Geometry

1103 Submissions

[6] viXra:1103.0119 [pdf] submitted on 31 Mar 2011

The Trisection of Any Angle

Authors: Markos Georgallides
Comments: 7 pages.

Universe is following Euclid Spaces. In Euclidean geometry points do not exist , but their position and correlation is doing geometry and physics . The universe cannot be created , because becomes and never is . According to Euclidean geometry , and since the position of points ( empty Space ) creates geometry and Spaces , the trisection of any angle exists in these Spaces and in this way. Infinite points exist always between points.
Category: Geometry

[5] viXra:1103.0076 [pdf] submitted on 19 Mar 2011

Geometry: Problems of Dividing Objects. Thales`s Theorem and an Idea Which Can Arose When You Applied the Theorem, for Solving an Interesting and Simple Problem in Geometry.

Authors: Martiros Khurshudyan
Comments: 3 pages.

Geometry it is not a word, moreover it is not just mathematical research area. It is art, it is the base of our Nature, it is language of Nature. The aim of this article is to present how Thales`s theorem is working for simple cases, when we need to divide a geometrical object into equal parts: mainly, we considered the problem of dividing a straight segment of length N into n equal parts. On the base of this simple case, we proposed a generalizations of the problem. We presented they as questions. Purpose of this article is to ask to find solutions for the questions. It seems, that for the positive answer, here must be developed geometrical techniques.
Category: Geometry

[4] viXra:1103.0043 [pdf] replaced on 23 May 2011

The Euclidean Philosophy of Universe ( Nature )

Authors: Markos Georgallides
Comments: 12 pages.

This article explains what is a Point, a Positive Space and a negative Anti-Space for their equilibrium, how points exist and their correlation also in Spaces . Any two points A,B on Spaces consist the first dimensional Unit AB, which has infinite bounded Spaces, Anti-Spaces and Sub-Spaces on unit AB . It is proved that when points A, B exist in a constant distance ds = AB, which is then a Restrained System of this Unit, then equilibrium under equal and opposite Impulses Pa, Pb on points A, B . This means that any distance AB of the Space is a DIPOLE or [ FMD = AB - Pa, Pb ], which is the first material unit . The unique case where at the points of Space and Anti-Space exist null Impulses, then is the Primary Neutral Space and it is obvious that the infinite Dipole ds = 0 → AB → ∞ move in this P.N.S . The position of points on Space /Space, Anti-Space/ Anti-Space Space / Anti-Space, Anti-Space / Space, creates (+) matter (-) antimatter (±) Neutral matter which moves in this Space with finite velocity and in case of the bounded Neutral Space AB, which may have zero Inertia, moves with infinite velocity . Since Neutral Space is the interval between Impulse ( which Impulse is the Principle of movement ) and Spaces ( which Spaces are the medium of movement ), therefore, Motion can alternatively occur itself as that of a Dipole = matter ( which is particle ) and as that of Impulses Pa, Pb ( which is a wave ) in the Neutral matter and Neutral Anti-matter . [ The one thing, say the light, is then as Particle and as Wave Structure ] Following the principle < Cause on → Communicator → the Obvious > is then explained that, Monads, can reproduce themselves through their bounded Communicator ( we may refer this as the DNA of the Monad ) . Following Euclidean logic for Spaces, and since one may use them as the first dimensional Unit ds = 0 → AB → ∞ in Geometry, Algebra, etc either as Dipole ds = AB, [ FMD = AB - Pa, Pb ] and since also Primary Neutral Space is proved to be Homogenous and Isotropic, then also in Mechanics and Physics and in all laws of Universe .
Category: Geometry

[3] viXra:1103.0042 [pdf] submitted on 13 Mar 2011

The Parallel Postulate is Depended on the Other Axioms

Authors: Markos Georgallides
Comments: 20 pages

This article was sent to some specialists in Euclidean Geometry for criticism . The geometrical solution of this problem is based on the four Postulates for Constructions in Euclid geometry
Category: Geometry

[2] viXra:1103.0035 [pdf] replaced on 13 Mar 2011

A Property of the Circumscribed Octagon

Authors: Ion Patrascu, Florentin Smarandache
Comments: 3 pages

In this article we'll obtain through the duality method a property in relation to the contact cords of the opposite sides of a circumscribable octagon.
Category: Geometry

[1] viXra:1103.0034 [pdf] submitted on 11 Mar 2011

Triplets of Tri-Homological Triangles

Authors: Ion Patrascu, Florentin Smarandache
Comments: 9 pages

In this article will prove some theorems in relation to the triplets of homological triangles two by two. These theorems will be used later to build triplets of triangles two by two trihomological.
Category: Geometry