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Legendre-like Theorems in a General Absolute Geometry
Results in Mathematics, 2007In this paper the axiomatic basis will be a general absolute plane A = (\({\mathcal{P}}, {\mathcal{L}}, \alpha, \equiv\)) in the sense of [6], where \({\mathcal{P}}\) and \({\mathcal{L}}\) denote respectively the set of points and the set of lines, α the order structure and ≡ the congruence, and where furthermore the word “general” means that no claim ...
Pianta, Silvia +2 more
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Absolute curvatures in integral geometry
Mathematical Proceedings of the Cambridge Philosophical Society, 1980Surface integrals of curvature arise naturally in integral geometry and geometrical probability, most often in connection with the Quermassintegrale or cross-section integrals of convex bodies. They enjoy many desirable properties, such as the ability to be determined by summing or averaging over lower-dimensional sections or projections.
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Absolute distance interferometer in LaserTracer geometry
2013An absolute distance interferometer based on a hybrid measurement technique was developed with the goal to achieve optimum performance in a LaserTracer. The challenges lie in the compact dimensions as very limited space is available and in the special design of the LaserTracer with a steel sphere as an interferometer reflector.
Meiners-Hagen, Karl +4 more
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New Foundations of Absolute Geometry
1966Publisher Summary This chapter discusses the absolute geometry that is treated as a common part of Euclidean, including parabolic and hyperbolic geometries. Absolute geometry can also be treated as a common part of three geometries, such as parabolic, hyperbolic, and elliptic. The problem of a uniform description of all models of these three theories
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The elementary Archimedean axiom in absolute geometry
Journal of Geometry, 2019The author studies absolute plane geometry. He discusses a number of axioms for plane geometry and investigates their relations. He works inside Tarski's first-order language. He investigates consequences of the elementary Archimedean axiom introduced by \textit{W. Rautenberg} [Z. Math. Logik Grundlagen Math.
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2010
Critical Analysis-aesthetics of the poetry collection of L. Salvucci, in the key of aesthetics of the sacred.
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Critical Analysis-aesthetics of the poetry collection of L. Salvucci, in the key of aesthetics of the sacred.
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The absolute anabelian geometry of canonical curves
2003Summary: We continue our study of the issue of the extent to which a hyperbolic curve over a finite extension of the field of \(p\)-adic numbers is determined by the profinite group structure of its étale fundamental group. Our main results are that: (i) the theory of correspondences of the curve -- in particular, its arithmeticity -- is completely ...
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