| Issue |
E3S Web Conf.
Volume 223, 2020
Regional Problems of Earth Remote Sensing (RPERS 2020)
|
|
|---|---|---|
| Article Number | 02005 | |
| Number of page(s) | 6 | |
| Section | Models and Methods of Remote Sensing Data Processing | |
| DOI | https://doi.org/10.1051/e3sconf/202022302005 | |
| Published online | 21 December 2020 | |
About the geographic grid of the three-dimensional hypersphere
Federal State Budgetary Institution of Science Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences, 6, Ac. Lavrentieva ave., Novosibirsk, 630090, Russia
* Corresponding author: kim@ooi.sscc.ru
According to the Poincaré conjecture (1904) proved by Grigory Perelman (2002-2003) that any simply connected compact three- dimensional manifold without edges is homeomorphic to a three- dimensional hypersphere [1], to solve the problems of visualizing four- dimensional objects in three-dimensional space [2], it is proposed to choose a suitable manifold, in in this case, a ball, establishing a homeomorphism between objects located in different spaces by technological means of cartography. As a result of this work, it seems possible to build a dynamic video of the population distribution process on a map of the globe, which provides informational four-dimensional data flow, following the ideas embodied in 4D Anatomy [3]. The proposed technology opens up new ways of visualizing four-dimensional space This work was performed within the framework of the state assignment of the ICM MG SB RAS (project 0315-2019-0003).
© The Authors, published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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