Coxeter, H. S. M. (Harold Scott Macdonald) 19072003
Overview
Works:  123 works in 1,010 publications in 10 languages and 20,769 library holdings 

Genres:  Puzzles and games Biography Conference papers and proceedings Criticism, interpretation, etc Art Documentary films History 
Roles:  Author, Editor, Honoree, Author of introduction, Dedicatee, Contributor, Publishing director, Other 
Classifications:  QA95, 513 
Publication Timeline
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Most widely held works about
H. S. M Coxeter
 King of infinite space : Donald Coxeter, the man who saved geometry by Siobhan Roberts( Book )
 The Coxeter legacy : reflections and projections( Book )
 Tamentai to uchū no nazo ni sematta kikagakusha by Siobhan Roberts( Book )
 Coxeter, Harold Scott Macdonald : Mathematics( )
 Martin Gardner papers by Martin Gardner( )
 Vandiver, H.S., Papers by Harry Schultz Vandiver( )
 Math and aftermath : a tribute to H.S.M. (Donald) Coxeter( Recording )
 Solid progress : how five regular solids turned into seventyfive by H. Stephen Morse( Recording )
 Dedicated to H.S.M. Coxeter, cofounder of this journal( Book )
more
fewer
Most widely held works by
H. S. M Coxeter
NonEuclidean geometry by
H. S. M Coxeter(
Book
)
94 editions published between 1941 and 2017 in English and Undetermined and held by 2,940 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, nonEuclidean 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
94 editions published between 1941 and 2017 in English and Undetermined and held by 2,940 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, nonEuclidean 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(
)
51 editions published between 1967 and 2014 in English and Undetermined and held by 2,669 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
51 editions published between 1967 and 2014 in English and Undetermined and held by 2,669 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
)
111 editions published between 1961 and 1994 in 7 languages and held by 2,312 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 selfcontained 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 4color map problem, and provides answers to most of the exercises
111 editions published between 1961 and 1994 in 7 languages and held by 2,312 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 selfcontained 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 4color map problem, and provides answers to most of the exercises
Generators and relations for discrete groups by
H. S. M Coxeter(
Book
)
79 editions published between 1957 and 2017 in 5 languages and held by 1,452 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 es), the reader cannot do better than consult the tables of JosEPHINE BuRNS (1915), while keeping an eye open for misprints. Our own tables (on pages 134142) deal with groups of low order, finite and infinite 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 for a more extensive 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
79 editions published between 1957 and 2017 in 5 languages and held by 1,452 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 es), the reader cannot do better than consult the tables of JosEPHINE BuRNS (1915), while keeping an eye open for misprints. Our own tables (on pages 134142) deal with groups of low order, finite and infinite 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 for a more extensive 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
Mathematical recreations & essays by
W. W. Rouse Ball(
Book
)
69 editions published between 1939 and 2015 in English and Russian and held by 1,420 WorldCat member libraries worldwide
This classic work offers scores of stimulating, mindexpanding games and puzzles: arithmetical and geometrical problems, chessboard recreations, magic squares, mapcoloring problems, cryptography and cryptanalysis, much more
69 editions published between 1939 and 2015 in English and Russian and held by 1,420 WorldCat member libraries worldwide
This classic work offers scores of stimulating, mindexpanding games and puzzles: arithmetical and geometrical problems, chessboard recreations, magic squares, mapcoloring problems, cryptography and cryptanalysis, much more
The real projective plane by
H. S. M Coxeter(
Book
)
93 editions published between 1949 and 1993 in 4 languages and held by 1,339 WorldCat member libraries worldwide
Contain: Files, scenes, narrations, and projectivities for Mathematica
93 editions published between 1949 and 1993 in 4 languages and held by 1,339 WorldCat member libraries worldwide
Contain: Files, scenes, narrations, and projectivities for Mathematica
Projective geometry by
H. S. M Coxeter(
Book
)
62 editions published between 1946 and 2003 in 4 languages and held by 1,322 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 selfcontained 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
62 editions published between 1946 and 2003 in 4 languages and held by 1,322 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 selfcontained 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
Regular polytopes by
H. S. M Coxeter(
Book
)
48 editions published between 1947 and 2013 in English and Undetermined and held by 1,232 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 wellknown authority on them. Professor Coxeter begins with the fundamental concepts of plane and solid geometry and then moves on to multidimensionality. Among the many subjects covered are Euler's formula, rotation groups, starpolyhedra, truncation, forms, vectors, coordinates, kaleidoscopes, Petrie polygons, sections and projections, and starpolytopes. 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
48 editions published between 1947 and 2013 in English and Undetermined and held by 1,232 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 wellknown authority on them. Professor Coxeter begins with the fundamental concepts of plane and solid geometry and then moves on to multidimensionality. Among the many subjects covered are Euler's formula, rotation groups, starpolyhedra, truncation, forms, vectors, coordinates, kaleidoscopes, Petrie polygons, sections and projections, and starpolytopes. 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
Regular complex polytopes by
H. S. M Coxeter(
Book
)
32 editions published between 1973 and 1991 in English and Undetermined and held by 842 WorldCat member libraries worldwide
32 editions published between 1973 and 1991 in English and Undetermined and held by 842 WorldCat member libraries worldwide
M.C. Escher, art and science : proceedings of the International Congress on M.C. Escher, Rome, Italy, 2628 March 1985 by
H. S. M Coxeter(
Book
)
44 editions published between 1985 and 1988 in English and French and held by 683 WorldCat member libraries worldwide
44 editions published between 1985 and 1988 in English and French and held by 683 WorldCat member libraries worldwide
The fiftynine icosahedra by
H. S. M Coxeter(
Book
)
35 editions published between 1938 and 2011 in English and German 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
35 editions published between 1938 and 2011 in English and German 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
)
13 editions published in 1968 in English and Undetermined and held by 450 WorldCat member libraries worldwide
13 editions published in 1968 in English and Undetermined and held by 450 WorldCat member libraries worldwide
Twisted honeycombs by
H. S. M Coxeter(
Book
)
21 editions published between 1970 and 2009 in English and Undetermined and held by 396 WorldCat member libraries worldwide
21 editions published between 1970 and 2009 in English and Undetermined and held by 396 WorldCat member libraries worldwide
Zerosymmetric graphs : trivalent graphical regular representations of groups by
H. S. M Coxeter(
Book
)
17 editions published in 1981 in English and Undetermined and held by 380 WorldCat member libraries worldwide
17 editions published in 1981 in English and Undetermined and held by 380 WorldCat member libraries worldwide
The Geometric vein : the Coxeter festschrift by
Chandler Davis(
Book
)
10 editions published between 1981 and 1982 in English and held by 377 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, socalled, 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, outoftheway art. Today there is no longer anything that outoftheway about it. Coxeter has contributed to, exemplified, we could almost say presided over an unanticipated and dra matic revival of geometry
10 editions published between 1981 and 1982 in English and held by 377 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, socalled, 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, outoftheway art. Today there is no longer anything that outoftheway 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 326 WorldCat member libraries worldwide
Through colleagues' accounts and computer animated recreations of his work, this documentary explores the genius of the Dutch graphic artist. Learn about the man behind the intricate and mysterious designs and his sources of inspiration for them
2 editions published between 1994 and 2006 in English and held by 326 WorldCat member libraries worldwide
Through colleagues' accounts and computer animated recreations of his work, this documentary explores the genius of the Dutch graphic artist. Learn about the man behind the intricate and mysterious designs and his sources of inspiration for them
Kaleidoscopes : selected writings of H.S.M. Coxeter by
H. S. M Coxeter(
Book
)
9 editions published in 1995 in English and held by 215 WorldCat member libraries worldwide
9 editions published in 1995 in English and held by 215 WorldCat member libraries worldwide
The Coxeter legacy : reflections and projections(
Book
)
7 editions published between 2005 and 2006 in English and held by 203 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
7 editions published between 2005 and 2006 in English and held by 203 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
The beauty of geometry : twelve essays by
H. S. M Coxeter(
Book
)
12 editions published in 1999 in English and held by 144 WorldCat member libraries worldwide
12 editions published in 1999 in English and held by 144 WorldCat member libraries worldwide
Redécouvrons la géométrie by
H. S. M Coxeter(
Book
)
14 editions published between 1971 and 1997 in French and held by 105 WorldCat member libraries worldwide
14 editions published between 1971 and 1997 in French and held by 105 WorldCat member libraries worldwide
more
fewer
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Related Identities
 Greitzer, Samuel L.
 Moser, W. O. J.
 Ball, W. W. Rouse (Walter William Rouse) 18501925 Author
 Escher, M. C. (Maurits Cornelis) 18981972 Illustrator Honoree
 Roberts, Siobhan Author
 Davis, Chandler Editor
 Sherk, F. A. Other Editor
 Powers, David L. Other Author
 Frucht, Roberto
 Grünbaum, Branko Editor
Useful Links
Associated Subjects
Algebra Art and science Art and science Art in motion pictures Artists Astrology Bees Canada Ciphers Combinatorial analysis Coxeter, H. S. M.(Harold Scott Macdonald), Coxeter groups Cryptography Discrete groups Escher, M. C.(Maurits Cornelis), Geometry Geometry, Algebraic Geometry, Analytic Geometry, Descriptive Geometry, Modern Geometry, NonEuclidean Geometry, Projective Geometry, ProjectiveData processing GeometryFamous problems Geometry in art Graphic arts Graph theory Group theory Group theoryGenerators Group theoryRelations Hyperspace Icosahedra Infinite groups Italy Lefschetz, Solomon, Magic squares Mathematical recreations Mathematicians Mathematics Matter Netherlands Polyhedra Polytopes Printmakers Representations of groups Space and time Spain String figures Symmetry Themes, motives
Covers
Alternative Names
Coexter, Harold Scott Macdonald
Coxeter, Donald
Coxeter, Donald 19072003
Coxeter, H.S.
Coxeter, H. S. M.
Coxeter, H. S. M. 19072003
Coxeter, H. S. M. (Harold Scott Macdonald), 1907
Coxeter, Harold S. 19072003
Coxeter, Harold S. M.
Coxeter, Harold Scott Macdonald
Coxeter, Harold Scott Macdonald 1907
Coxeter, Harold Scott Macdonald 19072003
CoxeterMoser, .. 19072003
Donald Coxeter Brits wiskundige (19072003)
H.S.M. Coxeter
Harold Coxeter matematico inglese
Harold Scott MacDonald Coxeter britischkanadischer Mathematiker
Harold Scott MacDonald Coxeter matematician canadian
Harold Scott MacDonald Coxeter matemático canadense
Harold Scott MacDonald Coxeter matemático canadiense
Harold Scott MacDonald Coxeter mathématicien canadien
Kokseter, G.
Kokseter, G. 19072003
Kokseter, G. S. M.
Kokseter, G.S.M. 19072003
Kokseter, G. S. Makdonal'd.
Kokseter, G. S. Makdonal'd 19072003
Kokster, Ch. S. M. 19072003
Kokster, G. S. M.
Kokster, H. S. M.
Macdonald Coxeter, Harold Scott 19072003
Гарольд Коксетер
Коксетер, Гарольд
Коксетер, Гарольд С. М..
Кокстер, Г. С. М 19072003
Кокстер, Г. С. М. (Гарольд Скотт Макдональд), 19072003
Кокстер, Х. С. М..
Кокстер, Х. С. М 19072003
Кокстер, Х. С. М. (Х. Скотт Макдональд), 19072003
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
コクセター
ハロルド・スコット・マクドナルド・コクセター
哈罗德·斯科特·麦克唐纳·考克斯特
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