Famous Problems of Elementary Geometry: The Duplication of the Cube, the Trisection of an Angle, the Quadrature of the Circle. (Cosimo Classics)

Jean-Daniel Boissonnat, Mariette Yvinec; Translated By Hervé Brönnimann

The design and analysis of geometric algorithms has seen remarkable growth in recent years, due to their application in, for example, computer vision, graphics, medical imaging and CAD. The goal of this book is twofold: first to present a coherent and systematic treatment of the foundations; second to present algorithmic solutions to problems that are simple to state but which nevertheless are applicable in practical situations. The prerequisites for using the book are few which will make it ideal for teaching advanced courses in computational geometry.DjVulibre:DjVu2TIFF2PDF,loss of text data and larger file sizes.Calibre:produces poorly formatted PDFs and may encounter parsing errorsDjVuToy:1. Maintain the original compression rate of DjVu files.2. Preserve the OCR metadata of DjVu documents.3. The software is very lightweight and completely free.4. Only for Windows DjVuToy Download:https://url26.ctfile.com/f/41895126-925895940-3a0fec?p=9167Password:9167 Leer más…

Derek Smith, John Horton Conway, Derek A. Smith

This book investigates the geometry of quaternion and octonion algebras. Following a comprehensive historical introduction, the book illuminates the special properties of 3- and 4-dimensional Euclidean spaces using quaternions, leading to enumerations of the corresponding finite groups of symmetries. The second half of the book discusses the less familiar octonion algebra, concentrating on its remarkable "triality symmetry" after an appropriate study of Moufang loops. The authors also describe the arithmetics of the quaternions and octonions. The book concludes with a new theory of octonion factorization. Topics covered include the geometry of complex numbers, quaternions and 3-dimensional groups, quaternions and 4-dimensional groups, Hurwitz integral quaternions, composition algebras, Moufang loops, octonions and 8-dimensional geometry, integral octonions, and the octonion projective plane.DjVulibre:DjVu2TIFF2PDF,loss of text data and larger file sizes.Calibre:produces poorly formatted PDFs and may encounter parsing errorsDjVuToy:1. Maintain the original compression rate of DjVu files.2. Preserve the OCR metadata of DjVu documents.3. The software is very lightweight and completely free.4. Only for Windows DjVuToy Download:https://url26.ctfile.com/f/41895126-925895940-3a0fec?p=9167Password:9167 Leer más…

Miklos Bona, Miklós Bóna

There are 650 articles with the word permutation in the title whose primary classification is combinatorics, but, until now, there have been no books addressing the topic. The very first book to be published on the subject, Combinatorics of Permutations contains a comprehensive, up to date treatment of the subject. Covering both enumerative and external combinatorics, this book can be used as either a graduate text or as a reference for professional mathematicians. The book includes many applications from computer science, molecular biology, probabilistic methods, and pattern avoidance, and the numerous exercises show readers a fairly comprehensive list of recent results from the field. Leer más…

Rey Casse

This lucid and accessible text provides an introductory guide to projective geometry, an area of mathematics concerned with the properties and invariants of geometric figures under projection. Including numerous worked examples and exercises throughout, the book covers axiomatic geometry, field planes and PG(r, F), coordinating a projective plane, non-Desarguesian planes, conics and quadrics in PG(3, F). Assuming familiarity with linear algebra, elementary group theory, partial differentiation and finite fields, as well as some elementary coordinate geometry, this text is ideal for 3rd and 4th year mathematics undergraduates. Leer más…

H. S. M. Coxeter

This classic work is now available in an unabridged paperback edition. The Second Edition retains all the characterisitcs that made the first edition so popular: brilliant exposition, the flexibility permitted by relatively self-contained chapters, and broad coverage ranging from topics in the Euclidean plane, to affine geometry, projective geometry, differential geometry, and topology. The Second Edition incorporates improvements in the text and in some proofs, takes note of the solution of the 4-color map problem, and provides answers to most of the exercises. This unabridged paperback edition contains complete coverage, ranging from topics in the Euclidean plane to affine geometry, projective geometry, differential geometry and topology. Leer más…

Harold Scott Macdonald Coxeter

This is a reissue of Professor Coxeter's classic text on non-Euclidean geometry. It begins with a historical introductory chapter, and then devotes three chapters to surveying real projective geometry, and three to elliptic geometry. After this the Euclidean and hyperbolic geometries are built up axiomatically as special cases of a more general 'descriptive geometry'. This is essential reading for anybody with an interest in geometry. Leer más…

Klein, Felix

This text begins with the simplest geometric manifolds, the Grassmann determinant principle for the plane and the Grassmann principle for space; and more. Also explores affine and projective transformations; higher point transformations; transformations with change of space element; and the theory of the imaginary. Concludes with a systematic discussion of geometry and its foundations. 1939 edition. 141 figures. Leer más…

By Felix Klein; Translated By M. Ackerman

By Felix Klein ; Translated By M. Ackerman. Translation Of Vorlesungen über Die Entwicklung Der Mathematik Im 19. Jahrhundert. Appendices: Kleinian Mathematics From An Advanced Standpoint, By R. Hermann: P. 363-630. Includes Bibliographies. Leer más…

Titu Andreescu, Oleg Mushkarov, Luchezar Stoyanov, Titu Andreescu

Questions Of Maxima And Minima Have Great Practical Significance, With Applications To Physics, Engineering, And Economics; They Have Also Given Rise To Theoretical Advances, Notably In Calculus And Optimization. Indeed, While Most Texts View The Study Of Extrema Within The Context Of Calculus, This Carefully Constructed Problem Book Takes A Uniquely Intuitive Approach To The Subject: It Presents Hundreds Of Extreme-value Problems, Examples, And Solutions Primarily Through Euclidean Geometry. Key Features And Topics: * Comprehensive Selection Of Problems, Including Greek Geometry And Optics, Newtonian Mechanics, Isoperimetric Problems, And Recently Solved Problems Such As Malfatti’s Problem * Unified Approach To The Subject, With Emphasis On Geometric, Algebraic, Analytic, And Combinatorial Reasoning * Presentation And Application Of Classical Inequalities, Including Cauchy--schwarz And Minkowski’s Inequality; Basic Results In Calculus, Such As The Intermediate Value Theorem; And Emphasis On Simple But Useful Geometric Concepts, Including Transformations, Convexity, And Symmetry * Clear Solutions To The Problems, Often Accompanied By Figures * Hundreds Of Exercises Of Varying Difficulty, From Straightforward To Olympiad-caliber Written By A Team Of Established Mathematicians And Professors, This Work Draws On The Authors’ Experience In The Classroom And As Olympiad Coaches. By Exposing Readers To A Wealth Of Creative Problem-solving Approaches, The Text Communicates Not... Leer más…

Benjamin Bold

Each chapter devoted to single type of problem with accompanying commentary and set of practice problems. Amateur puzzlists, students of mathematics and geometry will enjoy this rare opportunity to match wits with civilization’s great mathematicians and witness the invention of modern mathematics.<br Leer más…

Heinrich Dörrie

"The collection, drawn from arithmetic, algebra, pure and algebraic geometry and astronomy, is extraordinarily interesting and attractive." — __Mathematical Gazette__ This uncommonly interesting volume covers 100 of the most famous historical problems of elementary mathematics. Not only does the book bear witness to the extraordinary ingenuity of some of the greatest mathematical minds of history — Archimedes, Isaac Newton, Leonhard Euler, Augustin Cauchy, Pierre Fermat, Carl Friedrich Gauss, Gaspard Monge, Jakob Steiner, and many others — but it provides rare insight and inspiration to any reader, from high school math student to professional mathematician. This is indeed an unusual and uniquely valuable book. The one hundred problems are presented in six categories: 26 arithmetical problems, 15 planimetric problems, 25 classic problems concerning conic sections and cycloids, 10 stereometric problems, 12 nautical and astronomical problems, and 12 maxima and minima problems. In addition to defining the problems and giving full solutions and proofs, the author recounts their origins and history and discusses personalities associated with them. Often he gives not the original solution, but one or two simpler or more interesting demonstrations. In only two or three instances does the solution assume anything more than a knowledge of theorems of elementary mathematics; hence, this is a book with an extremely wide appeal. Some of the most celebrated and intriguing items are:... Leer más…

Liang-Shin Hahn

The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully, resulting in easy proofs and natural generalizations of many theorems in plane geometry such as the theorems of Napoleon, Simson, Cantor and Morley.Beginning with a construction of complex numbers, readers are taken on a guided tour that includes something for everyone, even veteran professional mathematicians. Yet, the entire book is accessible to students at the high school level.The book is self-contained- no background in complex numbers is assumed- and it can be covered at a leisurely place in a one-semester course. Over 100 exercises are included. The book would be suitable as a text for a geometry course, for a problem solving seminar, or as enrichment for students who are interested in mathematics as part of culture. Leer más…

Frederick Mosteller

Can you solve the problem of "The Unfair Subway"? Marvin gets off work at random times between 3 and 5 p.m. His mother lives uptown, his girlfriend downtown. He takes the first subway that comes in either direction and eats dinner with the one he is delivered to. His mother complains that he never comes to see her, but he says she has a 50-50 chance. He has had dinner with her twice in the last 20 working days. Explain. Marvin's adventures in probability are one of the fifty intriguing puzzles that illustrate both elementary ad advanced aspects of probability, each problem designed to challenge the mathematically inclined. From "The Flippant Juror" and "The Prisoner's Dilemma" to "The Cliffhanger" and "The Clumsy Chemist," they provide an ideal supplement for all who enjoy the stimulating fun of mathematics. Professor Frederick Mosteller, who teaches statistics at Harvard University, has chosen the problems for originality, general interest, or because they demonstrate valuable techniques. In addition, the problems are graded as to difficulty and many have considerable stature. Indeed, one has "enlivened the research lives of many excellent mathematicians." Detailed solutions are included. There is every probability you'll need at least a few of them. Leer más…

D. O. Shklarsky, N. N. Chentzov, I. M. Yaglom

Over 300 challenging problems in algebra, arithmetic, elementary number theory and trigonometry, selected from the archives of the Mathematical Olympiads held at Moscow University. Most presuppose only high school mathematics but some are of uncommon difficulty and will challenge any mathematician. Complete solutions to all problems. 27 black-and-white illustrations. 1962 edition. Leer más…

A M Yaglom; Basil Gordon; I M Yaglom

Over 170 challenging problems ranging from the relatively simple to the extremely difficult. Volume 1 contains 100 problems on probability theory and combinatorial analysis. Leer más…

A M Yaglom; Basil Gordon; I M Yaglom

Over 170 challenging problems ranging from the relatively simple to the extremely difficult. Volume 2 contains 74 problems on points and lines, topology, convex polygons, nondecimal counting and other topics. Includes solutions. Leer más…

Titu Andreescu; Zuming Feng; Mathematical Association Of America

Contained here are solutions to challenging problems from algebra, geometry, combinatorics and number theory featured in the earlier book, together with selected questions (without solutions) from national and regional Olympiads given during the year 2000. Intended for the serious student/problem solver, these books can help to improve performance in the Mathematical Olympiad competition. However, for those not entering the competition, there is much to challenge any mathematician, even those with advanced degrees. Different nations have different mathematical cultures, so you will find that some of the questions are extremely difficult and some rather easy. There are a wide variety of problems especially from those countries that have often done well in the IMO. Anyone interested in mathematical problem solving will encounter some beautiful mathematics in the pages of this book. If you are up to a real challenge, take some of these problems on! Leer más…

Rene Descartes, David Eugene Smith, Marcia L. Latham

The great work that founded analytical geometry. Included here is the original French text, Descartes' own diagrams, together with the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences." — John Stuart Mill. Leer más…

Editor, Alfred S. Posamentier; Associate Editor, Wolfgang Schulz

As a mathematics teacher, you know how hard it can be for students to understand and solve mathematics problems. The old ways of solving problems don't always work. Even the most innovative teachers need some fresh ideas to make mathematics something students comprehend and enjoy.In The Art of Problem Solving the contributors look at the problem solving in a completely new light. The result is an enticing, entertaining and useful resource.Mathematics professionals from all over the world offer their personal favourite strategies for problem solving - the practical and theoretical, straightforward and colourful. The chapters are independent of each other, and the editors encourage you to use the chapters in whatever order suits your needs.With 20 diverse and diverting chapters on ways to solve problems, this book is an invalauble resource for teachers of mathematics.DjVulibre:DjVu2TIFF2PDF,loss of text data and larger file sizes.Calibre:produces poorly formatted PDFs and may encounter parsing errorsDjVuToy:1. Maintain the original compression rate of DjVu files.2. Preserve the OCR metadata of DjVu documents.3. The software is very lightweight and completely free.4. Only for Windows DjVuToy Download:https://url26.ctfile.com/f/41895126-925895940-3a0fec?p=9167Password:9167 Leer más…

Alfred S. Posamentier, Charles T. Salkind

I liked this book very much. I solved every single problem in the book with two students that I tutor for International Math Olympiads and carefully read the hints and solutions proposed at the end of the book. They really teach how to "attack" geometry problems using simple stuff like angle chasing, drawing parallel lines etc. I cannot recommend this book more to the readers with some mathematical sophistication. I even have a suggestion for parents that have some sort of mathematical background (engineers, bankers, doctors, etc.): If you want to spend quality time with your children, get this book and enjoy solving the problems together. I cannot imagine a more amusing pastime. I am looking forward to seeing new titles from the authors. Leer más…