THE GEOMETRY OF THE ORTHOLOGICAL TRIANGLES

THE GEOMETRY OF THE ORTHOLOGICAL TRIANGLES
Author: Ion Pătrașcu
Publisher: Infinite Study
Total Pages: 310
Release:
Genre: Mathematics
ISBN:

The book is addressed to both those who have studied and love geometry, as well as to those who discover it now, through study and training, in order to obtain special results in school competitions. In this regard, we have sought to prove some properties and theorems in several ways: synthetic, vectorial, analytical.

Variance of Topics of Plane Geometry

Variance of Topics of Plane Geometry
Author: Ion Patrascu
Publisher: Infinite Study
Total Pages: 114
Release: 2013
Genre: Geometry, Modern
ISBN: 1599732475

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 n 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. Special attention is given in this book to orthological triangles, biorthological triangles, ortho-homological triangles, and trihomological triangles. 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 for the AMATYC (American Mathematical Association for Two Year Colleges) student competition, Putnam competition, Gheorghe Ţiţeica Romanian competition, and so on. The book is also useful for geometrical researchers.

Two Remarkable Ortho-Homological Triangles

Two Remarkable Ortho-Homological Triangles
Author: Ion Pătraşcu
Publisher: Infinite Study
Total Pages: 11
Release:
Genre:
ISBN:

In a previous paper we have introduced the ortho-homological triangles, which are triangles that are orthological and homological simultaneously.

Complements to Classic Topics of Circles Geometry

Complements to Classic Topics of Circles Geometry
Author: Ion Patrascu
Publisher: Infinite Study
Total Pages: 182
Release:
Genre:
ISBN: 1599734656

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 authors’ aspiration and attraction, as a poet writes lyrics about spring according to his emotions.

Art Gallery Theorems and Algorithms

Art Gallery Theorems and Algorithms
Author: Joseph O'Rourke
Publisher: Oxford University Press, USA
Total Pages: 312
Release: 1987
Genre: Computers
ISBN:

Art gallery theorems and algorithms are so called because they relate to problems involving the visibility of geometrical shapes and their internal surfaces. This book explores generalizations and specializations in these areas. Among the presentations are recently discovered theorems on orthogonal polygons, polygons with holes, exterior visibility, visibility graphs, and visibility in three dimensions. The author formulates many open problems and offers several conjectures, providing arguments which may be followed by anyone familiar with basic graph theory and algorithms. This work may be applied to robotics and artificial intelligence as well as other fields, and will be especially useful to computer scientists working with computational and combinatorial geometry.

The Triangle Book

The Triangle Book
Author: John Horton Conway
Publisher: A K Peters Limited
Total Pages: 400
Release: 2004
Genre: Mathematics
ISBN: 9781568811659

With the advent of computer programs such as SketchPad, many high school students and amateur mathematicians are rediscovering interesting facts and theorems about triangles. The authors have created a nearly encyclopedoc collection of known and not so known aspects of the subject and present them in a beautifully illustrated triangular volume

Lucas’s Inner Circles

Lucas’s Inner Circles
Author: Ion Patrascu
Publisher: Infinite Study
Total Pages: 11
Release:
Genre:
ISBN:

In this article, we define the Lucas’s inner circles and we highlight some of their properties.