# Geometry

## 1010 Submissions

[5] **viXra:1010.0060 [pdf]**
*submitted on 28 Oct 2010*

### Let's Flying by Wing

**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*

### Generalization of the Theorem of Menelaus Using a Self-Recurrent Method

**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*

### Limits of Recursive Triangle and Polygon Tunnels

**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*

### Two Applications of Desargues' Theorem

**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*

### Two Triangles with the Same Orthocenter and a Vectorial Proof of Stevanovic's Theorem

**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