Geometry of complex numbers : circle geometry, Moebius transformation, non-euclidean geometry

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…

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…

Felix Klein, Wooster Woodruff Beman, David Eugene Smith

This short book, first published in 1897, addresses three geometry puzzles that have been passed down from ancient times. Written for high school students, this book aims to show a younger audience why math should matter and to make the problems found in math intriguing. Klein presents for his readers an investigation of the possibility or impossibility of finding solutions for the following problems in light of mathematics available to him: duplication of the cube trisection of an angle quadrature of the circle Mathematicians and students of the history of math will find this an intriguing work. German mathematician FELIX KLEIN (1849-1925), a great teacher and scientific thinker, significantly advanced the field of mathematical physics and made a number of profound discoveries in the field of geometry. His published works include Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis and Elementary Mathematics from an Advanced Standpoint: 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…

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…

Les Evans; David Leigh-Lancaster

Complex Numbers and Vectors is an informative resource for advanced mathematics teachers or students undertaking advanced maths courses that draws on the power of intrigue and uses appealing applications from navigation, global positioning systems, earthquakes and stories from mathematical history to explain the mathematics of vectors and the discoveries in complex numbers. The title is split into two parts: Part 1 provides teachers with background material, ideas and teaching approaches to complex numbers: o Including models for complex numbers and their geometric and algebraic properties, their role in providing completeness with respect to the solution of polynomial equations of a single complex variable (the fundamental theorem of algebra) and the specification of curves and regions in the complex plane; and simple transformations of the complex plane. Part 2 provides an introduction to vectors and vector spaces: o Including matrix representation (covers vectors in two- and three-dimensions), their application to specification of curves and vector calculus and their elementary application to geometric proof Technology has been used throughout the text to construct images of curves, graphs and two and three dimensional shapes. 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…

Ross Honsberger

mathematics Is Often Studied With An Air Of Such Seriousness That It Doesn't Always Seem To Be Much Fun. However, It Is Quite Amazing How Many Surprising Results And Brilliant Arguments One Is In A Position To Enjoy With Just A High School Background. This Is A Book Of Miscellaneous Delights, Presented Not In An Attempt To Instruct But As A Harvest Of Rewards That Are Due To Good High School Students And, Of Course, Those More Advanced - Their Teachers And Everyone In The University Mathematics Community. A Half Dozen Essays Are Sprinkled Among Some Hundred Problems. Many Subjects Are Represented - Combinatorics, Geometry, Number Theory, Algebra, Probability. The Sections May Be Read In Any Order. The Book Concludes With Twenty-five Exercises And Their Detailed Solutions. Something To Delight Will Be Found In Every Section - A Surprising Result, An Intriguing Approach, A Stroke Of Ingenuity - And The Leisurely Pace And Generous Explanations Make The Book A Pleasure To Read. Leer más…

Luther Pfahler Eisenhart

A thorough, complete, and unified introduction, this volume affords exceptional insights into coordinate geometry. Invariants of conic sections and quadric surfaces receive full treatments. Algebraic equations on the first degree in two and three unknowns are carefully reviewed. Throughout the book, results are formulated precisely, with clearly stated theorems. More than 500 helpful exercises. 1939 edition. Leer más…

Ledermann W.

lgrsnf/dvd60/Ledermann W. - Complex Numbers(1960)(62).djvu Leer más…

Roland Deaux; Translated By Howard Eves

Geared toward readers unfamiliar withВ complex numbers, this text explains how to solve the kinds of problems that frequently arise in the applied sciences, especially electrical studies. To assure an easy and complete understanding, topics are developed from the beginning, with emphasis on constructions related to algebraic operations. 1956 edition. Leer más…

Eugene F. Krause

Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Topics include applications to urban geography and planning plus comparisons to Euclidean geometry. Every principle is illustrated and clarified with numerous research problems, exercises, and graphs. Selected answers to problems. Develops a simple non-Euclidean geometry and explores some of its practical applications through graphs, research problems, and exercises. Includes selected answers. Leer más…

Nathan Altshiller-Court

Thank you Dover!! This is one of the two English books in print that give a fairly complete introduction to advanced Euclidean geometry, the other one being the comparable text by R A Johnson, Advanced Euclidean Geometry (Dover Books on Mathematics). The book contains all the classical theorems with full proofs, including many theorems that belong to the so called triangle geometry that was developed in the last quarter of the nineteenth century. Due to geometry software the subject is becoming popular again. The book also contains a treasure of exercises, but no solutions which could be a nuisance. But what use are the solutions? Problems should be solved and not looked up!. Many problems are about geometric constructions. If you prepare for a mathematical contest or if you are interested in a complete overview of the classical plane geometry (for instance after reading Ross Honsberger's "Episodes"), this is your book. The book assumes that you are familiar with simple geometrical concepts like congruence of triangles, parallelograms, circles and the most elementary theorems and constructions as can be found in Kiselev's book Kiselev's Geometry / Book I. Planimetry. Leer más…

Roland Deaux; Translated By Howard Eves

Geared toward readers unfamiliar withВ complex numbers, this text explains how to solve the kinds of problems that frequently arise in the applied sciences, especially electrical studies. To assure an easy and complete understanding, topics are developed from the beginning, with emphasis on constructions related to algebraic operations. 1956 edition. Leer más…

M. N. Aref, William Wernick

Based on classical principles, this book is intended for a second course in Euclidean geometry and can be used as a refresher. Each chapter covers a different aspect of Euclidean geometry, lists relevant theorems and corollaries, and states and proves many propositions. Includes more than 200 problems, hints, and solutions. 1968 edition. Leer más…

Harold Scott Macdonald Coxeter

In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, repectively. The next three chapters develop a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry. Leer más…

Walter Ledermann (Auth.)

THE purpose of this book is to prescnt a straightforward introduction to complex numbers and their properties. Complex numbers, like other kinds of numbers, are essen­ tially objects with which to perform calculations a:cording to certain rules, and when this principle is borne in mind, the nature of complex numbers is no more mysterious than that of the more familiar types of numbers. This formal approach has recently been recommended in a Reportt prepared for the Mathematical Association. We believe that it has distinct advantages in teaching and that it is more in line with modern algebraical ideas than the alternative geometrical or kinematical definitions of v -1 that used to be proposed. On the other hand, an elementary textbook is clearly not the place to enter into a full discussion of such questions as logical consistency, which would have to be included in a rigorous axiomatic treatment. However, the steps that had to be omitted (with due warning) can easily be filled in by the methods of abstract algebra, which do not conflict with the 'naive' attitude adopted here. I should like to thank my friend and colleague Dr. J. A. Green for a number of valuable suggestions, especially in connection with the chapter on convergence, which is a sequel to his volume Sequences and Series in this Library. 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…

I. M. Yaglom, Henry Booker, D. Allan Bromley And Nicholas Declaris (Auth.)

Content: ACADEMIC PAPERBACKS, Page ii Front Matter, Page iii Copyright, Page iv Translator's Note, Page v Preface, Pages vii-x CHAPTER I - Three Types of Complex Numbers, Pages 1-25 CHAPTER II - Geometrical Interpretation of Complex Numbers, Pages 26-129 CHAPTER III - Circular Transformations and Circular Geometry, Pages 130-194 APPENDIX - Non-Euclidean Geometries in the Plane and Complex Numbers, Pages 195-219 ADDENDA, Pages 220-239 Index, Pages 241-243 Leer más…