## Mathematics and Statistics Faculty and Staff Publications

#### Document Type

Book

#### Publication Date

2012

#### Abstract

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 “filter” through which remarkable notions and theorems from the geometry of the triangle are unitarily passed. Our research is structured in seven chapters, the first four are dedicated to the homology of the triangles while the last ones to their applications. In the first chapter one proves the theorem of homological triangles (Desargues, 1636), one survey the remarkable pairs of homological triangles, making various connections between their homology centers and axes. Second chapter boards the theorem relative to the triplets of homological triangles. The Veronese Theorem is proved and it is mentioned a remarkable triplet of homological triangles, and then we go on with the study of other pairs of homological triangles. Third chapter treats the bihomological and trihomological triangles. One proves herein that two bihomological triangles are trihomological (Rosanes, 1870), and the Theorem of D. Barbilian (1930) related to two equilateral triangles that have the same center.

#### Publisher

The Education Publisher, Ohio

#### ISSN

978-1-934849-75-0

#### Language (ISO)

English

#### Keywords

Homological Triangles, homology, geometry, Veronese theorem

#### Recommended Citation

Smarandache, Florentin and Ion Patrascu. "THE GEOMETRY OF HOMOLOGICAL TRIANGLES." (2012). https://digitalrepository.unm.edu/math_fsp/259

#### Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

#### Included in

Algebraic Geometry Commons, Applied Mathematics Commons, Geometry and Topology Commons, Logic and Foundations Commons, Other Mathematics Commons