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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

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3 results for “Bolyai”

J{\' a}nos Bolyai, Carl Friedrich Gauss, Nikolai Lobachevsky and the New Geometry: Forewordmath.DG

This foreword discusses the contributions of Bolyai, Gauss, and Lobachevsky to non-Euclidean geometry.

problem The development of non-Euclidean geometries by Bolyai, Gauss, and Lobachevsky.

method Historical review of the contributions of these mathematicians.

result The foundational work on non-Euclidean geometries by Bolyai, Gauss, and Lobachevsky.

non-Euclidean geometry Bolyai Gauss Lobachevsky mathematics history

2023-03-22abs ↗pdf ↗

Two-parabolic-generator subgroups of hyperbolic 3-manifold groupsmath.GT

Generalized Agol's theorem to 3-manifold groups.

problem Two-parabolic-generator subgroups in hyperbolic 3-manifold groups.

method Generalization of Agol's proof for 2-bridge link groups to 3-manifold groups.

result Refinement of Boileau-Weidmann's result.

hyperbolic 3-manifold two-parabolic-generator Agol's theorem Boileau-Weidmann

2023-02-21abs ↗pdf ↗

C.F. Gauss' Präzisionsmessungen terrestrischer Dreiecke und seine Überlegungen zur empirischen Fundierung der Geometrie in den 1820er Jahren (C.F. Gauss' high precion measurements of terrestrial triangles and his thoughts on the empirical foundations of geometry in the 1820s)math.HO

In the historical literature there has been an extended discussion on the question, whether the report of Sartorius von Waltershausen about C. F. Gauss checking the largest triangle of the geodetical measurement campaign in the kingdom of Hannover as a kind of ``test'' for the Euclididean nature of physical space can b…

2004-09-29abs ↗pdf ↗