THE GEOMETRY OF THE ORTHOLOGICAL TRIANGLES PDF Download
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Author: Ion Pătrașcu
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 312
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Book Description
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.
Author: Ion Pătrașcu
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 312
Get Book Here
Book Description
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.
Author: Florentin Smarandache, Ion Patrascu
Publisher: Infinite Study
ISBN: 1934849758
Category : Geometry
Languages : en
Pages : 246
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Book Description
Author: Ion Pătraşcu
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 13
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Book Description
Also, we introduce the notion of Orthohomological Triangles, which means two triangles that are simultaneously orthological and homological.
Author: Ion Patrascu
Publisher: Infinite Study
ISBN: 1599732475
Category : Geometry, Modern
Languages : en
Pages : 114
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Book Description
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.
Author: Ion Pătraşcu
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 11
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Book Description
In a previous paper we have introduced the ortho-homological triangles, which are triangles that are orthological and homological simultaneously.
Author: Joseph O'Rourke
Publisher: Oxford University Press, USA
ISBN:
Category : Computers
Languages : en
Pages : 312
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Book Description
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.
Author: John Horton Conway
Publisher: A K Peters Limited
ISBN: 9781568811659
Category : Mathematics
Languages : en
Pages : 400
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Book Description
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
Author: Howard Whitley Eves
Publisher: Jones & Bartlett Learning
ISBN: 9780867204759
Category : Computers
Languages : en
Pages : 392
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Book Description
College Geometry is divided into two parts. Part I is a sequel to basic high school geometry and introduces the reader to some of the important modern extensions of elementary geometry- extension that have largely entered into the mainstream of mathematics. Part II treats notions of geometric structure that arose with the non-Euclidean revolution in the first half of the nineteenth century.
Author: Franco P. Preparata
Publisher: Springer Science & Business Media
ISBN: 1461210984
Category : Mathematics
Languages : en
Pages : 413
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Book Description
From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2
Author: Ion Patrascu
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 16
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Book Description
In this article, we review some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius’s Circle.
