Geodesic
On the distinction between one-dimensional Euclidean and hyperbolic spaces
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2015), pp. 97-102.

Voir la notice de l'article provenant de la source Math-Net.Ru

The difference between Euclidean and hyperbolic spaces is clear starting with dimension two. However, the difference between elliptic space and both Euclidean and hyperbolic ones can be described also for dimension one. Does it mean that there is no difference between one-dimensional Euclidean and hyperbolic lines, or it is necessary to better define the difference between them? This paper proposes one possible way to draw clear distinction between one-dimensional Euclidean and hyperbolic lines. 
@article{BASM_2015_1_a5,
     author = {Alexandru Popa},
     title = {On the distinction between one-dimensional {Euclidean} and hyperbolic spaces},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {97--102},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2015_1_a5/}
}
TY  - JOUR
AU  - Alexandru Popa
TI  - On the distinction between one-dimensional Euclidean and hyperbolic spaces
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2015
SP  - 97
EP  - 102
IS  - 1
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2015_1_a5/
LA  - en
ID  - BASM_2015_1_a5
ER  - 
%0 Journal Article
%A Alexandru Popa
%T On the distinction between one-dimensional Euclidean and hyperbolic spaces
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2015
%P 97-102
%N 1
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2015_1_a5/
%G en
%F BASM_2015_1_a5
Alexandru Popa. On the distinction between one-dimensional Euclidean and hyperbolic spaces. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2015), pp. 97-102. https://geodesic-test.mathdoc.fr/item/BASM_2015_1_a5/

[1] Kobayashi S., Nomizu K., Foundations of differential geometry, Interscience Tracts in Pure and Applied Math., 15, John Wiley and Sons, Inc., New York, 1963, xi+329 pp. | MR

[2] Faber R. L., Foundations of Euclidean and Non-Euclidean Geometry, Marcel Dekker, New York, 1983, 329 pp. | MR | Zbl

[3] Gans D., “Axioms for elliptic geometry”, Canad. J. Math., 4 (1952), 81–92 | MR | Zbl

[4] Klein F., “A comparative review of recent researches in geometry”, Bull. New York Math. Soc., 3 (1893), 215–249 | MR

[5] Klein F., Vorlesungen über nicht-Euklidische Geometrie, Grundlehren Math. Wiss., 26, Springer, 1968, 326 pp. | MR

[6] Rosenfeld B. B., Non-Euclidean Spaces, Nauka, Moscow, 1969, 547 pp. (in Russian)

[7] Yaglom. I. M., A simple non–euclidean geometry and its physical basis, Springer-Verlag, New York, 1969, 307 pp. | MR

[8] Artykbaev A., Sokolov D. D., Geometry in large in flat space-time, Fan, Tashkent, 1991, 180 pp. (in Russian)

[9] Romakina L. N., Geometry of co-Euclidean and co-pseudo-Euclidean planes, Nauchnaya kniga, Saratov, 2008, 280 pp. (in Russian)

[10] Popa A., Analytic Geometry of Homogeneous Spaces, Monograph, 2014, 150 pp. http://sourceforge.net/projects/geomspace/files/Theory/Homogeneous-2014.04.12-en.pdf/download