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NonEuclidean geometry and gravitation
 Progress in Physics
, 2006
"... A great deal of misunderstandings and mathematical errors are involved in the currently accepted theory of the gravitational field generated by an isotropic spherical mass. The purpose of the present paper is to provide a short account of the rigorous mathematical theory and exhibit a new formulatio ..."
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formulation of the problem. The solution of the corresponding equations of gravitation points out several new and unusual features of the stationary gravitational field which are related to the nonEuclidean structure of the space. Moreover it precludes the black hole from being a mathematical and physical
The Elements of NonEuclidean Geometry
, 1927
"... This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or reuse it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org ..."
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This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or reuse it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org
HERBRAND’S THEOREM AND NONEUCLIDEAN GEOMETRY
"... Abstract. We use Herbrand’s theorem to give a new proof that Euclid’s parallel axiom is not derivable from the other axioms of firstorder Euclidean geometry. Previous proofs involve constructing models of nonEuclidean geometry. This proof uses a very old and basic theorem of logic together with s ..."
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Abstract. We use Herbrand’s theorem to give a new proof that Euclid’s parallel axiom is not derivable from the other axioms of firstorder Euclidean geometry. Previous proofs involve constructing models of nonEuclidean geometry. This proof uses a very old and basic theorem of logic together
Visualizing NonEuclidean Geometry A Bolyai Bicentennial Survey
, 2002
"... The setting Like many fundamental mathematical discoveries, noneuclidean geometry was first received as a bizarre oddity, but with time it has entered the mainstream of scientific thought. Indeed, there is growing acceptance of the idea that the universe we live in, is locally or globally noneucli ..."
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The setting Like many fundamental mathematical discoveries, noneuclidean geometry was first received as a bizarre oddity, but with time it has entered the mainstream of scientific thought. Indeed, there is growing acceptance of the idea that the universe we live in, is locally or globally noneuclidean
Orientation Maps in V1 and NonEuclidean Geometry
, 2014
"... distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Abstract In the primary visual cortex, the processing of information uses the distribution ..."
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, and we use representation theory as a symmetrybased toolbox to build orientation maps adapted to the most famous nonEuclidean geometries, viz. spherical and hyperbolic geometry. We find that most of the dominant traits of V1 maps are preserved in these; we also study the link between symmetry
Euclidean Geometry before nonEuclidean Geometry
"... this paper is to clear up this point. As an illustration of the di#culties, consider the following characterization of Western geometry and the Navajo conception of space from [2, pp. 157163]: 1. The Western Case. I see three main points in the description of Western psychological development of f ..."
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this paper is to clear up this point. As an illustration of the di#culties, consider the following characterization of Western geometry and the Navajo conception of space from [2, pp. 157163]: 1. The Western Case. I see three main points in the description of Western psychological development
1 Kant’s Theory of Geometry in Light of the Development of NonEuclidean Geometries
"... With the development of nonEuclidean geometries in the nineteenth century, the concern arose as to whether these alternatives constituted a refutation of Kant’s theory of geometry. Partly the concerns were related to Kant’s argument that geometric judgments were a priori synthetic judgments, meanin ..."
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With the development of nonEuclidean geometries in the nineteenth century, the concern arose as to whether these alternatives constituted a refutation of Kant’s theory of geometry. Partly the concerns were related to Kant’s argument that geometric judgments were a priori synthetic judgments
NonTuring Computers are the new NonEuclidean Geometries
"... While it goes without saying that computing devices need space and time (spacetime), nothing in Turing’s theory of idealized computation prepares one for the rich nature of a computer’s dependence on the underlying spacetime geometry. Nor does that theory prepare one for the vast array of nonTuring ..."
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While it goes without saying that computing devices need space and time (spacetime), nothing in Turing’s theory of idealized computation prepares one for the rich nature of a computer’s dependence on the underlying spacetime geometry. Nor does that theory prepare one for the vast array of non
Results 1  10
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