Two Remarkable Ortho-Homological Triangles PDF Download
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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 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: 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 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: Michael Davis
Publisher: Princeton University Press
ISBN: 0691131384
Category : Mathematics
Languages : en
Pages : 601
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Book Description
The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.
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.
Author: Nathan Altshiller-Court
Publisher: Dover Publications
ISBN: 9780486788470
Category :
Languages : en
Pages : 336
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Book Description
The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.
Author: John Willard Milnor
Publisher: Princeton University Press
ISBN: 9780691081229
Category : Mathematics
Languages : en
Pages : 342
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Book Description
The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.
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:
Publisher:
ISBN:
Category : Prosthodontics
Languages : en
Pages : 80
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Book Description
