A heuristic overview of curvature

Moghadassi, Mohammad

doi:10.22108/msci.2021.127330.1414

A heuristic overview of curvature

Document Type : Promotional Paper

Author

Mohammad Moghadassi

Department of Physics, Faculty of Basic Sciences, University of Neyshabur, Neyshabur, Iran

10.22108/msci.2021.127330.1414

Abstract

In this article, we aim to examine the concepts of curvature using simple and relatively intuitive explanations. We will see that curvature differs from the perspective of inhabitants of a flat world compared to what individuals outside of it perceive, and this curvature is defined using the concept of distance. In particular, it is possible to define quantities based on geometric concepts that determine whether a surface is flat or curved based on the vanishing or non-vanishing of that quantity.

Keywords

Main Subjects

Mathematical generalization

References

[1] S. Carroll, Spacetime and Geometry, Addison Wesley, New York, 2004.
[2] K. F. Gauss, General Investigations of Curved Surfaces of 1827 and 1825, translated by A. Hiltebeitel and J. More-head, The Princeton Library Publishing Association, Princeton, NJ, 1902.
[3] A. Pressley, Elementary Diﬀerential Geometry, Springer, London, 2001.
[4] S. Weinberg, Gravitation and Cosmology: Principle and Applications of General Ttheory of Relativity, John Wiley and Sons, New York, 1972.