Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Pătraşcu, Ion"'
Autor:
Patrascu, Ion, Smarandache, Florentin
Publikováno v:
Pons Editions, Brussels, 2016
We approach several themes of classical geometry of the circle and complete them with some original results, showing that not everything in traditional math is revealed, and that it still has an open character. The topics were chosen according to aut
Externí odkaz:
http://arxiv.org/abs/1605.03275
This book is addressed to students, professors and researchers of geometry, who will find herein many interesting and original results. The originality of the book The Geometry of Homological Triangles consists in using the homology of triangles as a
Autor:
Smarandache, Florentin, Patrascu, Ion
Publikováno v:
Book published by Educ. Publ., Ohio, 2012
This book is addressed to students, professors and researchers of geometry, who will find herein many interesting and original results. The originality of the book The Geometry of Homological Triangles consists in using the homology of triangles as a
Externí odkaz:
http://arxiv.org/abs/1204.1585
Autor:
Patrascu, Ion, Smarandache, Florentin
In this article we prove some theorems related to the triplets of triangles, homological two by two. These theorems will be used later to build triplets of triangles two by two tri-homological.
Comment: 8 pages, 5 geometrical figures
Comment: 8 pages, 5 geometrical figures
Externí odkaz:
http://arxiv.org/abs/1104.2559
In this article we determine the class of triangles $A_iB_iC_i$ which are orthohomological with a given triangle $ABC$ and inscribed in the triangle $ABC$ (with $A_i \in BC$, $B_i \in CA$ and $C_i \in AB$).
Comment: 5 pages. Accepted by Italian
Comment: 5 pages. Accepted by Italian
Externí odkaz:
http://arxiv.org/abs/1103.0459
Autor:
Patrascu, Ion, Smarandache, Florentin
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 ortho
Externí odkaz:
http://arxiv.org/abs/1102.0209
Autor:
Smarandache, Florentin, Patrascu, Ion
In this article we use the Desargues' theorem and its reciprocal to solve two problems.
Comment: 6 pages, 3 figures
Comment: 6 pages, 3 figures
Externí odkaz:
http://arxiv.org/abs/1101.2264
Autor:
Patrascu, Ion, Smarandache, Florentin
In this article we'll present an elementary proof of a theorem of Alexandru Pantazi (1896-1948), Romanian mathematician, regarding the bi-orthological triangles.
Comment: 5 pages, 3 geometric figures
Comment: 5 pages, 3 geometric figures
Externí odkaz:
http://arxiv.org/abs/1010.0194
Autor:
Patrascu, Ion, Smarandache, Florentin
In a previous paper 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 and
Externí odkaz:
http://arxiv.org/abs/1009.0789
In this article we prove a theorem that will generalize the concurrence theorems that are leading to the Franke's point, Kariya's point, and to other remarkable points from the triangle geometry.
Comment: 5 pages
Comment: 5 pages
Externí odkaz:
http://arxiv.org/abs/1008.2665