[5] viXra:1010.0060 [pdf] submitted on 28 Oct 2010
Authors: Linfan Mao
Comments: 83 pages, in Chinese
Mathematical Combinatorics
& Smarandache Multi-Spaces
Category: Geometry
[4] viXra:1010.0055 [pdf] submitted on 20 Mar 2010
Authors: Florentin Smarandache
Comments: 3 pages
This generalization of the Theorem of Menelaus from a triangle to a polygon with n sides is
proven by a self-recurrent method which uses the induction procedure and the Theorem of
Menelaus itself.
Category: Geometry
[3] viXra:1010.0050 [pdf] submitted on 20 Mar 2010
Authors: Florentin Smarandache
Comments: 5 pages
In this paper we present unsolved problems that involve infinite tunnels of recursive triangles or
recursive polygons, either in a decreasing or in an increasing way. The "nedians or order i in a
triangle" are generalized to "nedians of ratio r"
and "nedians of angle α" or "nedians at angle β",
and afterwards one considers their corresponding "nedian triangles" and "nedian polygons".
This tunneling idea came from physics.
Category: Geometry
[2] viXra:1010.0038 [pdf] submitted on 25 Oct 2010
Authors: Florentin Smarandache, Ion Pătraşcu
Comments: 6 pages
In this article we will use the Desargues' theorem and its reciprocal to solve two
problems.
Category: Geometry
[1] viXra:1010.0008 [pdf] submitted on 4 Oct 2010
Authors: Ion Pătraşcu, Florentin Smarandache
Comments: 4 pages
In this article we'll emphasize on two triangles and provide a vectorial proof of
the fact that these triangles have the same orthocenter. This proof will, further allow us to
develop a vectorial proof of the Stevanovic's theorem relative to the orthocenter of the
Fuhrmann's triangle.
Category: Geometry