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## Riemannian space. Recognition of formulas (structures) of riemannian manifolds by a neural network Ludmila Naumova

ISBN 978-5-4498-0844-8

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RIEMANNIAN SPACE. RECOGNITION OF FORMULAS (STRUCTURES) OF RIEMANNIAN MANIFOLDS BY A NEURAL NETWORK

## INTRODUCTION

In 1854, in Gottingen, Riemann gave the famous lecture “On hypotheses underlying geometry”, where he gave an extended concept of space. This lecture was a messenger in shaping Einstein’s future theory of relativity in physics. Penetrating into the depth of Riemann’s thought and developing it, the author logically states the following: Riemannian manifolds in the broad sense, in the concept that Riemann himself attached, are innumerable and exist in the real world. It remains to comprehend and accept the fact of their existence in the real world. As a proof of the existence of Riemann spaces in reality, the author shows how, before our eyes in the XXI century, artificial neural networks already reveal the structure of Riemannian manifolds (manifolds in an extended concept, as Riemann imagined). Our geometric metric space is a special case of Riemannian manifolds. Mathematicians are still discovering new spaces in mathematical symbols that have nothing to do with reality. But real spaces and their structure (formula) are revealed in the symbolism of programming languages using neural networks.

## RIEM ANNIAN GEOMETRY. A BROAD CONCEPT OF SPACE

In general, geometry presupposes both the concept of space and the first basic concepts that are necessary for performing spatial constructions. It gives nominal definitions of concepts, while the essential properties of defined objects are included in the form of axioms. But the relationship between concepts and axioms can be different. Riemann drew attention to the General concept of repeatedly extended quantities, which include spatial quantities. Based on the General concept of magnitude, Riemann constructed

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# Riemannian space. Recognition of formulas (structures) of riemannian manifolds by a neural network

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На этой странице вы можете прочитать онлайн книгу «Riemannian space. Recognition of formulas (structures) of riemannian manifolds by a neural network», автора Ludmila Naumova. Данная книга имеет возрастное ограничение 12+,.. Книга «Riemannian space. Recognition of formulas (structures) of riemannian manifolds by a neural network» была издана в 2020 году. Приятного чтения!