WorldCat Identities

Coxeter, H. S. M. (Harold Scott Macdonald) 1907-2003

Publication Timeline
Most widely held works by H. S. M Coxeter
Non-Euclidean geometry by H. S. M Coxeter( Book )

70 editions published between 1941 and 2017 in English and Undetermined and held by 2,949 WorldCat member libraries worldwide

The MAA is delighted to be the publisher of the sixth edition of this book, updated with a new section 15.9 on the author's useful concept of inversive distance. Throughout most of this book, non-Euclidean geometries in spaces of two or three dimensions are treated as specializations of real projective geometry in terms of a simple set of axioms concerning points, lines, planes, incidence, order and continuity, with no mention of the measurement of distances or angles. This synthetic development is followed by the introduction of homogeneous coordinates, beginning with Von Staudt's idea of regarding points as entities that can be added or multiplied. Transformations that preserve incidence are called colineations. They lead in a natural way to elliptic isometries or "congruent transformations". Following a recommendation by Bertrand Russell, continuity is described in terms of order. Elliptic and hyperbolic geometries are derived from real projective geometry by specializing an elliptic or hyperbolic polarity which transforms points into lines (in two dimensions) or planes (in three dimensions) and vice versa. This treatment can be enjoyed by anyone who is familiar with algebra up to the elements of group theory. - Publisher
Geometry revisited by H. S. M Coxeter( )

41 editions published between 1967 and 2012 in English and Undetermined and held by 2,689 WorldCat member libraries worldwide

The chief purpose of this book is to revisit those regions of elementary geometry that were enjoyed by our ancestors, making use of the idea of transformations: an idea that facilitates geometric understanding and links the subject with other branches of mathematics. In particular, Chapter 5 introduces the reader to inversive geometry, which has an important application to analysis, and Chapter 6 introduces conics with special emphasis on the notions of focus and eccentricity, notions obviously relevant to the study of orbits of comets, planets, and satellites. The early chapters take the reader by easy stages from very simple ideas to the core of the subject. The problems throughout the book contain extensions of the text as well as challenges to the reader
Introduction to geometry by H. S. M Coxeter( Book )

103 editions published between 1961 and 1994 in 6 languages and held by 2,239 WorldCat member libraries worldwide

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
Mathematical recreations & essays by W. W. Rouse Ball( Book )

78 editions published between 1939 and 2015 in 3 languages and held by 1,426 WorldCat member libraries worldwide

This classic work offers scores of stimulating, mind-expanding games and puzzles: arithmetical and geometrical problems, chessboard recreations, magic squares, map-coloring problems, cryptography and cryptanalysis, much more
Projective geometry by H. S. M Coxeter( Book )

66 editions published between 1946 and 2003 in 4 languages and held by 1,319 WorldCat member libraries worldwide

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, respectively. 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
The real projective plane by H. S. M Coxeter( Book )

88 editions published between 1949 and 1993 in 4 languages and held by 1,294 WorldCat member libraries worldwide

Contain: Files, scenes, narrations, and projectivities for Mathematica
Regular polytopes by H. S. M Coxeter( Book )

46 editions published between 1947 and 2013 in English and Undetermined and held by 1,226 WorldCat member libraries worldwide

Polytopes are geometrical figures bounded by portions of lines, planes, or hyperplanes. In plane (two dimensional) geometry, they are known as polygons and comprise such figures as triangles, squares, pentagons, etc. In solid (three dimensional) geometry they are known as polyhedra and include such figures as tetrahedra (a type of pyramid), cubes, icosahedra, and many more; the possibilities, in fact, are infinite! H.S.M. Coxeter's book is the foremost book available on regular polyhedra, incorporating not only the ancient Greek work on the subject, but also the vast amount of information that has been accumulated on them since, especially in the last hundred years. The author, professor of Mathematics, University of Toronto, has contributed much valuable work himself on polytopes and is a well-known authority on them. Professor Coxeter begins with the fundamental concepts of plane and solid geometry and then moves on to multi-dimensionality. Among the many subjects covered are Euler's formula, rotation groups, star-polyhedra, truncation, forms, vectors, coordinates, kaleidoscopes, Petrie polygons, sections and projections, and star-polytopes. Each chapter ends with a historical summary showing when and how the information contained therein was discovered. Numerous figures and examples and the author's lucid explanations also help to make the text readily comprehensible. Although the study of polytopes does have some practical applications to mineralogy, architecture, linear programming, and other areas, most people enjoy contemplating these figures simply because their symmetrical shapes have an aesthetic appeal. But whatever the reasons, anyone with an elementary knowledge of geometry and trigonometry will find this one of the best source books available on this fascinating study
Generators and relations for discrete groups by H. S. M Coxeter( Book )

65 editions published between 1957 and 2017 in 5 languages and held by 1,067 WorldCat member libraries worldwide

When we began to consider the scope of this book, we envisaged a catalogue supplying at least one abstract definition for any finitely generated group that the reader might propose. But we soon realized that more or less arbitrary restrictions are necessary, because interesting groups are so numerous. For permutation groups of degree 8 or less (i. e., subgroups of e), the reader cannot do better than consult the 8 tables of JosEPHINE BuRNS (1915), while keeping an eye open for misprints. Our own tables (on pages 134-143) deal with groups of low order, finiteandinfinite groups of congruent transformations, symmetric and alternating groups, linear fractional groups, and groups generated by reflections in real Euclidean space of any number of dimensions. The best substitute foramoreextensive catalogue is the description (in Chapter 2) of a method whereby the reader can easily work out his own abstract definition for almost any given finite group. This method is sufficiently mechanical for the use of an electronic computer. There is also a topological method (Chapter 3), suitable not only for groups of low order but also for some infinite groups. This involves choosing a set of generators, constructing a certain graph (the Cayley diagram or DEHNsehe Gruppenbild), and embedding the graph into a surface. Cases in which the surface is a sphere or a plane are described in Chapter 4, where we obtain algebraically, and verify topologically, an abstract definition for each of the 17 space groups of two-dimensional crystallography
Regular complex polytopes by H. S. M Coxeter( Book )

29 editions published between 1973 and 1991 in English and Undetermined and held by 846 WorldCat member libraries worldwide

M.C. Escher, art and science : proceedings of the International Congress on M.C. Escher, Rome, Italy, 26-28 March 1985 by Interdisciplinary Congress on M.C. Escher( Book )

23 editions published in 1986 in English and French and held by 584 WorldCat member libraries worldwide

The fifty-nine icosahedra by H. S. M Coxeter( Book )

34 editions published between 1938 and 2011 in 3 languages and held by 471 WorldCat member libraries worldwide

For this new edition, the plans and illustrations of all 59 icosahedra have been redrawn and there is a new introduction by Professor Coxeter. For an understanding of the process of stellation, this book should be a useful addition to any mathematics library
Twelve geometric essays by H. S. M Coxeter( Book )

14 editions published in 1968 in English and Undetermined and held by 451 WorldCat member libraries worldwide

Twisted honeycombs by H. S. M Coxeter( Book )

23 editions published between 1970 and 2009 in English and Undetermined and held by 400 WorldCat member libraries worldwide

Mathematic recreations & essays by W. W. Rouse Ball( )

8 editions published between 1939 and 2016 in English and Undetermined and held by 390 WorldCat member libraries worldwide

For over eighty years this delightful classic has provided entertainment through mathematical problems commonly known as recreations. This new edition upholds the original, but the terminology and treatment of problems have been updated and much new material has been added
Zero-symmetric graphs : trivalent graphical regular representations of groups by H. S. M Coxeter( Book )

19 editions published between 1981 and 2014 in English and Undetermined and held by 386 WorldCat member libraries worldwide

Zero-Symmetric Graphs: Trivalent Graphical Regular Representations of Groups describes the zero-symmetric graphs with not more than 120 vertices. The graphs considered in this text are finite, connected, vertex-transitive and trivalent. This book is organized into three parts encompassing 25 chapters. The first part reviews the different classes of zero-symmetric graphs, according to the number of essentially different edges incident at each vertex, namely, the S, T, and Z classes. The remaining two parts discuss the theorem and characteristics of type 1Z and 3Z graphs. These parts explo
The Geometric vein : the Coxeter festschrift by Chandler Davis( Book )

9 editions published in 1981 in English and held by 373 WorldCat member libraries worldwide

Geometry has been defined as that part of mathematics which makes appeal to the sense of sight; but this definition is thrown in doubt by the existence of great geometers who were blind or nearly so, such as Leonhard Euler. Sometimes it seems that geometric methods in analysis, so-called, consist in having recourse to notions outside those apparently relevant, so that geometry must be the joining of unlike strands; but then what shall we say of the importance of axiomatic programmes in geometry, where reference to notions outside a restricted reper tory is banned? Whatever its definition, geometry clearly has been more than the sum of its results, more than the consequences of some few axiom sets. It has been a major current in mathematics, with a distinctive approach and a distinc ti v e spirit. A current, furthermore, which has not been constant. In the 1930s, after a period of pervasive prominence, it appeared to be in decline, even passe. These same years were those in which H.S.M. Coxeter was beginning his scientific work. Undeterred by the unfashionability of geometry, Coxeter pursued it with devotion and inspiration. By the 1950s he appeared to the broader mathematical world as a consummate practitioner of a peculiar, out-of-the-way art. Today there is no longer anything that out-of-the-way about it. Coxeter has contributed to, exemplified, we could almost say presided over an unanticipated and dra matic revival of geometry
The fantastic world of M.C. Escher by Michele Emmer( Visual )

2 editions published between 1994 and 2006 in English and held by 319 WorldCat member libraries worldwide

A tribute to the artist M.C. Escher. Described as the master of impossible objects - possible to conceive, but impossible to convey in 3-dimensional space, Escher used light, geometry and higher mathematics to instruct and to entertain. His art has been hailed as the meeting of science and imagination
Kaleidoscopes : selected writings of H.S.M. Coxeter by H. S. M Coxeter( Book )

9 editions published in 1995 in English and held by 213 WorldCat member libraries worldwide

The Coxeter legacy : reflections and projections( Book )

7 editions published between 2005 and 2006 in English and held by 201 WorldCat member libraries worldwide

This collection of essays on the legacy of mathematician Donald Coxeter is a mixture of surveys, updates, history, storytelling and personal memories covering both applied and abstract maths. Subjects include: polytopes, Coxeter groups, equivelar polyhedra, Ceva's theorum, and Coxeter and the artists
Geometry revisited by H. S. M Coxeter( )

2 editions published between 1996 and 2014 in English and held by 7 WorldCat member libraries worldwide

Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed
moreShow More Titles
fewerShow Fewer Titles
Audience Level
Audience Level
  Kids General Special  
Audience level: 0.39 (from 0.09 for Geometry r ... to 1.00 for Dedicated ...)

Introduction to geometry
Geometry revisitedIntroduction to geometryMathematical recreations & essaysProjective geometryThe real projective planeRegular polytopesRegular complex polytopesThe fifty-nine icosahedra
Alternative Names
Coexter, Harold Scott Macdonald

Coxeter, Donald

Coxeter, Donald 1907-2003

Coxeter, H.S.

Coxeter H.S.M.

Coxeter, H. S. M. 1907-2003

Coxeter, H. S. M. (Harold Scott Macdonald), 1907-

Coxeter, Harold S. 1907-2003

Coxeter, Harold S. M.

Coxeter, Harold Scott Macdonald.

Coxeter, Harold Scott Macdonald 1907-

Coxeter, Harold Scott Macdonald 1907-2003

Coxeter-Moser, .. 1907-2003

Donald Coxeter Brits wiskundige (1907-2003)

H.S.M. Coxeter

H.S.M. Coxeter brittisk-kanadensisk matematiker

Harold Coxeter matematico inglese

Harold Scott MacDonald Coxeter britisch-kanadischer Mathematiker

Harold Scott MacDonald Coxeter matemàtic canadenc

Harold Scott MacDonald Coxeter matematician canadian

Harold Scott MacDonald Coxeter matemático canadense

Harold Scott MacDonald Coxeter matemático canadiense

Harold Scott MacDonald Coxeter matematikan kanadez

Harold Scott MacDonald Coxeter mathématicien canadien

Kokseter, G.

Kokseter, G. 1907-2003

Kokseter, G. S. M.

Kokseter, G.S.M. 1907-2003

Kokseter, G. S. Makdonal'd.

Kokseter, G. S. Makdonal'd 1907-2003

Kokster, Ch. S. M. 1907-2003

Kokster, G. S. M.

Kokster, H. S. M.

Macdonald Coxeter, Harold Scott 1907-2003

Гарольд Коксетер

Коксетер Г.С.М.

Коксетер, Гарольд

Коксетер, Гарольд С. М..

Коксетер, Гарольд Скотт Макдональд

Кокстер, Г. С. М 1907-2003

Кокстер, Г. С. М. (Гарольд Скотт Макдональд), 1907-2003

Кокстер Х.С.М.

Кокстер, Х. С. М 1907-2003

Кокстер, Х. С. М. (Х. Скотт Макдональд), 1907-2003

Հարոլդ Քոքսեթեր

הרולד סקוט מקדונלד קוקסטר

הרולד סקוט מקדונלד קוקסטר מתמטיקאי קנדי

سكوت ماكدونالد كوكستر

سكوت ماكدونالد كوكستر رياضياتي كندي

해럴드 스콧 맥도널드 콕서터

コークスター, H