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Preprints

Zamboj, M., & Řada, J. (2023). 3-D shadows of 4-D algebraic hypersurfaces in a 4-D perspective [Preprint]. arXiv. https://doi.org/10.48550/arXiv.2307.12986 (submitted)

Submitted papers and papers in progress

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

Zamboj, M. (submitted). Von Staudt’s constructions on complex numbers. [Video of Gaussian primes constructive algorithm]
Zamboj, M., & Řada, J. (in progress). Four-dimensional linear perspective from double orthogonal projections on 3-spaces [Manuscript in preparation].
Zamboj, M. (n.d.). Spatial interpretation of the method of dilation in Apollonius' problems [in preparation / postponed].
Zamboj, M. (planned). Constructive tasks as a gate to direct proofs [educational].
Zamboj, M. (n.d.). Proof of the juggling average theorem [in a drawer / postponed].

Journal articles

2024
Suzuki, H., Bertocci, S., Cai, H., Cheng, L.-Y., Cocchiarella, L., Schröcker, H.-P., Wohlleben, E., Zamboj, M., & Yasufuku, K. (2024). ISGG: Cooperative mission in the AI era. Journal for Geometry and Graphics, 28(2), 229–240.
2023
Zamboj, M. (2023). Rapsódie na parabole [Rhapsodies on a parabola]. G – slovenský časopis pre geometriu a grafiku, 20(40), 49–59.
2021
Zamboj, M. (2021). Synthetic construction of the Hopf fibration in a double orthogonal projection of 4-space. Journal of Computational Design and Engineering, 8(3), 836–854. https://doi.org/10.1093/jcde/qwab018. arXiv
2018
Zamboj, M. (2018). Sections and shadows of four-dimensional objects. Nexus Network Journal: Architecture and Mathematics, 20(2), 475–487. https://doi.org/10.1007/s00004-018-0384-x
Zamboj, M. (2018). Double orthogonal projection of four-dimensional objects onto two perpendicular three-dimensional spaces. Nexus Network Journal: Architecture and Mathematics, 20(1), 267–281. https://doi.org/10.1007/s00004-017-0368-2
2017
Zamboj, M. (2017). Vrkoče žonglovacích vzorov. G – slovenský časopis pre geometriu a grafiku, 14(27), 45–56.
2016
Zamboj, M. (2016). Projective proof and generalization of Chasles's theorem along non-torsal lines. Journal for Geometry and Graphics, 20(2), 243–251.

Articles in conference proceedings + talks

2025
Zamboj, M. (in press). Lízátkové úlohy z Planimetrie. In Dva dny s didaktikou matematiky 2025. Prague, Czech Republic.
2024
Zamboj, M. (2024). A ruler construction of imaginary numbers on a conic. In Proceedings of the Czech-Slovak Conference on Geometry and Graphics 2024 (pp. 143–148). Pilsen, Czech Republic.
Zamboj, M., & Řada, J. (2024). Geometric illumination of implicit algebraic surfaces. In K. Takenouchi (Ed.), ICGG 2024 – Proceedings of the 21st International Conference on Geometry and Graphics (Vol. 216). Springer, Cham. https://doi.org/10.1007/978-3-031-71225-8_7, arXiv preprint.
2023
Zamboj, M. (2023). Calculating on a parabola. In Proceedings of the 9th Slovak-Czech Conference on Geometry and Graphics 2023 (pp. 203–210). Kremnica, Slovak Republic.
Řada, J., & Zamboj, M. (2023). Four-dimensional visual exploration of the complex number plane. In L. Y. Cheng (Ed.), ICGG 2022 – Proceedings of the 20th International Conference on Geometry and Graphics (Vol. 146). Springer, Cham. https://doi.org/10.1007/978-3-031-13588-0_12, ResearchGate preprint.
2022
Zamboj, M. (2022). Higher-dimensional spaces arising from robot kinematics. In Proceedings of the Czech-Slovak Conference on Geometry and Graphics 2022 (pp. 201–208). Olomouc, Czech Republic.
Zamboj, M. (2022). Aritmetické operace na přímce a kružnici. In Dva dny s didaktikou matematiky 2022. Prague, Czech Republic. ResearchGate preprint.
2021
Zamboj, M. (2021). Twisted filaments with polyhedral symmetries. In Proceedings of the Slovak-Czech Conference on Geometry and Graphics 2021 (pp. 167–172). Kočovce, Slovakia.
Řada, J., & Zamboj, M. (2021). 3-Sphere in a 4-perspective. In Proceedings of moNGeometrija 2021 (pp. 52–61). Belgrade, Serbia. ResearchGate full text.
Zamboj, M. (2021). Interactive 4-D visualization of stereographic images from the double orthogonal projection. In L. Y. Cheng (Ed.), ICGG 2020 – Proceedings of the 19th International Conference on Geometry and Graphics (Vol. 1296). Springer, Cham. https://doi.org/10.1007/978-3-030-63403-2_11, ResearchGate preprint.
2020
Zamboj, M., & Řada, J. (2020). Graphical models of the projective extension of the real 3-space. In Proceedings of the Czech-Slovak Conference on Geometry and Graphics 2020 (pp. 195–202). Pardubice, Czech Republic.
Řada, J., & Zamboj, M. (2020). 3-D printed models of a tesseract in the double orthogonal projection and 4-D perspective. In Proceedings of the Czech-Slovak Conference on Geometry and Graphics 2020 (pp. 153–158). Pardubice, Czech Republic.
Zamboj, M. (2020). Visualization of singular quadric sections of four-dimensional cones. In Proceedings of moNGeometrija 2020 (pp. 89–98). Belgrade, Serbia. (Selected for publication in FME Transactions, 49(2), 2021.)
Zamboj, M. (2020). Matematické úlohy inšpirované žonglovaním II. In Dva dny s didaktikou matematiky 2020 (pp. 174–179). Prague, Czech Republic.
Zamboj, M. (2020). 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 (pp. 1140–1164). Bratislava, Slovakia. ResearchGate preprint
2019
Zamboj, M. (2019). 1-2-3-sphere in the 4-space. In Proceedings of the Slovak-Czech Conference on Geometry and Graphics 2019 (pp. 217–222). Trenčianske Teplice, Slovakia.
Zamboj, M. (2019). Matematické úlohy inšpirované žonglovaním I. In Dva dny s didaktikou matematiky 2019 (pp. 103–109). Prague, Czech Republic.
Zamboj, M. (2019). Quadric sections of four-dimensional cones. In M. Cocchiarella (Ed.), ICGG 2018 – Proceedings of the 18th International Conference on Geometry and Graphics (Vol. 809, pp. 500–513). Springer, Cham. https://doi.org/10.1007/978-3-319-95588-9_41
2018
Zamboj, M. (2018). A four-dimensional construction of the pole of a tetrahedron with respect to a plane. In Proceedings of the Czech-Slovak Conference on Geometry and Graphics 2018. Blansko, Skalní mlýn, Czech Republic.
Zamboj, M. (2018). Žonglování s matematikou, matematika v žonglování (invited talk). In Elixír do škol 2018. Hradec Králové, Czech Republic.
Zamboj, M. (2018). Parabola a jej podobenstvá. In Dva dny s didaktikou matematiky 2018 (pp. 73–77). Prague, Czech Republic.
2017
Zamboj, M. (2017). On methods of synthetic projective geometry. In Proceedings of the Slovak-Czech Conference on Geometry and Graphics 2017 (pp. 179–184). Vršatské podhradie, Slovakia.
2016
Zamboj, M. (2016). Braids of juggling patterns. In Proceedings of the Czech-Slovak Conference on Geometry and Graphics 2016 (pp. 207–216). Rožnov pod Radhoštěm, Czech Republic.
Zamboj, M. (2016). Non-projective problems of the Chasles theorem. In Bečvář, J., & Bečvářová, M. (Eds.), Proceedings of the 37th International Conference on History of Mathematics (pp. 189–194). Matfyzpress, Prague, Czech Republic.

Theses

Zamboj, M. (2018). Synthetic projective geometry (Doctoral dissertation). Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic.
Zamboj, M. (2014). Matematická teória žonglovania [Mathematical theory of juggling] (Master’s thesis). Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic.

Other

Geometric illumination of implicit algebraic surfaces by Michal Zamboj, Jakub Řada, Wolfram Community, STAFF PICKS, September 25, 2024, https://community.wolfram.com/groups/-/m/t/3283344, Mathematica notebook with code for the paper on ICGG 2024.

Talks

2024
Zamboj, M. (2024). „Trojúhelníky jsou k ničemu!“ Seminář o výuce matematiky pro učitele SŠ a 2. st. ZŠ, Ostravská Univerzita, Ostrava, Czech Republic.
2023
Zamboj, M. (2023). A parabola in a square grid and its use across school levels and topics. 54. doktorandská škola didaktiky matematiky, Brandýs nad Labem, PedF UK, Czech Republic.
Zamboj, M. (2023). 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.
Zamboj, M. (2023). Mezi analogií a paradoxem ve čtvrté dimenzi. Noc vědců, Univerzita Karlova, Praha, Czech Republic.
Zamboj, M. (2023). „Trojúhelníky jsou k ničemu!“ neboli: co se skrývá ve formální struktuře konstrukční úlohy. Praha, Czech Republic.
Zamboj, M. (2023). Mezi analogií a paradoxem ve vyšších dimenzích. Letní škola geometrie 2023, Česká Lípa, Czech Republic.
Zamboj, M. (2023). Čtvrtá dimenze: mezi analogií a paradoxem. Povídání o učení, MFF UK, Praha, Czech Republic.
Zamboj, M. (2023). AI in the academic space: benefits and challenges (discussion). 53. doktorandská škola didaktiky matematiky, Brandýs nad Labem, PedF UK, Czech Republic.
Zamboj, M. (2023). Prostorová interpretace metody dilatace v rovině. Dva dny s didaktikou matematiky 2023, Praha, Czech Republic.
2022
Zamboj, M. (2022). Triangles are good for nothing II (still). 52. doktorandská škola didaktiky matematiky, Brandýs nad Labem, PedF UK, Czech Republic.
Zamboj, M. (2022). Mezi analogií a paradoxem ve čtyřrozměrné geometrii. Seminář KM, PedF MUNI, Brno, Czech Republic.
Zamboj, M. (2022). Pohledy do čtvrtého rozměru. Konference českých matematiků, VŠB TU, Ostrava, Czech Republic.
2021
Zamboj, M. (2021). Trojúhelníky jsou k ničemu I. 50. doktorandská škola didaktiky matematiky, Brandýs nad Labem, PedF UK, Czech Republic.
Zamboj, M. (2021). Four dimensions of the fourth dimension. Seminář katedry matematiky a didaktiky matematiky, PedF UK, Czech Republic.
2020
Zamboj, M. (2020). O antickém důkazu. Tábor mladých matematiků, Bezdědice, Czech Republic.
Zamboj, M. (2020). 4 rozměry 4-rozměrné vizualizace. Seminář KDM, MFF UK, Czech Republic.
2019
Zamboj, M. (2019). The Field of Cows. 48. doktorandská škola didaktiky matematiky, Brandýs nad Labem, Czech Republic.
Zamboj, M. (2019). Four-Dimensional Visual Construction of the Hopf Fibration. 47. doktorandská škola didaktiky matematiky, Brandýs nad Labem, Czech Republic.
2018
Zamboj, M. (2018). Visualization of the Four-Dimensional Space. 46. doktorandská škola didaktiky matematiky, Brandýs nad Labem, Czech Republic.
Zamboj, M. (2018). Visualization of four-dimensional objects onto mutually perpendicular 3-spaces. Seminar of the Institut für Diskrete Mathematik und Geometrie, TU Wien, Austria.
Zamboj, M. (2018). Monge projection of the four-dimensional space. PhD afternoon, MFF UK, Czech Republic.
2017
Zamboj, M. (2017). Synthetic projective methods used for solving problems in geometry. WDS-M 2017 Book of abstracts, Reprostředisko MFF UK, Praha, Czech Republic, p. 12. 2015
Zamboj, M. (2015). Synthetic approach to Chasles theorem for timelike ruled surface. WDS-M 2015 Book of abstracts, Reprostředisko MFF UK, Praha, Czech Republic, p. 16. + presentation
List of talks on Mathematics of Juggling