[7] **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.

**Category:** Geometry

[6] **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

**Category:** Geometry

[5] **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

**Category:** Geometry

[4] **viXra:1006.0024 [pdf]**
*submitted on 13 Mar 2010*

**Authors:** Ion Pătraşcu, Florentin Smarandache

**Comments:**
13 pages.

In this paper we prove that if P_{1},P_{2} are isogonal points in the triangle ABC ,
and if A_{1}B_{1}C_{1} and A_{2}B_{2}C_{2} are their ponder triangle such that the triangles ABC and
A_{1}B_{1}C_{1} are homological (the lines AA_{1} , BB_{1} , CC_{1} are concurrent), then the triangles
ABC and A_{2}B_{2}C_{2} are also homological.

**Category:** Geometry

[3] **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).

**Category:** Geometry

[2] **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)

**Category:** Geometry

[1] **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.

**Category:** Geometry