Two Remarkable Ortho-Homological Triangles

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

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

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.

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.

Some Properties of the Harmonic Quadrilateral

Some Properties of the Harmonic Quadrilateral
Author: Ion Patrascu
Publisher: Infinite Study
Total Pages: 16
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In this article, we review some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius’s Circle.

College Geometry

College Geometry
Author: Nathan Altshiller-Court
Publisher: Dover Publications
Total Pages: 336
Release: 2013-12-30
Genre:
ISBN: 9780486788470

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.

Characteristic Classes

Characteristic Classes
Author: John Willard Milnor
Publisher: Princeton University Press
Total Pages: 342
Release: 1974
Genre: Mathematics
ISBN: 9780691081229

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.

Persistence Theory: From Quiver Representations to Data Analysis

Persistence Theory: From Quiver Representations to Data Analysis
Author: Steve Y. Oudot
Publisher: American Mathematical Soc.
Total Pages: 229
Release: 2017-05-17
Genre: Mathematics
ISBN: 1470434431

Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.

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.