC Technical Report TR 2014/01, University of Coimbra
[27] Schreck, P.; Mathis, P., Using jointly geometry and algebra to determine RC-constructibility, J. Symb. Comput., 90, 124-148 (2019) · Zbl 1395.68352
[28] Šukilović, T., Curvature based shape detection, Comput. Geom., 48, 180-188 (2015) · Zbl 1304.65109
[29] Wernick, W., Triangle constructions with three located points, Math. Mag., 55, 4, 227-230 (1982) · Zbl 0497.51016
[30] Wu, W.-T., On the decision problem and the mechanization of theorem proving in elementary geometry, Sci. Sin., 21, 157-179 (1978)
[31] Yerushalmy, M.; Houde, R. A., The geometric supposer: promoting thinking and learning, Math. Teach., 79, 6, 418-422 (1986)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.