Geometry

1006 Submissions

[7] viXra:1006.0069 [pdf] submitted on 30 Jun 2010

An Application of Sondat's Theorem Regarding the Orthohomological Triangles

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

Properties of a Hexagon Circumscribed to a Circle

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

A Multiple Theorem with Isogonal and Concyclic Points

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

A Theorem about Simultaneous Orthological and Homological Triangles

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.
Category: Geometry

[3] viXra:1006.0015 [pdf] submitted on 11 Mar 2010

An Economics Model for the Smarandache Anti-Geometry

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

A Class of Orthohomological Triangles

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

The Hyperbolic Menelaus Theorem in The Poincaré Disc Model of Hyperbolic Geometry

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