## Mathematics and Statistics Faculty and Staff Publications

#### Document Type

Book

#### Publication Date

2020

#### Abstract

Plants and trees grow perpendicular to the plane tangent to the soil surface, at the point of penetration into the soil; in vacuum, the bodies fall perpendicular to the surface of the Earth - in both cases, if the surface is horizontal. Starting from the property of two triangles to be orthological, the two authors have designed this work that seeks to provide an integrative image of elementary geometry by the prism of this "filter". Basically, the property of orthology is the skeleton of the present work, which establishes many connections of some theorems and geometric properties with it. The book "The Geometry of The Orthological Triangles" is divided into ten chapters. In the first seven, the topic is introduced and developed by connecting it with other beautiful properties of geometry, such as the homology of triangles. Chapter 8 includes three annexes intended to clarify to the readers some results used in the rest of the chapters. Chapter 9 is a collection of problems where orthological triangles usually appear; it is especially intended for students preparing for participation in different mathematics competitions. The last chapter contains solutions and answers to the problems in chapter 9.

#### Publisher

Pons Editions, Brussels

#### ISSN

978-1-59973-653-2

#### Language (ISO)

English

#### Keywords

Orthological Triangles, orthology, triangles, soil surface

#### Recommended Citation

Smarandache, Florentin and Ion Patrascu. "THE GEOMETRY OF THE ORTHOLOGICAL TRIANGLES." (2020). https://digitalrepository.unm.edu/math_fsp/260

#### Creative Commons License

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

#### Included in

Applied Mathematics Commons, Earth Sciences Commons, Geometry and Topology Commons, Other Mathematics Commons, Other Physical Sciences and Mathematics Commons