Geometry

1003 Submissions

[11] viXra:1003.0272 [pdf] replaced on 3 Apr 2010

Eight Solved and Eight Open Problems in Elementary Geometry

Authors: Florentin Smarandache
Comments: 12 pages

In this paper we review nine previous proposed and solved problems of elementary 2D geometry [4] and [6], and we extend them either from triangles to polygons or polyhedrons,or from circles to spheres (from 2D-space to 3D-space), and make some comments about them.
Category: Geometry

[10] viXra:1003.0256 [pdf] submitted on 8 Mar 2010

Degree of Negation of an Axiom

Authors: Florentin Smarandache
Comments: 4 pages

In this article we present the two classical negations of Euclid's Fifth Postulate (done by Lobachevski-Bolyai-Gauss, and respectively by Riemann), and in addition of these we propose a partial negation (or a degree of negation) of an axiom in geometry. The most important contribution of this article is the introduction of the degree of negation (or partial negation) of an axiom and, more general, of a scientific or humanistic proposition (theorem, lemma, etc.) in any field - which works somehow like the negation in fuzzy logic (with a degree of truth, and a degree of falsehood) or like the negation in neutrosophic logic [with a degree of truth, a degree of falsehood, and a degree of neutrality (i.e. neither truth nor falsehood, but unknown, ambiguous, indeterminate)].
Category: Geometry

[9] viXra:1003.0254 [pdf] submitted on 26 Mar 2010

Smarandache's Cevian Triangle Theorem in The Einstein Reletivistic Velocity Model of Hyperbolic Geometry

Authors: Cătălin Barbu
Comments: 4 pages

In this note, we present a proof of Smarandache's cevian triangle hyperbolic theorem in the Einstein relativistic velocity model of hyperbolic geometry.
Category: Geometry

[8] viXra:1003.0245 [pdf] submitted on 25 Mar 2010

Smarandache's Pedal Polygon Theorem in The Poincaré Disc Model of Hyperbolic Geometry

Authors: Cătălin Barbu
Comments: 4 pages

In this note, we present a proof of the hyperbolic a Smarandache's pedal polygon theorem in the Poincaré disc model of hyperbolic geometry.
Category: Geometry

[7] viXra:1003.0187 [pdf] submitted on 6 Mar 2010

A Generalization of a Leibniz Geometrical Theorem

Authors: Mihály Bencze, Florin Popovici, Florentin Smarandache
Comments: 5 pages

In this article we present a generalization of a Leibniz's theorem in geometry and an application of this.
Category: Geometry

[6] viXra:1003.0164 [pdf] submitted on 6 Mar 2010

Generalizations of Ceva's Theorem and Applications

Authors: Florentin Smarandache
Comments: 7 pages

In these paragraphs one presents three generalizations of the famous theorem of Ceva
Category: Geometry

[5] viXra:1003.0162 [pdf] submitted on 6 Mar 2010

A Generalization in Space of Jung's Theorem

Authors: Florentin Smarandache
Comments: 2 pages

In this short note we will prove a generalization of Joung's theorem in space.
Category: Geometry

[4] viXra:1003.0116 [pdf] submitted on 6 Mar 2010

Mixed Noneuclidean Geometries

Authors: Florentin Smarandache
Comments: 23 pages

The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way. To transform the apparently unscientific ideas into scientific ones, and to develop their study (The Theory of Imperfections). And finally, to interconnect opposite (and not only) human fields of knowledge into as-heterogeneous-as-possible another fields.
Category: Geometry

[3] viXra:1003.0058 [pdf] submitted on 6 Mar 2010

The Dual of the Orthopole Theorem

Authors: Ion Pătraşcu
Comments: 5 pages, Translated by Prof. Florentin Smarandache

In this article we prove the theorems of the orthopole and we obtain, through duality, its dual, and then some interesting specific examples of the dual of the theorem of the orthopole.
Category: Geometry

[2] viXra:1003.0057 [pdf] submitted on 6 Mar 2010

DE Longchamps' Point, Line and Circle

Authors: Ion Pătraşcu
Comments: 7 pages, Translated by Prof. Florentin Smarandache

The purpose of this article is to familiarize the reader with these notions, emphasizing on connections between them.
Category: Geometry

[1] viXra:1003.0056 [pdf] submitted on 6 Mar 2010

The Dual Theorem Relative to the Simson's Line

Authors: Ion Pătraşcu
Comments: 5 pages, Translated by Prof. Florentin Smarandache

In this article we elementarily prove some theorems on the poles and polars theory, we present the transformation using duality and we apply this transformation to obtain the dual theorem relative to the Samson's line.
Category: Geometry