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Displaying similar documents to “A geometric interpretation of the third order e-systems”

On the geometric concomitants

Zenon Moszner (2019)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this note the necessary and sufficient conditon it would the concomitant of the geometric object was the geometric object too is given.

Basic concepts of the theory of geometric objects

M. Kucharzewski, M. Kuczma

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ContentsIntroduction............................................................................................................................................................................... 3§ 1. Historical development of the concept of a geometric object..................................................................................4§ 2. Manifold, coordinate system, transformations of the coordinate system............................................................. 7§ 3. Group,...

Autonomy of Geometry

John T. Baldwin, Andreas Mueller (2019)

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia

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In this paper we present three aspects of the autonomy of geometry. (1) An argument for the geometric as opposed to the ‘geometric algebraic’ interpretation of Euclid’s Books I and II; (2) Hilbert’s successful project to axiomatize Euclid’s geometry in a first order geometric language, notably eliminating the dependence on the Archimedean axiom; (3) the independent conception of multiplication from a geometric as opposed to an arithmetic viewpoint.

Arithmetic labelings and geometric labelings of countable graphs

Gurusamy Rengasamy Vijayakumar (2010)

Discussiones Mathematicae Graph Theory

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An injective map from the vertex set of a graph G-its order may not be finite-to the set of all natural numbers is called an arithmetic (a geometric) labeling of G if the map from the edge set which assigns to each edge the sum (product) of the numbers assigned to its ends by the former map, is injective and the range of the latter map forms an arithmetic (a geometric) progression. A graph is called arithmetic (geometric) if it admits an arithmetic (a geometric) labeling. In this article,...