Výsledky vyhledávání - "Parallel postulate"

Euclid’s fifth postulate has been accepted as a theorem since the time of ancient Greece. The efforts to prove it have been going on for nearly 2 000 years. Non-Euclidean geometry, based on its rejection, emerged in the first half of the 19th centu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::1c28dae896445411e25eb42b95589c3a
https://doi.org/10.5377/nexo.v34i01.11306

Zobrazit plný text záznamu

Akademický článek

Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.

Riemannian rigidity of the parallel postulate in total curvature

Autor: Pedro Solórzano, Luis Guijarro, Jian Ge

Publikováno v: Mathematische Annalen. 376:177-185

Without any symmetry assumptions and under natural integrability conditions on the Gaussian curvature, we show that the Euclidean plane is unique among all the complete 2-dimensional Riemannian manifolds that satisfy the Euclid’s fifth postulate. N

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::44885cd345efe44cfad2c0473193f11a
https://doi.org/10.1007/s00208-019-01883-8

Zobrazit plný text záznamu

Lippmann’s axiom and Lebesgue’s axiom are equivalent to the Lotschnittaxiom

Autor: Victor Pambuccian, Celia Schacht

Publikováno v: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. 60:733-748

We prove that both Lippmann’s axiom of 1906, stating that for any circle there exists a triangle circumscribing it, and Lebesgue’s axiom of 1936, stating that for every quadrilateral there exists a triangle containing it, are equivalent, with res

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::d134bb0bee4189f3ab42cb71c6e63ddf
https://doi.org/10.1007/s13366-019-00445-y

Zobrazit plný text záznamu

Euclid’s Fifth Postulate and Convergence of Non-Parallel Straight Lines

Autor: Kabenge Hamiss

Publikováno v: Advances in Pure Mathematics. :1059-1070

This paper proves Euclid’s fifth postulate and convergence of straight lines using the formula for the area of trapezoids and assuming straight lines, it derives a general formula for the area of trapezoids involving ratios and we assume that the s

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::e7304b2378f1bdf2c9cf207f6eff064c
https://doi.org/10.4236/apm.2019.912052

Zobrazit plný text záznamu

Parallel postulates and continuity axioms: a mechanized study in intuitionistic logic using Coq

Autor: Charly Gries, Pascal Schreck, Pierre Boutry, Julien Narboux

Publikováno v: Journal of Automated Reasoning
Journal of Automated Reasoning, Springer Verlag, 2019, 62 (1), pp.68. ⟨10.1007/s10817-017-9422-8⟩
Journal of Automated Reasoning, 2019, 62 (1), pp.68. ⟨10.1007/s10817-017-9422-8⟩

online first; International audience; In this paper we focus on the formalization of the proofs of equivalence between different versions of Euclid's 5 th postulate. Our study is performed in the context of Tarski's neutral geometry, or equivalently

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5295cfedebbea0e5f43a1d51340f29ca
https://hal.inria.fr/hal-01178236v2/document

Zobrazit plný text záznamu

Absolute isotropic geometry

Autor: Horst Struve, Rolf Struve

Publikováno v: Journal of Geometry. 112

The term ‘absolute geometry’ was coined by Janos Bolyai to characterize the part of Euclidean geometry that does not depend on the parallel postulate. In the framework of Cayley–Klein geometries the parallel axiom characterizes three classical

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::731c86ffcb3eda4c486e748769739a3a
https://doi.org/10.1007/s00022-020-00558-z

Zobrazit plný text záznamu

Vyhledávací nástroje:

Upřesnit hledání