Advances in Geometry: A Review of Recent Developments

Authors

  • Ronald Wei Department of Applied Mathematics, Nanyang Polytechnic, Singapore

DOI:

https://doi.org/10.61424/gjme.v1i1.55

Keywords:

Geometry, algebraic equations, Riemannian geometry, discrete geometry

Abstract

This study presents a comprehensive review of recent developments in the field of geometry. It aims to provide an overview of the advances made in various branches of geometry, including differential geometry, algebraic geometry, and discrete geometry. The research methodology adopted for this study is secondary data analysis. The study has extensively reviewed a wide range of academic articles, conference papers, and book chapters published in the last decade. The data was collected from various databases and libraries, ensuring a diverse and representative sample of the current state of the field. The study begins by providing a brief introduction to the historical context of geometry and its fundamental principles. It then delves into each branch of geometry separately, discussing the key theoretical developments and practical applications. In differential geometry, the study highlights recent advancements in the understanding of curvature, connections, and geometric flow. It discusses the emerging field of Riemannian geometry and its relevance in understanding complex geometric structures. The study also explores the advancements in algebraic geometry, focusing on geometric methods used for solving algebraic equations and studying algebraic varieties. It discusses the role of computational algebraic geometry and algebraic topology in solving complex geometric problems. Furthermore, the study reviews the recent developments in discrete geometry, including the study of geometric structures in discrete spaces and combinatorial optimization problems. It discusses the applications of discrete geometry in computer science, robotics, and network analysis. The findings of this study reveal that there have been significant advancements in various branches of geometry in recent years. These developments have expanded our understanding of geometric structures and their applications in various fields. The findings of this study can serve as a valuable resource for researchers, academics, and practitioners interested in the latest developments in geometry.

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Published

2024-05-20 — Updated on 2024-11-23

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How to Cite

Wei, R. (2024). Advances in Geometry: A Review of Recent Developments. Global Journal of Mathematics and Statistics, 1(1), 10–20. https://doi.org/10.61424/gjme.v1i1.55 (Original work published May 20, 2024)