Geometry

1009 Submissions

[7] viXra:1009.0046 [pdf] submitted on 12 Sep 2010

Pantazi's Theorem Regarding the Bi-orthological Triangles

Authors: Ion Pătraşcu, Florentin Smarandache
Comments: 5 pages

In this article we'll present an elementary proof of a theorem of Alexandru Pantazi (1896-1948), Romanian mathematician, regarding the bi-orthological triangles.
Category: Geometry

[6] viXra:1009.0015 [pdf] submitted on 13 Mar 2010

Smarandache's Concurrent Lines Theorem

Authors: M. Khoshnevisan
Comments: 2 pages.

In this paper we present the Smarandache's Concurrent Lines Theorem in the geometry of the triangle.
Category: Geometry

[5] viXra:1009.0013 [pdf] submitted on 13 Mar 2010

Smarandache's Cevians Theorem (II)

Authors: M. Khoshnevisan
Comments: 2 pages.

In this paper we present the Smarandache's Cevians Theorem (II) in the geometry of the triangle.
Category: Geometry

[4] viXra:1009.0012 [pdf] submitted on 13 Mar 2010

Smarandache's Cevians Theorem (I)

Authors: M. Khoshnevisan
Comments: 2 pages.

We present the Smarandache's Cevians Theorem in the geometry of the triangle.
Category: Geometry

[3] viXra:1009.0011 [pdf] submitted on 13 Mar 2010

Smarandache's Ratio Theorem

Authors: M. Khoshnevisan
Comments: 2 pages.

In this paper we present the Smarandache's Ratio Theorem in the geometry of the triangle.
Category: Geometry

[2] viXra:1009.0010 [pdf] submitted on 13 Mar 2010

The Smarandache-Pătraşcu Theorem of Orthohomological Triangles

Authors: Mihai Dicu
Comments: 1 page.

The Smarandache-Pătraşcu Theorem of Orthohomological Triangles is the folllowing:
Category: Geometry

[1] viXra:1009.0006 [pdf] replaced on 5 Sep 2010

Two Remarkable Ortho-Homological Triangles

Authors: Ion Pătraşcu, Florentin Smarandache
Comments: 11 pages

In a previous paper [5] 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. Orthological / homological / orthohomological triangles in the 2D-space are generalized to orthological / homological / orthohomological polygons in 2D-space, and even more to orthological / homological / orthohomological triangles, polygons, and polyhedrons in 3D-space.
Category: Geometry