Episodes In Nineteenth And Twentieth Century Euclidean Geometry

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Episodes in Nineteenth and Twentieth Century Euclidean Geometry

Ross Honsberger
Episodes in Nineteenth and Twentieth Century Euclidean Geometry Book PDF

Author : Ross Honsberger
Publisher : Cambridge University Press
Page : 196 pages
File Size : 46,7 Mb
Release : 1995
Category : Mathematics
ISBN : 0883856395

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Episodes in Nineteenth and Twentieth Century Euclidean Geometry by Ross Honsberger Pdf

Professor Honsberger has succeeded in 'finding' and 'extricating' unexpected and little known properties of such fundamental figures as triangles, results that deserve to be better known. He has laid the foundations for his proofs with almost entirely synthetic methods easily accessible to students of Euclidean geometry early on. While in most of his other books Honsberger presents each of his gems, morsels, and plums, as self contained tidbits, in this volume he connects chapters with some deductive treads. He includes exercises and gives their solutions at the end of the book. In addition to appealing to lovers of synthetic geometry, this book will stimulate also those who, in this era of revitalizing geometry, will want to try their hands at deriving the results by analytic methods. Many of the incidence properties call to mind the duality principle; other results tempt the reader to prove them by vector methods, or by projective transformations, or complex numbers.

Geometry for College Students

I. Martin Isaacs
Geometry for College Students Book PDF

Author : I. Martin Isaacs
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 52,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847947

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Geometry for College Students by I. Martin Isaacs Pdf

One of the challenges many mathematics students face occurs after they complete their study of basic calculus and linear algebra, and they start taking courses where they are expected to write proofs. Historically, students have been learning to think mathematically and to write proofs by studying Euclidean geometry. In the author's opinion, geometry is still the best way to make the transition from elementary to advanced mathematics. The book begins with a thorough review of high school geometry, then goes on to discuss special points associated with triangles, circles and certain associated lines, Ceva's theorem, vector techniques of proof, and compass-and-straightedge constructions. There is also some emphasis on proving numerical formulas like the laws of sines, cosines, and tangents, Stewart's theorem, Ptolemy's theorem, and the area formula of Heron. An important difference of this book from the majority of modern college geometry texts is that it avoids axiomatics. The students using this book have had very little experience with formal mathematics. Instead, the focus of the course and the book is on interesting theorems and on the techniques that can be used to prove them. This makes the book suitable to second- or third-year mathematics majors and also to secondary mathematics education majors, allowing the students to learn how to write proofs of mathematical results and, at the end, showing them what mathematics is really all about.

From Erdös to Kiev

Ross Honsberger
From Erd s to Kiev Book PDF

Author : Ross Honsberger
Publisher : Cambridge University Press
Page : 276 pages
File Size : 40,6 Mb
Release : 1996
Category : Mathematics
ISBN : 0883853248

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From Erdös to Kiev by Ross Honsberger Pdf

Ross Honsberger's love of mathematics comes through very clearly in From Erds to Kiev. He presents intriguing, stimulating problems that can be solved with elementary mathematical techniques. It will give pleasure to motivated students and their teachers, but it will also appeal to anyone who enjoys a mathematical challenge. Most of the problems in the collection have appeared on national or international Olympiads or other contests. Thus, they are quite challenging (with solutions that are all the more rewarding). The solutions use straightforward arguments from elementary mathematics (often not very technical arguments) with only the occasional foray into sophisticated or advanced ideas. Anyone familiar with elementary mathematics can appreciate a large part of the book. The problems included in this collection are taken from geometry, number theory, probability, and combinatorics. Solutions to the problems are included.

Mathematical Diamonds

Ross Honsberger
Mathematical Diamonds Book PDF

Author : Ross Honsberger
Publisher : Cambridge University Press
Page : 260 pages
File Size : 45,9 Mb
Release : 2003-05-15
Category : Mathematics
ISBN : 0883853329

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Mathematical Diamonds by Ross Honsberger Pdf

Collection of elementary mathematical problems with solutions. Ideal for students, teachers and general readers.

CRC Concise Encyclopedia of Mathematics

Eric W. Weisstein
CRC Concise Encyclopedia of Mathematics Book PDF

Author : Eric W. Weisstein
Publisher : CRC Press
Page : 3253 pages
File Size : 50,5 Mb
Release : 2002-12-12
Category : Mathematics
ISBN : 9781420035223

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CRC Concise Encyclopedia of Mathematics by Eric W. Weisstein Pdf

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

Problem-Solving and Selected Topics in Euclidean Geometry

Sotirios E. Louridas,Michael Th. Rassias
Problem Solving and Selected Topics in Euclidean Geometry Book PDF

Author : Sotirios E. Louridas,Michael Th. Rassias
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 53,6 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9781461472735

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Problem-Solving and Selected Topics in Euclidean Geometry by Sotirios E. Louridas,Michael Th. Rassias Pdf

"Problem-Solving and Selected Topics in Euclidean Geometry: in the Spirit of the Mathematical Olympiads" contains theorems which are of particular value for the solution of geometrical problems. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geometry. Before the complete solution of every problem, a key idea is presented so that the reader will be able to provide the solution. Applications of the basic geometrical methods which include analysis, synthesis, construction and proof are given. Selected problems which have been given in mathematical olympiads or proposed in short lists in IMO's are discussed. In addition, a number of problems proposed by leading mathematicians in the subject are included here. The book also contains new problems with their solutions. The scope of the publication of the present book is to teach mathematical thinking through Geometry and to provide inspiration for both students and teachers to formulate "positive" conjectures and provide solutions.

Lectures on Euclidean Geometry - Volume 1

Paris Pamfilos
Lectures on Euclidean Geometry Volume 1 Book PDF

Author : Paris Pamfilos
Publisher : Springer Nature
Page : 608 pages
File Size : 43,5 Mb
Release : 2024
Category : Euclidean algorithm
ISBN : 9783031489068

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Lectures on Euclidean Geometry - Volume 1 by Paris Pamfilos Pdf

Zusammenfassung: This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume focuses on Euclidean Geometry of the plane, and the second volume on Circle measurement, Transformations, Space geometry, Conics. The book is based on lecture notes from more than 30 courses which have been taught over the last 25 years. Using a synthetic approach, it discusses topics in Euclidean geometry ranging from the elementary (axioms and their first consequences), to the complex (the famous theorems of Pappus, Ptolemy, Euler, Steiner, Fermat, Morley, etc.). Through its coverage of a wealth of general and specialized subjects, it provides a comprehensive account of the theory, with chapters devoted to basic properties of simple planar and spatial shapes, transformations of the plane and space, and conic sections. As a result of repeated exposure of the material to students, it answers many frequently asked questions. Particular attention has been given to the didactic method; the text is accompanied by a plethora of figures (more than 2000) and exercises (more than 1400), most of them with solutions or expanded hints. Each chapter also includes numerous references to alternative approaches and specialized literature. The book is mainly addressed to students in mathematics, physics, engineering, school teachers in these areas, as well as, amateurs and lovers of geometry. Offering a sound and self-sufficient basis for the study of any possible problem in Euclidean geometry, the book can be used to support lectures to the most advanced level, or for self-study

Euclid and His Twentieth Century Rivals

Nathaniel Miller
Euclid and His Twentieth Century Rivals Book PDF

Author : Nathaniel Miller
Publisher : Center for the Study of Language and Information Publica Tion
Page : 136 pages
File Size : 50,7 Mb
Release : 2007
Category : Mathematics
ISBN : STANFORD:36105131648672

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Euclid and His Twentieth Century Rivals by Nathaniel Miller Pdf

Twentieth-century developments in logic and mathematics have led many people to view Euclid's proofs as inherently informal, especially due to the use of diagrams in proofs. In Euclid and His Twentieth-Century Rivals, Nathaniel Miller discusses the history of diagrams in Euclidean Geometry, develops a formal system for working with them, and concludes that they can indeed be used rigorously. Miller also introduces a diagrammatic computer proof system, based on this formal system. This volume will be of interest to mathematicians, computer scientists, and anyone interested in the use of diagrams in geometry.

The Facts on File Geometry Handbook

Catherine A. Gorini
The Facts on File Geometry Handbook Book PDF

Author : Catherine A. Gorini
Publisher : Infobase Publishing
Page : 289 pages
File Size : 42,7 Mb
Release : 2014-05-14
Category : Mathematics
ISBN : 9781438109572

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The Facts on File Geometry Handbook by Catherine A. Gorini Pdf

Contains a history of the subject of geometry, including more than 3,000 entries providing definitions and explanations of related topics, plus brief biographies of over 300 scientists.

Topics in Elementary Geometry

O. Bottema
Topics in Elementary Geometry Book PDF

Author : O. Bottema
Publisher : Springer Science & Business Media
Page : 142 pages
File Size : 51,6 Mb
Release : 2008-12-10
Category : Mathematics
ISBN : 9780387781310

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Topics in Elementary Geometry by O. Bottema Pdf

This small book, translated into English for the first time, has long been a unique place to find classical results from geometry, such as Pythagoras' theorem, the nine-point circle, Morley's triangle, and many other subjects. In addition, this book contains recent, geometric theorems which have been obtained over the past years. There are 27 independent chapters on a wide range of topics in elementary plane Euclidean geometry, at a level just beyond what is usually taught in a good high school or college geometry course. The selection of topics is intelligent, varied, and stimulating, and the author provides many thought-provoking ideas.

Analytic Hyperbolic Geometry in N Dimensions

Abraham Albert Ungar
Analytic Hyperbolic Geometry in N Dimensions Book PDF

Author : Abraham Albert Ungar
Publisher : CRC Press
Page : 616 pages
File Size : 51,5 Mb
Release : 2014-12-17
Category : Mathematics
ISBN : 9781482236682

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Analytic Hyperbolic Geometry in N Dimensions by Abraham Albert Ungar Pdf

The concept of the Euclidean simplex is important in the study of n-dimensional Euclidean geometry. This book introduces for the first time the concept of hyperbolic simplex as an important concept in n-dimensional hyperbolic geometry. Following the emergence of his gyroalgebra in 1988, the author crafted gyrolanguage, the algebraic language t

Perspectives on the Teaching of Geometry for the 21st Century

C. Mammana,V. Villani
Perspectives on the Teaching of Geometry for the 21st Century Book PDF

Author : C. Mammana,V. Villani
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Education
ISBN : 9789401152266

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Perspectives on the Teaching of Geometry for the 21st Century by C. Mammana,V. Villani Pdf

In recent years geometry seems to have lost large parts of its former central position in mathematics teaching in most countries. However, new trends have begun to counteract this tendency. There is an increasing awareness that geometry plays a key role in mathematics and learning mathematics. Although geometry has been eclipsed in the mathematics curriculum, research in geometry has blossomed as new ideas have arisen from inside mathematics and other disciplines, including computer science. Due to reassessment of the role of geometry, mathematics educators and mathematicians face new challenges. In the present ICMI study, the whole spectrum of teaching and learning of geometry is analysed. Experts from all over the world took part in this study, which was conducted on the basis of recent international research, case studies, and reports on actual school practice. This book will be of particular interest to mathematics educators and mathematicians who are involved in the teaching of geometry at all educational levels, as well as to researchers in mathematics education.

Plane and Solid Geometry

J.M. Aarts
Plane and Solid Geometry Book PDF

Author : J.M. Aarts
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 43,8 Mb
Release : 2009-04-28
Category : Mathematics
ISBN : 9780387782416

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Plane and Solid Geometry by J.M. Aarts Pdf

This is a book on Euclidean geometry that covers the standard material in a completely new way, while also introducing a number of new topics that would be suitable as a junior-senior level undergraduate textbook. The author does not begin in the traditional manner with abstract geometric axioms. Instead, he assumes the real numbers, and begins his treatment by introducing such modern concepts as a metric space, vector space notation, and groups, and thus lays a rigorous basis for geometry while at the same time giving the student tools that will be useful in other courses.

An Excursion through Elementary Mathematics, Volume II

Antonio Caminha Muniz Neto
An Excursion through Elementary Mathematics Volume II Book PDF

Author : Antonio Caminha Muniz Neto
Publisher : Springer
Page : 550 pages
File Size : 40,6 Mb
Release : 2018-04-16
Category : Mathematics
ISBN : 9783319779744

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An Excursion through Elementary Mathematics, Volume II by Antonio Caminha Muniz Neto Pdf

This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This second volume covers Plane Geometry, Trigonometry, Space Geometry, Vectors in the Plane, Solids and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.

Collected Papers. Volume V

Florentin Smarandache
Collected Papers Volume V Book PDF

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 336 pages
File Size : 54,7 Mb
Release : 2014-10-14
Category : Mathematics
ISBN : 9781599733173

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Collected Papers. Volume V by Florentin Smarandache Pdf

This volum includes 37 papers of mathematics or applied mathematics written by the author alone or in collaboration.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 inhyperbolic geometry, about some properties of the harmonic quadrilateral related to triangle simedians and to Apollonius circles, etc.