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.

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.

Multispace & Multistructure. Neutrosophic Transdisciplinarity (100 Collected Papers of Science)

Multispace & Multistructure. Neutrosophic Transdisciplinarity (100 Collected Papers of Science)
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 802
Release: 2010
Genre: Science
ISBN: 9526734920

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.

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.

Scientia Magna Vol. 6, No. 1, 2010

Scientia Magna Vol. 6, No. 1, 2010
Author: Zhang Wenpeng
Publisher: Infinite Study
Total Pages: 132
Release: 2010
Genre: Mathematics
ISBN: 1599730995

Papers on Smarandache¿s codification used in computer programming, smarandacheials, totient and congruence functions, sequences, irrational constants in number theory, multi-space and geometries.

Grid Homology for Knots and Links

Grid Homology for Knots and Links
Author: Peter S. Ozsváth
Publisher: American Mathematical Soc.
Total Pages: 423
Release: 2015-12-04
Genre: Education
ISBN: 1470417375

Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.