Previous months: - 1003(14) - 1004(4) - 1005(2) - 1006(7) - 1007(2) - 1008(5) - 1009(1)
[35] viXra:1009.0006 [pdf] submitted on 2 Sep 2010
Authors: Ion Pătraşcu, Florentin Smarandache
Comments:
10 pages
In a previous paper we have introduced the ortho-homological triangles, which are triangles that are orthological and homological simultaneously. In this article we call attention to two remarkable ortho-homological triangles (the given triangle ABC and its first Brocard's triangle), and using the Sondat's theorem relative to orthological triangles, we emphasize on four important collinear points in the geometry of the triangle.
[34] viXra:1008.0081 [pdf] submitted on 28 Aug 2010
Authors: Catalin Barbu
Comments: 3 pages
In this note, we present a proof to the Smarandache's Minimum Theorem in the Einstein Relativistic Velocity Model of Hyperbolic Geometry.
[33] viXra:1008.0043 [pdf] submitted on 16 Aug 2010
Authors: Jeidsan A. C. Pereira
Comments: 10 Pages.
Given a vector space V of dimension n and a natural number k < n, the grassmannian Gk(V) is defined as the set of all subspaces W ⊂ V such that dim(W) = k. In the case of V = Rn, Gk(V) is the set of k-fl ats in Rn and is called real grassmannian [1]. Recently the study of these manifolds has found applicability in several areas of mathematics, especially in Modern Differential Geometry and Algebraic Geometry. This work will build two differential structures on the real grassmannian, one of which is obtained as a quotient space of a Lie group [1], [3], [2], [7]
[32] viXra:1008.0037 [pdf] submitted on 12 Aug 2010
Authors: Marian Dincă
Comments: 2 Pages.
In this paper it is given proof Yff's conjecture using convexity arguments.
[31] viXra:1008.0031 [pdf] submitted on 11 Aug 2010
Authors: Ion Pătraşcu, Florentin Smarandache
Comments: 3 pages
In [1] we proved, using barycentric coordinates, the following theorem
[30] viXra:1008.0030 [pdf] submitted on 11 Aug 2010
Authors: Marian Dincă
Comments: 4 Pages.
In this paper an elementary proof of the Wolstenholme-Lenhard ciclic inequality for real numbers and L.Fejes T&oactute;th conjecture( equivalent by Erdis-Mordell inequality for polygon) is given, using a remarcable identity We give the following:
[29] viXra:1007.0035 [pdf] submitted on 23 Jul 2010
Authors: Marian Dincă, J. L. Díaz-Barrero
Comments: 4 pages.
In this short note a new proof of a classical inequality involving the areas of a pair of triangles is presented.
[28] viXra:1007.0011 [pdf] submitted on 8 Jul 2010
Authors: Marian Dincă, Şcoala Generală
Comments: 1 page.
In the paper given a new proof the two inequalities using unitary method.
[27] viXra:1006.0069 [pdf] submitted on 30 Jun 2010
Authors: Ion Pătraşcu, Florentin Smarandache
Comments: 4 pages.
In this article we prove the Sodat's theorem regarding the orthohomological triangle and then we use this theorem and Smarandache-Patrascu's theorem in order to obtain another theorem regarding the orthohomological triangles.
[26] viXra:1006.0059 [pdf] submitted on 13 Mar 2010
Authors: Ion Pătraşcu, Florentin Smarandache
Comments:
3 pages.
In this paper we analyze and prove two properties of a hexagon circumscribed to a circle
[25] viXra:1006.0058 [pdf] submitted on 13 Mar 2010
Authors: Florentin Smarandache, Ion Pătraşcu
Comments:
3 pages.
A Multiple Theorem with Isogonal and Concyclic Points
[24] viXra:1006.0024 [pdf] submitted on 13 Mar 2010
Authors: Ion Pătraşcu, Florentin Smarandache
Comments:
13 pages.
In this paper we prove that if P1,P2 are isogonal points in the triangle ABC , and if A1B1C1 and A2B2C2 are their ponder triangle such that the triangles ABC and A1B1C1 are homological (the lines AA1 , BB1 , CC1 are concurrent), then the triangles ABC and A2B2C2 are also homological.
[23] viXra:1006.0015 [pdf] submitted on 11 Mar 2010
Authors: Roberto Torretti
Comments: 3 pages
The Smarandache anti-geometry is a non-euclidean geometry that denies all Hilbert's twenty axioms, each axiom being denied in many ways in the same space. In this paper one finds an economics model to this geometry by making the following correlations: (i) A point is the balance in a particular checking account, expressed in U.S. currency. (Points are denoted by capital letters). (ii) A line is a person, who can be a human being. (Lines are denoted by lower case italics). (iii) A plane is a U.S. bank, affiliated to the FDIC. (Planes are denoted by lower case boldface letters).
[22] viXra:1006.0004 [pdf] submitted on 3 Jun 2010
Authors: Claudiu Coandă, Florentin Smarandache, Ion Pătraşcu
Comments: 5 pages
In this article we propose to determine the triangles' class... (see paper for full abstract)
[21] viXra:1006.0003 [pdf] submitted on 3 Jun 2010
Authors: Florentin Smarandache, Catalin Barbu
Comments: 4 pages
In this note, we present the hyperbolic Menelaus theorem in the Poincaré disc of hyperbolic geometry.
[20] viXra:1005.0053 [pdf] submitted on 11 Mar 2010
Authors: Florentin Smarandache
Comments: 171 pages
Solved problems of geometry and trigonometry for college students.
[19] viXra:1005.0016 [pdf] submitted on 5 May 2010
Authors: Ion Pătraşcu, Florentin Smarandache
Comments: 3 pages
In [1] Professor Claudiu Coandă proves the following theorem using the barycentric coordinates.
[18] viXra:1004.0137 [pdf] submitted on 10 Mar 2010
Authors: L. Kuciuk, M. Antholy
Comments:
23 pages.
In this paper we make a presentation of these exciting geometries and present a model for a particular one.
[17] viXra:1004.0050 [pdf] submitted on 8 Apr 2010
Authors: Claudiu Coandă
Comments: 4 pages
In this article we prove the Smarandache-Pătrașcu's Theorem in relation to the inscribed orthohomological triangles using the barycentric coordinates.
[16] viXra:1004.0025 [pdf] submitted on 3 Apr 2010
Authors: Ion Pătraşcu, Florentin Smarandache
Comments: 3 pages
NIn this note we prove a problem given at a Romanian student mathematical competition, and we obtain an interesting result by using a Theorem of Orthohomological Triangles.
[15] viXra:1004.0003 [pdf] submitted on 8 Mar 2010
Authors: Mircea Eugen Șelariu
Comments: 14 pages, translated from Romanian by Marian Nitu and Florentin Smarandache
In this paper we talk about the so-called Super-Mathematics Functions (SMF), which often constitute the base for generating technical, neo-geometrical, therefore less artistic objects. These functions are the results of 38 years of research, which began at University of Stuttgart in 1969. Since then, 42 related works have been published, written by over 19 authors, as shown in the References.
[14] viXra:1003.0272 [pdf] submitted on 8 Mar 2010
Authors: Florentin Smarandache
Comments: 9 pages
In this paper we review eight previous proposed and solved problems of elementary 2D geometry [1], and we extend them either from triangle to polygons or from 2D to 3D-space and make some comments about them.
[13] viXra:1003.0256 [pdf] submitted on 8 Mar 2010
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)].
[12] viXra:1003.0254 [pdf] submitted on 26 Mar 2010
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.
[11] viXra:1003.0245 [pdf] submitted on 25 Mar 2010
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.
[10] viXra:1003.0227 [pdf] submitted on 7 Mar 2010
Authors: Linfan Mao
Comments: 124 pages
A combinatorial map is a connected topological graph cellularly embedded in a surface. As a linking of combinatorial configuration with the classical mathematics, it fascinates more and more mathematician's interesting. Its function and role in mathematics are widely accepted by mathematicians today.
[9] viXra:1003.0226 [pdf] submitted on 7 Mar 2010
Authors: Howard Iseri
Comments: 97 pages
A complete understanding of what something is must include an understanding of what it is not. In his paper, "Paradoxist Mathematics" [19], Florentin Smarandache proposed a number of ways in which we could explore "new math concepts and theories, especially if they run counter to the classical ones." In a manner consistent with his unique point of view, he defined several types of geometry that are purposefully not Euclidean and that focus on structures that the rest of us can use to enhance our understanding of geometry in general.
[8] viXra:1003.0221 [pdf] submitted on 7 Mar 2010
Authors: Linfan Mao
Comments: 499 pages
Anyone maybe once heard the proverb of the six blind men with an elephant, in which these blind men were asked to determine what an elephant looks like by touch different parts of the elephant's body. The man touched its leg, tail, trunk, ear, belly or tusk claims that the elephant is like a pillar, a rope, a tree branch, a hand fan, a wall or a solid pipe, respectively. Each of them insisted his view right. They entered into an endless argument. All of you are right! A wise man explains to them: why are you telling it differently is because each one of you touched the different part of the elephant. So, actually the elephant has all those features what you all said.
[7] viXra:1003.0187 [pdf] submitted on 6 Mar 2010
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.
[6] viXra:1003.0164 [pdf] submitted on 6 Mar 2010
Authors: Florentin Smarandache
Comments: 7 pages
In these paragraphs one presents three generalizations of the famous theorem of Ceva
[5] viXra:1003.0162 [pdf] submitted on 6 Mar 2010
Authors: Florentin Smarandache
Comments: 2 pages
In this short note we will prove a generalization of Joung's theorem in space.
[4] viXra:1003.0116 [pdf] submitted on 6 Mar 2010
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.
[3] viXra:1003.0058 [pdf] submitted on 6 Mar 2010
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.
[2] viXra:1003.0057 [pdf] submitted on 6 Mar 2010
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.
[1] viXra:1003.0056 [pdf] submitted on 6 Mar 2010
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.
[1] viXra:1003.0272 [pdf] replaced on 3 Apr 2010
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.