The Geometry of Homological Triangles
Author : Florentin Smarandache, Ion Patrascu
Publisher : Infinite Study
Page : 246 pages
File Size : 25,97 MB
Release : 2011
Category : Geometry
ISBN : 1934849758
Author : Florentin Smarandache, Ion Patrascu
Publisher : Infinite Study
Page : 246 pages
File Size : 25,97 MB
Release : 2011
Category : Geometry
ISBN : 1934849758
Author : Ion Pătrașcu
Publisher : Infinite Study
Page : 310 pages
File Size : 47,78 MB
Release :
Category : 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.
Author : Ion Pătraşcu
Publisher : Infinite Study
Page : 11 pages
File Size : 31,5 MB
Release :
Category :
ISBN :
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
Page : 114 pages
File Size : 21,92 MB
Release : 2013
Category : 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.
Author : Ion Pătraşcu
Publisher : Infinite Study
Page : 13 pages
File Size : 20,30 MB
Release :
Category :
ISBN :
Also, we introduce the notion of Orthohomological Triangles, which means two triangles that are simultaneously orthological and homological.
Author : Jesper Lützen
Publisher : Kgl. Danske Videnskabernes Selskab
Page : 306 pages
File Size : 26,73 MB
Release : 2001
Category : Cartography
ISBN : 9788778762368
Author : Ion Patrascu
Publisher : Infinite Study
Page : 182 pages
File Size : 23,69 MB
Release :
Category :
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.
Author : Florentin Smarandache
Publisher : Infinite Study
Page : 336 pages
File Size : 25,73 MB
Release : 2014-09-01
Category : Mathematics
ISBN :
This volume includes 37 papers of mathematics or applied mathematics written by the author alone or in collaboration with the following co-authors: Cătălin Barbu, Mihály Bencze, Octavian Cira, Marian Niţu, Ion Pătraşcu, Mircea E. Şelariu, Rajan Alex, Xingsen Li, Tudor Păroiu, Luige Vlădăreanu, Victor Vlădăreanu, Ştefan Vlăduţescu, Yingjie Tian, Mohd Anasri, Lucian Căpitanu, Valeri Kroumov, Kimihiro Okuyama, Gabriela Tonţ, A. A. Adewara, Manoj K. Chaudhary, Mukesh Kumar, Sachin Malik, Alka Mittal, Neetish Sharma, Rakesh K. Shukla, Ashish K. Singh, Jayant Singh, Rajesh Singh,V.V. Singh, Hansraj Yadav, Amit Bhaghel, Dipti Chauhan, V. Christianto, Priti Singh, and Dmitri Rabounski. They were written during the years 2010-2014, about the hyperbolic Menelaus theorem in the Poincare disc of hyperbolic geometry, and the Menelaus theorem for quadrilaterals in hyperbolic geometry, about some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius circles, about Luhn prime numbers, and also about the correspondences of the eccentric mathematics of cardinal and integral functions and centric mathematics, or ordinary mathematics; there are some notes on Crittenden and Vanden Eynden's conjecture, or on new transformations, previously non-existent in traditional mathematics, that we call centric mathematics (CM), but that became possible due to the new born eccentric mathematics, and, implicitly, to the supermathematics (SM); also, about extenics, in general, and extension innovation model and knowledge management, in particular, about advanced methods for solving contradictory problems of hybrid position-force control of the movement of walking robots by applying a 2D Extension Set, or about the notion of point-set position indicator and that of point-two sets position indicator, and the navigation of mobile robots in non-stationary and nonstructured environments; about applications in statistics, such as estimators based on geometric and harmonic mean for estimating population mean using information; about Godel’s incompleteness theorem(s) and plausible implications to artificial intelligence/life and human mind, and many more.
Author : Eric W. Weisstein
Publisher : CRC Press
Page : 3253 pages
File Size : 36,69 MB
Release : 2002-12-12
Category : Mathematics
ISBN : 1420035223
Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d
Author : William J. M'Clelland
Publisher :
Page : 384 pages
File Size : 20,97 MB
Release : 1891
Category : Circle
ISBN :