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Journal articles

2023
M. Zamboj: Rapsódie na parabole (Rhapsodies on a parabola). In G – slovenský časopis pre geometriu a grafiku, 20 (2023), No. 40, pp. 49-59.
2021
M. Zamboj: Synthetic construction of the Hopf fibration in a double orthogonal projection of 4-space. Journal of Computational Design and Engineering, Volume 8, Issue 3, June 2021, Pages 836–854, DOI: 10.1093/jcde/qwab018 (Open Access), arXiv
M. Zamboj: Visualization of singular quadric sections of four-dimensional cones. FME Transactions, (in press). (reprint of the paper in Proceedings moNGeometrija 2020)
2018
M. Zamboj: Sections and Shadows of Four-Dimensional Objects. In Nexus Network Journal: Architecture and Mathematics, 20 (2018), Issue 2, pp. 475-487, DOI: 10.1007/s00004-018-0384-x.
M. Zamboj: Double Orthogonal Projection of Four-Dimensional Objects Onto Two Perpendicular Three-Dimensional Spaces. In Nexus Network Journal: Architecture and Mathematics, 20 (2018), Issue 1, pp. 267-281, DOI: 10.1007/s00004-017-0368-2.
2017
M. Zamboj: Vrkoče žonglovacích vzorov. In G – slovenský časopis pre geometriu a grafiku, 14 (2017), No. 27, pp. 45-56.
2016
M. Zamboj: Projective Proof and Generalization of Chasles's Theorem Along Non-Torsal Lines. In Journal for Geometry and Graphics 20 (2016), No. 2, pp. 243-251.

Preprints

J. Řada, M. Zamboj: 3-D Shadows of 4-D Algebraic Hypersurfaces in a 4-D Perspective DOI: 10.48550/arXiv.2307.12986 (submitted)

Submitted papers and papers in progress

(* feel free to contact me if you want to participate)

M. Zamboj, J. Řada: Geometric Illumination of Implicit Surfaces. (submitted) M. Zamboj: Four-dimensional geometric arithmetics with complex numbers (visualization, almost done).
M. Zamboj, with J. Řada: Four-dimensional linear perspective from double orthogonal projections on 3-spaces (descriptive geometry, in progress).
M. Zamboj: Spatial interpretation of the method of dilation in Apollonius' problems. M. Zamboj: Constructive tasks as a gate to direct proofs. (planned, educational).

Articles in conference proceedings + talks

2023
M. Zamboj: Calculating on a parabola. In Proceedings of Slovak-Czech Conference on Geometry and Graphics 2023, Kremnica, Slovak Republic (in progress).
J. Řada, M. Zamboj: Four-Dimensional Visual Exploration of the Complex Number Plane. In Cheng LY. (eds) ICGG 2022 - Proceedings of the 20th International Conference on Geometry and Graphics. ICGG 2022. Lecture Notes on Data Engineering and Communications Technologies, vol 146. Springer, Cham. DOI: 10.1007/978-3-031-13588-0_12. ResearchGate preprint
2022
M. Zamboj: Higher-dimensional spaces arising from robot kinematics. In Proceedings of Czech-Slovak Conference on Geometry and Graphics 2022, Olomouc, Czech Republic, pp. 201-208.
M. Zamboj: Aritmetické operace na přímce a kružnici. In Dva dny s didaktikou matematiky 2022, Prague, Czech Republic. ResearchGate preprint.
2021
M. Zamboj: Twisted Filaments with Polyhedral Symmetries. In Proceedings of Slovak-Czech Conference on Geometry and Graphics 2021, Kočovce, Slovakia, pp. 167-172
J. Řada, M. Zamboj: 3-Sphere in a 4-Perspective. In Proceedings moNGeometrija 2021, 52-61, moNGeometrija 2021, Belgrade, Serbia. ResearchGate fulltext
M. Zamboj: Interactive 4-D Visualization of Stereographic Images from the Double Orthogonal Projection. In: Cheng LY. (eds) ICGG 2020 - Proceedings of the 19th International Conference on Geometry and Graphics. ICGG 2021. Advances in Intelligent Systems and Computing, vol 1296. Springer, Cham. DOI: 10.1007/978-3-030-63403-2_11. ResearchGate preprint.
2020
M. Zamboj, J. Řada: Graphical models of the projective extension of the real 3-space. In Proceedings of Czech-Slovak Conference on Geometry and Graphics 2020, Pardubice, Czech Republic, pp. 195-202.
J. Řada, M. Zamboj: 3-D printed models of a tesseract in the double orthogonal projection and 4-D perspective. In Proceedings of Czech-Slovak Conference on Geometry and Graphics 2020, Pardubice, Czech Republic, 153-158.
M. Zamboj: Visualization of singular quadric sections of four-dimensional cones. In Proceedings moNGeometrija 2020, 89-98, moNGeometrija 2020, Belgrade, Serbia. (selected to be published in FME Transactions, 49 (2021), No. 2. )
M. Zamboj: Matematické úlohy inšpirované žonglovaním II. Dva dny s didaktikou matematiky 2020, Sborník příspěvků, Prague, Czech Republic, pp. 174-179.
M. Zamboj: Visualizing Objects of Four-Dimensional Space: From Flatland to the Hopf Fibration (invited talk). In Proceedings of the 19th Conference on Applied Mathematics Aplimat 2020, Bratislava, Slovakia, pp. 1140-1164. ResearchGate preprint
2019
M. Zamboj: 1-2-3-Sphere in the 4-Space. In Proceedings of Slovak-Czech Conference on Geometry and Graphics 2019, Trenčianske Teplice, Slovakia, pp. 217-222.
M. Zamboj: Matematické úlohy inšpirované žonglovaním I. Dva dny s didaktikou matematiky 2019, Sborník příspěvků, Prague, Czech Republic, pp. 103-109.
M. Zamboj: Quadric Sections of Four-Dimensional Cones. In Cocchiarella (ed): ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics, Milan, Italy. Advances in Intelligent Systems and Computing, vol 809. Springer, Cham, 2019, pp. 500-513, DOI: 10.1007/978-3-319-95588-9_41.
2018
M. Zamboj: A Four-Dimensional Construction of the Pole of a Tetrahedron with Respect to a Plane. In Proceedings of Czech-Slovak Conference on Geometry and Graphics 2018, Blansko, Skalní mlýn, Czech Republic.
M. Zamboj: Žonglování s matematikou, matematika v žonglování (invited talk). Konference Elixír do škol 2018, Hradec Králové, Czech Republic.
M. Zamboj: Parabola a jej podobenstvá. Dva dny s didaktikou matematiky 2018, Prague, Czech Republic, pp. 73-77.
2017
M. Zamboj: On Methods of Synthetic Projective Geometry. In Proceedings of Slovak-Czech Conference on Geometry and Graphics 2017, Vršatské podhradie, Slovakia, pp. 179-184.
2016
M. Zamboj: Braids of Juggling Patterns. In Proceedings of Czech-Slovak Conference on Geometry and Graphics 2016, Rožnov pod Radhoštem, pp. 207-216.
M. Zamboj: Non-projective problems of the Chasles theorem. In Bečvář, Bečvářová (eds.): 37th International conference on History of mathematics, Matfyzpress, Praha, 2016, pp. 189–194.

Theses

M. Zamboj: Synthetic projective geometry, Ph.D. thesis, Mathematical Institute, Faculty of Mathematics and Physics, Charles University, 2018.
M. Zamboj: Matematická teória žonglovania (Mathematical Theory of Juggling), Master's thesis, Department of Mathematics Education, Faculty of Mathematics and Physics, Charles University, 2014.

Talks

2023
M. Zamboj: A parabola in a square grid and it use across chool levels and topics, The 54th PhD school of didactics of mathematics, Brandýs nad Labem, PedF UK, 2023.
M. Zamboj: Mezi analogií a paradoxem v různých dimenzích, Jak učit matematice žáky ve věku 10–16 let, Univerzita J. E. Purkyně, Ústí nad Labem, Czech Republic, 2023.
M. Zamboj: Mezi analogií a paradoxem ve čtvrté dimenzi, Noc vědců, Univerzita Karlova, Praha, Czech Republic, 2023.
M. Zamboj: „Trojúhelníky jsou k ničemu!“ neboli: co se skrývá ve formální struktuře konstrukční úlohy, Prague, Czech Republic, 2023.
M. Zamboj: Mezi analogií a paradoxem ve vyšších dimenzích, Letní škola geometrie 2023, Česká Lípa, Czech Republic, 2023.
M. Zamboj: Povídání o učení: Čtvrtá dimenze: mezi analogií a paradoxem, MFF UK, Prague, Czech Republic, 2023.
M. Zamboj: AI in the academic space: benefits and challenges (discussion), The 53rd PhD school of didactics of mathematics, Brandýs nad Labem, PedF UK, 2023.
M. Zamboj: Prostorová interpretace metody dilatace v rovině, Dva dny s didaktikou matematiky 2023, Prague, Czech Republic, 2023.
2022
M. Zamboj: Triangles are good for nothing II (still)., The 52nd PhD school of didactics of mathematics, Brandýs nad Labem, PedF UK, 2022.
M. Zamboj: Mezi analogií a paradoxem ve čtyřrozměrné geometrii, Seminář KM, Brno, PedF MUNI, 2022.
M. Zamboj: Pohledy do čtvrtého rozměru, Konference českých matematiků, Ostrava, VŠB TU, 2022.
2021
M. Zamboj: Trojúhelníky jsou k ničemu I., The 50th PhD school of didactics of mathematics, Brandýs nad Labem, PedF UK, 2021
M. Zamboj: Four dimensions of the fourth dimension, Mathematics education seminar of the Dep. of Mathematics and Mathematical Education, PedF UK, 2021.
2020
M. Zamboj: O antickém důkazu, Tábor mladých matematiků, Bezdědice, 2020.
M. Zamboj: 4 rozměry 4-rozměrné vizualizace, Seminář KDM, MFF UK, 2020.
2019
M. Zamboj: The Field of Cows, The 48th PhD school of didactics of mathematics, Brandýs nad Labem, 2019.
M. Zamboj: Four-Dimensional Visual Construction of the Hopf Fibration, The 47th PhD school of didactics of mathematics, Brandýs nad Labem, 2019.
2018
M. Zamboj: Visualization of the Four-Dimensional Space, The 46th PhD school of didactics of mathematics, Brandýs nad Labem, 2018.
M. Zamboj: Visualization of four-dimensional objects onto mutually perpendicular 3-spaces, Seminar of the Institut für Diskrete Mathematik und Geometrie, TU Wien, 2018.
M. Zamboj: Monge projection of the four-dimensional space, PhD afternoon, MFF UK, 2018.
2017
M. Zamboj: Synthetic projective methods used for solving problems in geometry. WDS-M 2017 Book of abstracts, Reprostředisko MFF UK Praha, 2017, p. 12. + presentation
2015
M. Zamboj: Synthetic approach to Chasles theorem for timelike ruled surface. WDS-M 2015 Book of abstracts, Reprostředisko MFF UK Praha, 2015, p. 16. + presentation
List of talks on Mathematics of Juggling