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Different conceptions of Euclidean geometry
, 2007
"... Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In Erepresentation there are three basic elements (point, segment, angle) and no additional structures. Vrepresentation c ..."
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Cited by 9 (2 self)
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Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In Erepresentation there are three basic elements (point, segment, angle) and no additional structures. V
Different representations of Euclidean geometry
, 2008
"... Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In Erepresentation there are three basic elements (point, segment, angle) and no additional structures. Vrepresentation c ..."
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Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In Erepresentation there are three basic elements (point, segment, angle) and no additional structures. V
Spacetime and Euclidean Geometry 1
, 2004
"... Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a twodimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski lin ..."
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Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a twodimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski
Partial Orders and Euclidean Geometry
 In Algorithms and Order, I. Rival
, 1987
"... The study of simple families of geometric objects on the plane has always been of great interest in mathematics. Incidence relations among families of points, lines and circles on the Euclidean plane were studied intensely long ago. In fact, most of what is now considered as basic Euclidean Geometry ..."
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Cited by 4 (1 self)
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The study of simple families of geometric objects on the plane has always been of great interest in mathematics. Incidence relations among families of points, lines and circles on the Euclidean plane were studied intensely long ago. In fact, most of what is now considered as basic Euclidean
DECISION PROBLEMS IN EUCLIDEAN GEOMETRY
, 2010
"... Abstract. We show the algorithmic unsolvability of a number of decision procedures in ordinary two dimensional Euclidean geometry, involving lines and integer points. We also consider formulations involving integral domains of characteristic 0, and ordered rings. The main tool is the solution to Hil ..."
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Abstract. We show the algorithmic unsolvability of a number of decision procedures in ordinary two dimensional Euclidean geometry, involving lines and integer points. We also consider formulations involving integral domains of characteristic 0, and ordered rings. The main tool is the solution
Euclidean Geometry before nonEuclidean Geometry
"... this paper is to clear up this point. As an illustration of the di#culties, consider the following characterization of Western geometry and the Navajo conception of space from [2, pp. 157163]: 1. The Western Case. I see three main points in the description of Western psychological development of f ..."
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this paper is to clear up this point. As an illustration of the di#culties, consider the following characterization of Western geometry and the Navajo conception of space from [2, pp. 157163]: 1. The Western Case. I see three main points in the description of Western psychological development
Why Euclidean Geometry?
 In Canadian Society for History and Philosophy of Mathematics. Proceedings of the Sixteenth Annual Meeting, Brock University, Ste. Catherines
, 1996
"... e of the things evey normal human child learns in infancy, and this learning appears to be part of our biological programming. It is true that modern physical theories tell us that it is not strictly true; objects actually change shape as they move. But we are programmed not to think about these cha ..."
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these changes. This would seem to commit us to one of three geometries: euclidean, hyperbolic, and elliptical. The second technical result is John Wallis' proof that, in the presence of the axioms common to euclidean and noneuclidean geometry, the existence of triangles that are similar but not congruent
A PROJECT IN EUCLIDEAN GEOMETRY
"... One of the most effective instructional approaches in teaching Mathematics is project work, which, in an earlier paper, I connected with active learning, see Klaoudatos (1998). And this approach is going to be more interesting for the students if the project has been developed in collaboration with ..."
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figure. The problem is expressed in terms of classical Euclidean geometry so that, at first glance, there is no evidence of the hidden difficulties. The aim of the paper is twofold: first, to attract the attention of mathematics teachers and educators to the problem above, in order to be considered
Generality and Euclidean Geometry
, 2015
"... Why did I have you read sections of Euclid’s Elements? To appreciate how different mathematics is during different time periods, and To know what philosophers prior to the 20th century are talking about when they discuss mathematics! ..."
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Why did I have you read sections of Euclid’s Elements? To appreciate how different mathematics is during different time periods, and To know what philosophers prior to the 20th century are talking about when they discuss mathematics!
NonEuclidean geometry and gravitation
 Progress in Physics
, 2006
"... A great deal of misunderstandings and mathematical errors are involved in the currently accepted theory of the gravitational field generated by an isotropic spherical mass. The purpose of the present paper is to provide a short account of the rigorous mathematical theory and exhibit a new formulatio ..."
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Cited by 7 (3 self)
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formulation of the problem. The solution of the corresponding equations of gravitation points out several new and unusual features of the stationary gravitational field which are related to the nonEuclidean structure of the space. Moreover it precludes the black hole from being a mathematical and physical
Results 1  10
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86,818