THE GEOMETRY OF THE ORTHOLOGICAL TRIANGLES PDF Download
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Author: Ion Pătrașcu
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 310
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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 : 310
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 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 : 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 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: Ion Patrascu
Publisher: Infinite Study
ISBN: 1599734656
Category :
Languages : en
Pages : 182
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Book Description
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.
Author: Ion Patrascu
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 11
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Book Description
In this article, we define the Lucas’s inner circles and we highlight some of their properties.
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: 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: Florentin Smarandache
Publisher: Infinite Study
ISBN: 9526734920
Category : Science
Languages : en
Pages : 802
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Book Description
This is an eclectic tome of 100 papers in various fields of sciences, alphabetically listed, such as: astronomy, biology, calculus, chemistry, computer programming codification, economics and business and politics, education and administration, game theory, geometry, graph theory,information fusion, neutrosophic logic and set, non-Euclidean geometry, number theory, paradoxes, philosophy of science, psychology, quantum physics, scientific research methods, and statistics ¿ containing 800 pages.It was my preoccupation and collaboration as author, co-author, translator, or co-translator, and editor with many scientists from around the world for long time. Many ideas from this book are to be developed and expanded in future explorations.
