On Geodesic Triangles in Non-Euclidean Geometry [PDF]
FoundationsIn this paper, we study centroids, orthocenters, circumcenters, and incenters of geodesic triangles in non-Euclidean geometry, and we discuss the existence of the Euler line in this context.
Antonella Nannicini, Donato Pertici
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Weaknesses of Euclidean Geometry: A Step of Needs Analysis of Non-Euclidean Geometry Learning through an Ethnomathematics Approach [PDF]
Edumatika, 2021 Non-Euclidean Geometry is a complex subject for students. It is necessary to analyze the weaknesses of Euclidean geometry to provide a basis for thinking about the need for learning non-Euclidean geometry.
Khathibul Umam Zaid Nugroho +2 more
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HERBRAND’S THEOREM AND NON-EUCLIDEAN GEOMETRY [PDF]
The Bulletin of Symbolic Logic, 2015 AbstractWe use Herbrand’s theorem to give a new proof that Euclid’s parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non-Euclidean geometry. This proof uses a very old and basic theorem of logic together with some simple properties of ruler-and-compass constructions ...
Michael Beeson +2 more
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Beyond Euclid: an illustrated guide to modern machine learning with geometric, topological, and algebraic structures [PDF]
Machine Learning: Science and TechnologyThe enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space.
Mathilde Papillon +10 more
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Divergence unveils further distinct phenotypic traits of human brain connectomics fingerprint [PDF]
iScienceSummary: The accurate identification of individuals from functional connectomes (FCs) is central to individualized neuro/psychiatric assessment. Traditional metrics (Pearson and Euclidean) fail to capture the non-Euclidean geometry of FCs, and geodesic ...
Md Kaosar Uddin +4 more
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Conical Perspective and Fractal Theory:A Comparative and Contrastive Approach [PDF]
Anastasis: Research in Medieval Culture and Art, 2022 This paper explores a possible connection between Euclidean geometry, which lies at the basis of conical perspective, and fractal geometry, which could, in turn, generate a new system of spatial representation in art. Founded by Renaissance theorists and
Daniel Sofron
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NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries [PDF]
Neutrosophic Sets and Systems, 2021 In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric spaces, by founding the NeutroGeometry & AntiGeometry.
Florentin Smarandache
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THE COMMON EVOLUTION OF GEOMETRY AND ARCHITECTURE FROM A GEODETIC POINT OF VIEW [PDF]
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2017 Throughout history the link between geometry and architecture has been strong and while architects have used mathematics to construct their buildings, geometry has always been the essential tool allowing them to choose spatial shapes which are ...
T. Bellone, F. Fiermonte, L. Mussio
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Substantia, 2022 The comprehension of form generally assumes a euclidean three-dimensional perspective. I argue here that non-euclidean geometry has much to offer in understanding structures of atomic crystals, molecular liquid crystals and related mesoporous inorganic
Stephen Hyde
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MoebInv: C++ libraries for manipulations in non-Euclidean geometry
SoftwareX, 2020 The introduced package MoebInv contains two C++ libraries for symbolic, numeric and graphical manipulations in non-Euclidean geometry. The first library cycle implements basic geometric operations on cycles, which are the zero sets of certain polynomials
Vladimir V. Kisil
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