Exploring new theorems in non-Euclidean geometry for advanced mathematical geometric applications

Mane, Vikramsinha V.; Shrivastav, Anjali; Abhyankar, Girish; Deshpande, Abhijeet; Prabhakar, Budigi; Khudaynazarov, Egambergan

doi:10.47974/JIM-2488

Open Access Research Article

Exploring new theorems in non-Euclidean geometry for advanced mathematical geometric applications

Vikramsinha V. Manevvmosmanabad@gmail.comDepartment of Mechanical EngineeringTerna Public Charitable Trust’s College of EngineeringOsmanabad, Maharashtra, 413501, IndiaView full profile → , ^*Anjali ShrivastavCorresponding authoranjali.shrivastav@pccoepune.orgDepartment of Electronics and TelecommunicationPimpri Chinchwad College of EngineeringPune, Maharashtra, 411044, IndiaView full profile → , Girish Abhyankargabhyankar@symlaw.ac.inSymbiosis Law School Pune (SLS-P)Symbiosis Centre for Advanced Legal Studies and Research (SCALSAR), Symbiosis International (Deemed University)Pune, Maharashtra, 411014, IndiaView full profile → , Abhijeet Deshpandeabhijeet.deshpande@vit.eduDepartment of Mechanical EngineeringVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , Budigi Prabhakarbudigi.prabhakar@niu.edu.inDepartment of PhysicsNoida International UniversityGreater Noida, Uttar Pradesh, 203201, IndiaView full profile → , Egambergan Khudaynazarove.xudaynazarov@mamunedu.uzDepartment of General Professional SciencesMamun UniversityKhiva, 220900, Uzbekistan0009-0000-1210-8113View full profile →

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pp. 537–546Vol. 29Issue 3March 2026DOI: 10.47974/JIM-2488XML

Received:: 01 Mar 2025
Published Online:: 18 Mar 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2488
Pages:: 537–546

Abstract

This study examines the new theories of non-Euclidean geometry to avoid issues of more complex mathematical applications of the normal geometry structures. In curved space cases, the older ones would not work. We enhance the reality of the structure modelling by introducing new theories through hyperbolic and elliptic shapes. There were advanced mathematics techniques in geometry, geodesic analysis and manifold theory. The results indicate that complex systems are characterized by a higher level of spatial forecasts and topological consistency. Physics, engineering, and computer modelling are also possible using these theories and they provide us with more information on the behaviour of shapes outside of Euclidean space.

Keywords

Non-euclidean geometry Geodesic analysis Hyperbolic space Advanced geometric modeling Manifold theory

Subject Classifications

53A35

References

[1] L. Jenkovszky, M. J. Lake, and V. Soloviev, “János Bolyai, Carl Friedrich Gauss, Nikolai Lobachevsky and the New Geometry: Foreword,” Symmetry, vol. 15, pp. 707 (2023).
[2] Y. He, J. Zou, X. Zhang, N. Zhu, and T. Leng, “FGeo-TP: A Language Model-Enhanced Solver for Euclidean Geometry Problems,” Symmetry, vol. 16, pp. 421 (2024).
[3] Z. Balajti, “Generalization Process of the Integrated Mathematical Model Created for the Development of the Production Geometry of Complicated Surfaces,” Symmetry, vol. 16, pp. 1618 (2024).
[4] Iddo Drori, Sarah Zhang, Reece Shuttleworth, Leonard Tang, Albert Lu, Elizabeth Ke, and Kevin Liu, “A neural network solves, explains, and generates university math problems by program synthesis and few-shot learning at human level,” Proceedings of the National Academy of Sciences of the USA, vol. 119, pp. e2123433119 (2022).
[5] T. N. Mundhenk, M. Landajuela, R. Glatt, C. P. Santiago, D. M. Faissol, and B. K. Petersen, “Symbolic regression via neural-guided genetic programming population seeding,” arXiv preprint, arXiv:2111.00053 (2021).
[6] S. Polu, J. M. Han, K. Zheng, M. Baksys, I. Babuschkin, and I. Sutskever, “Formal mathematics statement curriculum learning,” arXiv preprint, arXiv:2202.01344 (2022).
[7] Bolla Sai Durga Prasanna and Chiraparapu Srinivasa Rao, “Village Development System using Greedy Algorithm,” International Journal for Interdisciplinary Sciences and Engineering Applications, Volume 6, Issue 3, pp. 12–19 (2025), doi: 10.5281/zenodo.16728954
[8] S. Eddahmani, “More than two decades of attacks on the AES cryptosystem,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 28, no. 3, pp. 667–683 (2025).
[9] P. Lu, R. Gong, S. Jiang, L. Qiu, S. Huang, X. Liang, and S. C. Zhu, “Inter-GPS: Interpretable geometry problem solving with formal language and symbolic reasoning,” arXiv preprint, arXiv:2105.04165 (2021).
[10] J. Chen, J. Tang, J. Qin, X. Liang, L. Liu, E. Xing, and L. Lin, “GeoQA: A geometric question answering benchmark towards multimodal numerical reasoning,” arXiv preprint, arXiv:2105.14517 (2021).
[11] R. Patil, K. M. Upalkar, A. K. Pardeshi, A. S. Tashildar, and A. I. Khan, “Predicting Customer Churn In Banking Sector,” International Journal of Advanced Electronics and Communication Engineering (IJAECE), vol. 14, no. 1, pp. 19–30 (Apr. 2025).
[12] C. Deshpande, C. Ramtirthkar, T. A. Wani, V. K. Bhosale, M. Gulhane, and K. S. Kumar, “Topology and knot theory applications in quantum field theory,” Journal of Interdisciplinary Mathematics, vol. 28, no. 6, pp. 2281–2287 (2025), doi: 10.47974/JIM-2370.
[13] G. Kaur, M. Kaur, J. Singh, M. M. Laishram, S. Lakhanpal, and M. Kumar, “Effective strategies for writing maintainable code in cryptographic software development,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 29, no. 2-A, pp. 609–616 (2026), doi: 10.47974/JDMSC-2503.
[14] P. Sahane, M. Gulhane, N. Rakesh, S. M. M. Naidu, M. Grover, and V. Mahajan, “Evaluating lightweight encryption schemes for resource-constrained devices in wireless sensor networks,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 28, no. 5-A, pp. 1803–1812 (2025), doi: 10.47974/JDMSC-2180.

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