## Mathematics and Statistics Faculty and Staff Publications

#### Document Type

Book

#### Publication Date

2013

#### Abstract

This book contains 21 papers of plane geometry. It deals with various topics, such as: quasi-isogonal cevians, nedians, polar of a point with respect to a circle, anti-bisector, aalsonti-symmedian, anti-height and their isogonal. A nedian is a line segment that has its origin in a triangle’s vertex and divides the opposite side in Q equal segments. The papers also study distances between remarkable points in the 2D-geometry, the circumscribed octagon and the inscribable octagon, the circles adjointly ex-inscribed associated to a triangle, and several classical results such as: Carnot circles, Euler’s line, Desargues theorem, Sondat’s theorem, Dergiades theorem, Stevanovic’s theorem, Pantazi’s theorem, and Newton’s theorem.

The notion of “ortho-homological triangles” was introduced by the Belgium mathematician Joseph Neuberg in 1922 in the journal Mathesis and it characterizes the triangles that are simultaneously orthogonal (i.e. the sides of one triangle are perpendicular to the sides of the other triangle) and homological. We call this “ortho-homological of first type” in order to distinguish it from our next notation. In our articles, we gave the same denomination “ortho-homological triangles” to triangles that are simultaneously orthological and homological. We call it “ortho-homological of second type.” Each paper is independent of the others. Yet, papers on the same or similar topics are listed together one after the other.

The book is intended for College and University students and instructors that prepare for mathematical competitions such as National and International Mathematical Olympiads, or the AMATYC (American Mathematical Association for Two Year Colleges) student competition, or Putnam competition, Gheorghe Ţiteica Romanian student competition, and so on. The book is also useful for geometrical researchers.

#### Publisher

Educational Publishing

#### ISSN

978-1-59973-247-3

#### Language (ISO)

English

#### Keywords

circle, anti-bisector, anti-height, isogonal

#### Recommended Citation

Smarandache, Florentin and Ion Patrascu. "Variance on topics of plane geometry." (2013). https://digitalrepository.unm.edu/math_fsp/257

#### Creative Commons License

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

#### Included in

Algebra Commons, Analysis Commons, Applied Mathematics Commons, Logic and Foundations Commons, Number Theory Commons, Other Physical Sciences and Mathematics Commons, Set Theory Commons