Results 61 to 70 of about 1,591,753 (376)
A Pseudo-Euclidean Geometry [PDF]
Proceedings of the American Mathematical Society, 1959 The axioms to be used in this paper are, with only two exceptions, the same as those for abstract Euclidean vector spaces. We denote the elements by small letters and call them points. The null element 0, however, will not be considered a point. Capital letters will be used for scalars which are assumed to be real numbers.
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Interpretations of Euclidean Geometry [PDF]
Transactions of the American Mathematical Society, 1990 Following Tarski, we view n n -dimensional Euclidean geometry as a first-order theory E n {E_n} with an infinite set of axioms about the relations of betweenness (among points on a line) and equidistance (among pairs of points). We show that for k > n
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The Role of the Fifth Postulate in the Euclidean Construction of Parallels [PDF]
arXiv, 2022 We ascribe to the Euclidean Fifth Postulate a genuine constructive role, which makes it absolutely necessary in the parallel construction. For that, we present a reconstruction of the general principles underlying the Euclidean construction of a geometric property. As a consequence, the epistemological role of Euclidean constructions is revealed.
arxiv
Asymptotically Euclidean metrics without conjugate points are flat [PDF]
The Journal of Geometric Analysis 33 (2023), no. 2, Paper No. 37, 2019 We prove that any asymptotically Euclidean metric on $\mathbb{R}^n$ with no conjugate points must be isometric to the Euclidean metric.
arxiv +1 more source
Designing digital technologies and learning activities for different geometries [PDF]
, 2009 This chapter focuses on digital technologies and geometry education, a combination of topics that provides a suitable avenue for analysing closely the issues and challenges involved in designing and utilizing digital technologies for learning mathematics.
Jones, Keith +2 more
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The Journal for Transdisciplinary Research in Southern Africa, 2020 Virtual reality has taken the world by storm over the past decade where learners are allowed to gain experiences that are not possible with ordinary teaching methods.
Bernard M. Hlalele
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HERBRAND’S THEOREM AND NON-EUCLIDEAN GEOMETRY [PDF]
Bulletin of Symbolic Logic, 2014 We 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.
M. Beeson, P. Boutry, Julien Narboux
semanticscholar +1 more source
Conformal Powers of the Laplacian via Stereographic Projection [PDF]
, 2007 A new derivation is given of Branson's factorization formula for the conformally invariant operator on the sphere whose principal part is the k-th power of the scalar Laplacian. The derivation deduces Branson's formula from knowledge of the corresponding
Graham, C. Robin
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An Observer-Based View of Euclidean Geometry
MathematicsAn influence network of events is a view of the universe based on events that may be related to one another via influence. The network of events forms a partially ordered set which, when quantified consistently via a technique called chain projection ...
Newshaw Bahreyni +2 more
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On Klein's So-called Non-Euclidean geometry [PDF]
, 2014 In two papers titled "On the so-called non-Euclidean geometry", I and II, Felix Klein proposed a construction of the spaces of constant curvature -1, 0 and and 1 (that is, hyperbolic, Euclidean and spherical geometry) within the realm of projective ...
N. A'campo, A. Papadopoulos
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