[7] **viXra:1103.0119 [pdf]**
*submitted on 31 Mar 2011*

**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

[6] **viXra:1103.0077 [pdf]**
*replaced on 2012-04-04 03:24:03*

**Authors:** Morio Kikuchi

**Comments:** 4 Pages.

Spherical orthogonal coordinate system agrees with plane orthogonal coordinate system in coordinates, length, and angle of an intersection. Using spherical orthogonal coordinate system, we can realize complex sphere to which complex number is indicated with no stereographic projection. By the coordinate transformation of the inversion which is characterized by swap of origin and point at infinity, three-dimensional orthogonal coordinates are transformed into new coordinates, namely three-dimensional spherical orthogonal coordinates, however coordinates and so forth are constant.

**Category:** Geometry

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

**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*

**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*

**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*

**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*

**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