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Eighteen Essays in Non-Euclidean Geometry
, 2019 This book consists of a series of self-contained essays on non-Euclidean geometry in a broad sense, including the classical geometries of constant curvature (spherical and hyperbolic), de Sitter, anti-de Sitter, co-Euclidean, co-Minkowski geometries ...
Vincent Alberge, A. Papadopoulos
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An adaptive evolutionary algorithm based on non-euclidean geometry for many-objective optimization
Annual Conference on Genetic and Evolutionary Computation, 2019In the last decade, several evolutionary algorithms have been proposed in the literature for solving multi- and many-objective optimization problems.
Annibale Panichella
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, 2000 Certainly one of the greatest mathematical discoveries of the nineteenth century was that of non-Euclidean geometry: seen but not revealed by Gauss, and developed in all its glory by Bolyai and Lobachevsky. The purpose of this chapter is to give an account of this theory, but we do not always follow the historical development. Rather, with hindsight we
Ross, Skyler W.
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Taxicab Geometry: An Adventure in Non-Euclidean Geometry
, 1987 Develops a simple non-Euclidean geometry and explores some of its practical applications through graphs, research problems, and exercises.
F. Bellot, E.-H. Krause
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1989
Surprisingly, the geometry of curved surfaces throws light on the geometry of the plane. More than 2000 years after Euclid formulated axioms for plane geometry, differential geometry showed that the parallel axiom does not follow from the other axioms of Euclid.
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Surprisingly, the geometry of curved surfaces throws light on the geometry of the plane. More than 2000 years after Euclid formulated axioms for plane geometry, differential geometry showed that the parallel axiom does not follow from the other axioms of Euclid.
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2021
Four-dimensional theories match Virtual Reality because here time and space are configured through mutable lines. Since the discovery of non-Euclidean geometry, linearity has been submitted to a profound crisis. Mathematicians showed that there are not one but several geometries.
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Four-dimensional theories match Virtual Reality because here time and space are configured through mutable lines. Since the discovery of non-Euclidean geometry, linearity has been submitted to a profound crisis. Mathematicians showed that there are not one but several geometries.
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Non-Euclidean Broximal Point Method: A Blueprint for Geometry-Aware Optimization
arXiv.orgThe recently proposed Broximal Point Method (BPM) [Gruntkowska et al., 2025] offers an idealized optimization framework based on iteratively minimizing the objective function over norm balls centered at the current iterate.
Kaja Gruntkowska, Peter Richtárik
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