Coxeter, H. S. M. - Search - Anna’s Archive

lgli/M_Mathematics/MSch_School-level/Coxeter H.S.M., Greitzer S.L. Geometry revisited (AMS, 1967)(K)(T)(199s).djvu

Geometry revisited H. S. M. Coxeter, Samuel L. Greitzer The Mathematical Association of America, New Mathematical Library 19, 1967

English [en] · DJVU · 1.6MB · 1967 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

lgli/Coxeter, H. S. M. - Regular Polytopes (Dover Books on Mathematics) (2012, Dover Publications).pdf

Regular Polytopes (Dover Books on Mathematics) Coxeter, H. S. M. Dover Publications : Made available through hoopla, 3rd, 2012

Foremost book available on polytopes, incorporating ancient Greek and most modern work. Discusses polygons, polyhedrons, and multi-dimensional polytopes. Definitions of symbols. Includes 8 tables plus many diagrams and examples. 1963 edition.

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Geometry Revisited COXETER, H. S. M. & GREITZER, S. L. The Mathematical Association of America, First, 1967

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ia/projectivegeomet0000unse_m6n2.pdf

Projective geometry H. S. M Coxeter New York, Blaisdell Pub. Co, Blaisdell book in the pure and applied sciences, 1st ed, New York, 1964

162 p. 24 cm Bibliography: p. 158

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ia/noneuclideangeom0000coxe_y5w0.pdf

Non-Euclidean geometry H. S. M. Coxeter [Toronto] University Press, Mathematical expositions -- no. 2, 4th ed., Toronto, Canada, 1961

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.

English [en] · PDF · 10.3MB · 1961 · 📗 Book (unknown) · 🚀/ia · Save

ia/noneuclideangeom0000coxe_l6f0.pdf

Non-Euclidean geometry H. S. M. Coxeter Toronto: University of Toronto Press, Mathematical expositions, no 2, 4th ed, Toronto, Ontario, 1961

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.

English [en] · PDF · 10.8MB · 1961 · 📗 Book (unknown) · 🚀/ia · Save

ia/kaleidoscopessel0000coxe.pdf

Kaleidoscopes: Selected Writings of H.S.M. Coxeter (Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts) Coxeter, H. S. M. (Harold Scott Macdonald), 1907-, Sherk, F. A; Canadian Mathematical Society New York : Wiley & Sons, Canadian Mathematical Society series of monographs and advanced texts = Monographies et études de la Société mathématique du Canada, New York, ©1995

xxx, 439 p. : 26 cm, \"A Wiley-Interscience publication.\", \"Published in conjunction with the 50th anniversary of the Canadian Mathematical Society.\", Includes bibliographical references and index, 96 09 04

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ia/generatorsrelati0002edcoxe_d6n2.pdf

Generators and relations for discrete groups [by] H.S.M. Coxeter and W.O.J. Moser Berlin ; New York: Springer-Verlag, Ergebnisse der Mathematik und ihrer Grenzgebiete,, n.F., Bd. 14., Reihe: Gruppentheorie, Ergebnisse der Mathematik und ihrer Grenzgebiete ;, n.F., Bd. 14., Ergebnisse der Mathematik und ihrer Grenzgebiete., 2d ed., Berlin, New York, West Berlin, 1965

ix, 161 pages : 24 cm Bibliography: p. 143-156

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ia/renaissancebanff0000brid.pdf

Renaissance Banff (bridges: Mathematical Connections In Art, Music, Science) Procedings 2005 Reza Sarhangi and Robert V. Moody, editors Canadian Mathematical Society, The Banff Centre, Pims, [Phoenix, Ariz.], Arizona, 2005

xiv, 539 p. : 28 cm The four-day conference consists of two parts: a three-day Bridges Conference and a final day, set aside for geometry-arts connections that are either related to or inspired by the life and work of H.S.M. (Donald) Coxeter "Canadian Mathematical Society, the Banff Centre, Pacific Institute for the Mathematical Sciences"--Cover Includes bibliographical references and author index

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ia/geometricveincox0000unse.pdf

The Geometric Vein : The Coxeter Festschrift H. S. M. Coxeter, Chandler Davis, Branko Grünbaum, F. Arthur Sherk New York: Springer-Verlag, Springer Nature, New York, NY, 2012

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.

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ia/fiftynineicosahe0000unse.pdf

The Fifty-Nine Icosahedra (Lecture Notes in Statistics) H. S. M. Coxeter; P. DuVal; H. T. Flather; J. F. Petrie Springer New York, Springer Nature, New York, NY, 2012

The Fifty-Nine Icosahedra was originally published in 1938 as No. 6 of "University of Toronto Studies (Mathematical Series)". Of the four authors, only Coxeter and myself are still alive, and we two are the authors of the whole text of the book, in which any signs of immaturity may perhaps be regarded leniently on noting that both of us were still in our twenties when it was written. N either of the others was a professional mathematician. Flather died about 1950, and Petrie, tragically, in a road accident in 1972. Petrie's part in the book consisted in the extremely difficult drawings which consti tute the left half of each of the plates (the much simpler ones on the right being mine). A brief biographical note on Petrie will be found on p. 32 of Coxeter's Regular Polytopes (3rd. ed. , Dover, New York, 1973); and it may be added that he was still a schoolboy when he discovered the regular skew polygons that are named after him, and are the occasion for the note on him in Coxeter's book. (Coxeter also was a schoolboy when some of the results for which he will be most remembered were obtained; he and Petrie were schoolboy friends and used to work together on polyhedron and polytope theory. ) Flather's part in the book consisted in making a very beautiful set of miniature models of all the fifty-nine figures. These are still in existence, and in excellent preservation. Erscheinungsdatum: 04.11.1982

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ia/kingofinfinitesp00robe.pdf

King of infinite space : Donald Coxeter, the man who saved geometry Siobhan Roberts Walker & Company, First U.S. Edition, New York, USA, September 19, 2006

"There is perhaps no better way to prepare for the scientific breakthroughs of tomorrow than to learn the language of geometry." Brian Greene, author of The Elegant Universe The word "geometry" brings to mind an array of mathematical circles, triangles, the Pythagorean Theorem. Yet geometry is so much more than shapes and numbers; indeed, it governs much of our livesfrom architecture and microchips to car design, animated movies, the molecules of food, even our own body chemistry. And as Siobhan Roberts elegantly conveys in The King of Infinite Space , there can be no better guide to the majesty of geometry than Donald Coxeter, perhaps the greatest geometer of the twentieth century. Many of the greatest names in intellectual historyPythagoras, Plato, Archimedes, Euclid were geometers, and their creativity and achievements illuminate those of Coxeter, revealing geometry to be a living, ever-evolving endeavor, an intellectual adventure that has always been a building block of civilization. Coxeter's special contributionshis famed Coxeter groups and Coxeter diagramshave been called by other mathematicians "tools as essential as numbers themselves," but his greatest achievement was to almost single-handedly preserve the tradition of classical geometry when it was under attack in a mathematical era that valued all things austere and rational. Coxeter also inspired many outside the field of mathematics. Artist M. C. Escher credited Coxeter with triggering his legendary Circle Limit patterns, while futurist/inventor Buckminster Fuller acknowledged that his famed geodesic dome owed much to Coxeter's vision. The King of Infinite Space is an elegant portal into the fascinating, arcane world of geometry.

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nexusstc/Non-Euclidean Geometry/2d2adbfab67a7829c104cff3057189af.pdf

Non-Euclidean Geometry (Mathematical Association of America Textbooks) Harold Scott Macdonald Coxeter The Mathematical Association of America, Mathematical Association of America Textbooks, 6, 1998

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.

English [en] · PDF · 10.7MB · 1998 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

ia/noneuclideangeom0000coxe_w2k5.pdf

Non-Euclidean Geometry (Mathematical Association of America Textbooks) Harold Scott Macdonald Coxeter The Mathematical Association of America, American Mathematical Society, Washington, D.C., 1998

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 collineations. They lead in a natural way to 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 in elliptic or hyperbolic polarity which transforms points into lines (in two dimensions), planes (in three dimensions), and vice versa. An unusual feature of the book is its use of the general linear transformation of coordinates to derive the formulas of elliptic and hyperbolic trigonometry. The area of a triangle is related to the sum of its angles by means of an ingenious idea of Gauss. This treatment can be enjoyed by anyone who is familiar with algebra up to the elements of group theory. The present (sixth) edition clarifies some obscurities in the fifth, and includes a new section 15.9 on the author's useful concept of inversive distance.

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ia/beautyofgeometry0000coxe.pdf

The Beauty of Geometry: Twelve Essays (Dover Books on Mathematics) H. S. M. Coxeter; Harold Scott Macdonald Coxeter Dover Publications, Incorporated, Dover books on mathematics, Dover ed, Mineola, NY, 1999

These absorbing essays by a distinguished mathematician provide a compelling demonstration of the charms of mathematics. Stimulating and thought-provoking, this collection is sure to interest students, mathematicians, and any math buff with its lucid treatment of geometry and the crucial role geometry plays in a wide range of mathematical applications.

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lgli/M_Mathematics/MD_Geometry and topology/Coxeter H.S.M. Non-Euclidean geometry (6ed., 1998)(T)(ISBN 0883855224)(349s).djvu

Non-Euclidean Geometry (Mathematical Association of America Textbooks) Harold Scott Macdonald Coxeter The Mathematical Association of America, Spectrum series, MAA spectrum., 6th ed., Washington, D.C, District of Columbia, 1998

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.

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lgli/M_Mathematics/MD_Geometry and topology/Coxeter H.S.M. Regular Complex Polytopes (2ed., CUP, 1991)(ISBN 0521394902)(T)(224s)_MD_.djvu

Regular Complex Polytopes Harold Scott Macdonald Coxeter Cambridge University Press (Virtual Publishing), 2nd ed., Cambridge [England], New York, England, 1991

The properties of polytopes, the four-dimensional analog of polyhedra, exercise an intellectual fascination that appeals strongly to the mathematically inclined, whether they are professionals, students or amateurs. In this classic book, Professor Coxeter explores these properties in easy stages introducing the reader to complex polytopes (a beautiful generalization of regular solids derived from complex numbers) and the unexpected relationships that complex polytopes have with concepts from various branches of mathematics. In the first half of the book the author discusses magic squares, frieze patterns, kaleidoscopes, Cayley diagrams, Clifford surfaces, non-crystallographic groups, kinematics, spherical trigonometry, and algebraic geometry. Later these ideas are assembled to describe a natural generalization of the Five Platonic Solids. The fully updated second edition contains a new chapter on "Almost Regular Polytopes" and beautiful abstract art drawings. In addition, new exercises and discussions, including an introduction to Hopf fibration and real representations for two complex polyhedra, supplement the text.

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ia/generatorsrelati0000coxe.pdf

Generators and Relations for Discrete Groups (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge) Harold S.M. Coxeter; W.O.J. Moser Springer Berlin Heidelberg : Imprint : Springer, Springer Nature, Berlin, Heidelberg, 2013

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 restrietions are necessary, because interesting groups are so numerous. For permutation groups of degree 8 or less (i.e.,.subgroups of 2:), the reader cannot do better than consult the 8 tables of ]OSEPHINE BURNS (1915), while keeping an eye open for misprints. Our own tables (on pages 134-142) deal with groups of low order, finite and infinite groups ()f congruent transformations, symmetrie 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.

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ia/journeyintogeome0000sved.pdf

Journey into Geometries (Spectrum) Marta Sved; with foreword by H.S.M. Coxeter; illustrations by John Stillwell The Mathematical Association of America, Spectrum series, MAA spectrum., Washington, D.C, District of Columbia, 1991

This unique book gives an informal introduction into the non-Euclidean geometries through a series of dialogues between a somewhat grown-up Alice (of Looking Glass fame), her uncle Lewis Carroll, and a visitor from the twentieth century, Dr Whatif. In the story, Lewis Carroll's geometrical beliefs are cast into the Euclidean mould, Dr Whatif asks the penetrating and controversial questions, and Alice acts as a mediator and interested participant. The book is intentionally more mathematical than Lewis Carroll's books, but for those of us who enjoyed Alice's earlier adventures there are many interesting flashbacks to those inimitable the Red Queen, Tweedle-Dum and his twin brother, the Mad Hatter The text is filled with humour, wit, and verses of poetry. Part 1 contains the story in six chapters, each of which concludes with a problem set; Part 2 is more mathematical, and looks at the axiom systems, and gives solutions to the problems. The presentation, with its old-time borders, script headings, and cartoon drawings evokes the spirit of the original Alice.

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nexusstc/Journey into geometries/49c30a9b352c0cd4bcd42dcb2b7d7ac9.djvu

Journey into Geometries (Spectrum) Marta Sved, H. S. M. Coxeter, John Stillwell The Mathematical Association of America, Spectrum series, 1997

This charming book introduces us to topics in hyperbolic geometry in a delightfully informal style. Journey into Geometrics can be read at two levels. It can be studied as an informal introduction to post-Euclidean geometry, or it can serve as background material for university students. The material presented in the text is extended by carefully selected problems. The background required is minimal, standard high school geometry, yet the serious student, aided by problems attached to each chapter, should acquire a deeper understanding of the subject.

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ia/geometryrevisite0000coxe.pdf

Geometry Revisited H. S. M. Coxeter, Samuel L. Greitzer [New York]: Random House, New Mathematical library -- 19, New York, USA, District of Columbia, 1967

xiv, 193 p. : 23 cm Bibliography: p. 181-182

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ia/realprojectivepl0000coxe.pdf

The real projective plane H. S. M. Coxeter Cambridge [Eng.]: Cambridge University Press, 2d ed., Cambridge [Eng.], England, 1960

This introduction to projective geometry can be understood by anyone familiar with high-school geometry and algebra. The restriction to real geometry of two dimensions allows every theorem to be illustrated by a diagram. The subject is, in a sense, even simpler than Euclid, whose constructions involved a ruler and compass: here we have constructions using rulers alone. A strict axiomatic treatment is followed only to the point of letting the student see how it is done, but then relaxed to avoid becoming tedious. After two introductory chapters, the concept of continuity is introduced by means of an unusual but intuitively acceptable axiom. Subsequent chapters then treat one- and two-dimensional projectivities, conics, affine geometry, and Euclidean geometry. Chapter 10 continues the discussion of continuity at a more sophisticated level, and the remaining chapters introduce coordinates and their uses. An appendix by George Beck describes Mathematica scripts that can generate illustrations for several chapters; they are provided on a diskette included with the book. (Both PC and Macintosh versions are available) Mathematica is a registered trademark.

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ia/noneuclideangeom0000coxe.pdf

Non-Euclidean geometry by H. S. M. Coxeter .. The Unviversity of Toronto press, Mathematical expositions -- no. 2., 5th ed., [Toronto, Can.], Ontario, 1965

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.

English [en] · PDF · 11.1MB · 1965 · 📗 Book (unknown) · 🚀/ia · Save

lgli/R:\062020\springer2\10.1007%2F978-1-4613-8216-4.pdf

The Fifty-Nine Icosahedra (Lecture Notes in Statistics) H. S. M. Coxeter, P. Du Val, H. T. Flather, J. F. Petrie (auth.) Springer-Verlag New York, Lecture Notes in Statistics, 1, 1982

The Fifty-Nine Icosahedra was originally published in 1938 as No. 6 of "University of Toronto Studies (Mathematical Series)". Of the four authors, only Coxeter and myself are still alive, and we two are the authors of the whole text of the book, in which any signs of immaturity may perhaps be regarded leniently on noting that both of us were still in our twenties when it was written. N either of the others was a professional mathematician. Flather died about 1950, and Petrie, tragically, in a road accident in 1972. Petrie's part in the book consisted in the extremely difficult drawings which consti tute the left half of each of the plates (the much simpler ones on the right being mine). A brief biographical note on Petrie will be found on p. 32 of Coxeter's Regular Polytopes (3rd. ed. , Dover, New York, 1973); and it may be added that he was still a schoolboy when he discovered the regular skew polygons that are named after him, and are the occasion for the note on him in Coxeter's book. (Coxeter also was a schoolboy when some of the results for which he will be most remembered were obtained; he and Petrie were schoolboy friends and used to work together on polyhedron and polytope theory. ) Flather's part in the book consisted in making a very beautiful set of miniature models of all the fifty-nine figures. These are still in existence, and in excellent preservation. Erscheinungsdatum: 04.11.1982

English [en] · PDF · 1.8MB · 1982 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

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nexusstc/Twisted Honeycombs/c3db902012e222a5a6ee09be9b6de9bc.pdf

Twisted Honeycombs (CBMS regional conference series in mathematics) H S M Coxeter; Conference Board of the Mathematical Sciences Published For The Conference Board Of The Mathematical Sciences By The American Mathematical Society, Conference Board on the Mathematical Sciences Regional Conference Series in Mathematics 4, 1970

By H. S. M. Coxeter. Bibliography: P. 47.

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lgli/A:/compressed/10.1007%2F978-1-4613-8216-4.pdf

The Fifty-Nine Icosahedra (Lecture Notes in Statistics) H. S. M. Coxeter, P. Du Val, H. T. Flather, J. F. Petrie (auth.) Springer-Verlag New York, Lecture Notes in Statistics, 1, 1982

The Fifty-Nine Icosahedra was originally published in 1938 as No. 6 of "University of Toronto Studies (Mathematical Series)". Of the four authors, only Coxeter and myself are still alive, and we two are the authors of the whole text of the book, in which any signs of immaturity may perhaps be regarded leniently on noting that both of us were still in our twenties when it was written. N either of the others was a professional mathematician. Flather died about 1950, and Petrie, tragically, in a road accident in 1972. Petrie's part in the book consisted in the extremely difficult drawings which consti tute the left half of each of the plates (the much simpler ones on the right being mine). A brief biographical note on Petrie will be found on p. 32 of Coxeter's Regular Polytopes (3rd. ed. , Dover, New York, 1973); and it may be added that he was still a schoolboy when he discovered the regular skew polygons that are named after him, and are the occasion for the note on him in Coxeter's book. (Coxeter also was a schoolboy when some of the results for which he will be most remembered were obtained; he and Petrie were schoolboy friends and used to work together on polyhedron and polytope theory. ) Flather's part in the book consisted in making a very beautiful set of miniature models of all the fifty-nine figures. These are still in existence, and in excellent preservation. Erscheinungsdatum: 04.11.1982

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upload/newsarch_ebooks/2019/04/29/0387965327_Projective.djvu

Projective Geometry, Second Edition Harold Scott Macdonald Coxeter Springer-verlag, New York, 2, 2003

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.

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ia/projectivegeomet0000coxe.pdf

Projective geometry [by] H.S.M. Coxeter New York, Blaisdell Pub. Co, A Blaisdell book in the pure and applied sciences, [1st ed.]., New York, USA, New York State, 1964

162 p. 24 cm Bibliography: p. 158

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lgli/D:\!Genesis\!!ForLG\2391505-Наследие Г.С.М.Кокстера (книги и статьи)\TheProductOfGenerators_ofFiniteGr_1951.pdf

The Product Of Generators of Finite Generations by reflections Coxeter, H. S. M. Duke University Press (ISSN 0012-7094), Duke Mathematical Journal, #4, 18, pages 765-782, 1951 dec

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ia/mathematicalrecr0000ball_n1p5.pdf

Mathematical Recreations & Essays : Twelfth Edition by W. W. Rouse Ball and H. S. M. Coxeter Toronto ; Buffalo: University of Toronto Press, University of Toronto Press, Toronto, 1974

For over eighty years this delightful classic has provided entertainment through mathematical problems commonly known as recreations. Although they often involve fundamental mathematical methods and notions, their chief appeal is as games or puzzles rather than the usefulness of their conclusions. This new edition upholds the original, but the terminology and treatment of problems have been updated and much new material has been added. There are new selections on polyominoes and the notion of dragon designs, and a new chapter, ‘Introduction to Combinatorics.'Other topics dealt with in the fourteen chapters include arithmetical and geometrical recreations and problems, polyhedra, chess-board recreations, unicursal problems, cryptography and cryptanalysis, and calculating prodigies. Since no knowledge of calculus or analytic geometry is necessary to enjoy the recreations, this book will appeal widely to teachers of mathematics and students and to anyone who is mathematically inclined.

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nexusstc/Projective Geometry/fd40ecd1d8c409d83bfa069ac8c33c27.pdf

Projective Geometry, 2nd Edition Harold Scott Macdonald Coxeter Springer-verlag, New York, Second, 2003

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. Erscheinungsdatum: 09.10.2003

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ia/zerosymmetricgra0000coxe.pdf

Zero-Symmetric Graphs : Trivalent Graphical Regular Representations of Groups H. S. M. Coxeter; Roberto Frucht; David L. Powers Academic Press, Incorporated, Elsevier Ltd., New York, 1981

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 explore Cayley graphs of specific groups, including the parameters of Cayley graphs of groups. This book will prove useful to mathematicians, computer scientists, and researchers.

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lgli/G:\!genesis\_add\!woodhead\!\elsevier\9780121945800.pdf

Zero-Symmetric Graphs : Trivalent Graphical Regular Representations of Groups H. S. M. Coxeter, Roberto Frucht, David L. Powers Academic Press, Incorporated, Elsevier Ltd., New York, 1981

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 explore Cayley graphs of specific groups, including the parameters of Cayley graphs of groups. This book will prove useful to mathematicians, computer scientists, and researchers.

English [en] · PDF · 11.4MB · 1981 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/zlib · Save

scihub/10.1007/978-1-4612-2734-2.pdf

The Real Projective Plane: With an Appendix for Mathematica® by George Beck Macintosh Version H. S. M. Coxeter, George Beck (auth.) Springer New York : Imprint: Springer, 10.1007/97, 1993

Along with many small improvements, this revised edition contains van Yzeren's new proof of Pascal's theorem (§1.7) and, in Chapter 2, an improved treatment of order and sense. The Sylvester-Gallai theorem, instead of being introduced as a curiosity, is now used as an essential step in the theory of harmonic separation (§3.34). This makes the logi cal development self-contained: the footnotes involving the References (pp. 214-216) are for comparison with earlier treatments, and to give credit where it is due, not to fill gaps in the argument. H.S.M.C. November 1992 v Preface to the Second Edition Why should one study the real plane? To this question, put by those who advocate the complex plane, or geometry over a general field, I would reply that the real plane is an easy first step. Most of the prop erties are closely analogous, and the real field has the advantage of intuitive accessibility. Moreover, real geometry is exactly what is needed for the projective approach to non· Euclidean geometry. Instead of introducing the affine and Euclidean metrics as in Chapters 8 and 9, we could just as well take the locus of 'points at infinity' to be a conic, or replace the absolute involution by an absolute polarity.

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lgli/M_Mathematics/MD_Geometry and topology/Coxeter, Du Val, Flather, Petrie. The fifty-nine icosahedra (Toronto, 1938)(ISBN 1899618325)(T)(46s)_MD_.djvu

The Fifty-Nine Icosahedra H. S. M. Coxeter, P. Du Val, H. T. Flather, J. F. Petrie, P. DuVal The University of Toronto Press, University of Toronto Studies: Mathematical Series 6, Reprint of 1938 edition, 1951

This is a completely new edition of the classic book which has been out of print for many years. The plans and illustrations of all 59 of the stellations of the icosahedron have been redrawn by Kate and David Krennell and there is a new introduction by Professor Coxeter. For a thorough understanding of the process of stellation and for splendid examples of polyhedra, this book will be a valuable addition to any mathematics library.

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lgli/M_Mathematics/MD_Geometry and topology/Coxeter H.S.M. Introduction to geometry (2ed., Wiley, 1969)(ISBN 0471504580)(KA)(T)(O)(487s)_MD_.djvu

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.

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lgli/M_Mathematics/MD_Geometry and topology/Coxeter H.S.M. Introduction to geometry (2ed., Wiley, 1969)(ISBN 0471504580)(KA)(T)(486s)_MD_.djvu

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.

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lgli/Introduction to Geometry (1969)Coxeter-B5.pdf

Some characters are lost in the original version due to the scanning deficiency. In this version, most of the lost characters are provided by the annotation.

English [en] · PDF · 17.6MB · 1989 · 📘 Book (non-fiction) · 🚀/lgli/lgrs · Save

ia/mathematicalrecr0000ball_x7u3.pdf

Mathematical Recreations and Essays (Dover Math Games & Puzzles) Walter William Rouse Ball; Harold Scott Macdonald Coxeter Dover Publications, Incorporated, Dover books on mathematical & logical puzzles, cryptography, and word recreations, 13. ed., [Nachdr, New York, NY, ca. 2009

" The classic work on recreational math in English."Martin Gardner For nearly a century, this sparkling classic has provided stimulating hours of entertainment to the mathematically inclined. The problems posed here often involve fundamental mathematical methods and notions, but their chief appeal is their capacity to tease and delight. In these pages you will find scores of "recreations" to amuse you and to challenge your problem-solving facultiesoften to the limit. Now in its 13th edition, Mathematical Recreations and Essays has been thoroughly revised and updated over the decades since its first publication in 1892. This latest edition retains all the remarkable character of the original, but the terminology and treatment of some problems have been updated and new material has been added. Among the challenges in store for Arithmetical and geometrical recreations; Polyhedra; Chess-board recreations; Magic squares; Map-coloring problems; Unicursal problems; Cryptography and cryptanalysis; Calculating prodigies; and more. You'll even find problems which mathematical ingenuity can solve but the computer cannot. No knowledge of calculus or analytic geometry is necessary to enjoy these games and puzzles. With basic mathematical skills and the desire to meet a challenge you can put yourself to the test and win. "A must to add to your mathematics library." The Mathematics Teacher

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lgli/N:\libgen djvu ocr\23000\799d21a2bec4ab10ed55ea602155f365-ocr.djvu

Non-Euclidean Geometry (Mathematical Association of America Textbooks) Coxeter, H. S. M. The Mathematical Association of America, Spectrum series, MAA spectrum., 6th ed., Washington, D.C, District of Columbia, 1998

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.An unusual feature of the book is its use of the general linear transformation of coordinates to derive the formulas of elliptic and hyperbolic trigonometry. The area of a triangle is related to the sum of its angles by means of an ingenious idea of Gauss. This treatment can be enjoyed by anyone who is familiar with algebra up to the elements of group theory.

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lgli/U:\!Genesis\!!ForLG\2391505-Наследие Г.С.М.Кокстера (книги и статьи)\Non-EuclideanGeometry-SixEdition-1998.djvu

Non-Euclidean Geometry (Mathematical Association of America Textbooks) Harold Scott Macdonald Coxeter The Mathematical Association of America, Spectrum series, MAA spectrum., 6th ed., Washington, D.C, District of Columbia, 1998

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.

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upload/newsarch_ebooks_2025_10/2020/07/05/0486614808.azw3

Regular Polytopes (Dover Books on Mathematics) Coxeter, H. S. M. Dover Publications : Made available through hoopla, INscribe Digital, [N.p.], 2012

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.

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ia/realprojectivepl0000coxe_3ed.pdf

The real projective plane Macintosh Version H.S.M. Coxeter; with an appendix for Mathematica by George Beck New York: Springer-Verlag, Springer Nature (Textbooks & Major Reference Works), New York, NY, 2012

Along with many small improvements, this revised edition contains van Yzeren's new proof of Pascal's theorem (§1.7) and, in Chapter 2, an improved treatment of order and sense. The Sylvester-Gallai theorem, instead of being introduced as a curiosity, is now used as an essential step in the theory of harmonic separation (§3.34). This makes the logi cal development self-contained: the footnotes involving the References (pp. 214-216) are for comparison with earlier treatments, and to give credit where it is due, not to fill gaps in the argument. H.S.M.C. November 1992 v Preface to the Second Edition Why should one study the real plane? To this question, put by those who advocate the complex plane, or geometry over a general field, I would reply that the real plane is an easy first step. Most of the prop erties are closely analogous, and the real field has the advantage of intuitive accessibility. Moreover, real geometry is exactly what is needed for the projective approach to non· Euclidean geometry. Instead of introducing the affine and Euclidean metrics as in Chapters 8 and 9, we could just as well take the locus of'points at infinity'to be a conic, or replace the absolute involution by an absolute polarity.

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lgli/M_Mathematics/MPop_Popular-level/Sved M. Journey into geometries (MAA, 1991)(ISBN 0883855003)(600dpi)(T)(199s)_MPop_.djvu

Journey into Geometries (Spectrum) Marta Sved, H. S. M. Coxeter, John Stillwell The Mathematical Association of America, Spectrum series, 1997

This charming book introduces us to topics in hyperbolic geometry in a delightfully informal style. Journey into Geometrics can be read at two levels. It can be studied as an informal introduction to post-Euclidean geometry, or it can serve as background material for university students. The material presented in the text is extended by carefully selected problems. The background required is minimal, standard high school geometry, yet the serious student, aided by problems attached to each chapter, should acquire a deeper understanding of the subject.

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upload/wll/ENTER/Science/Physics & Math/1 - More Books on IT & Math/Geometry/Non-Euclidean Geometry 6th ed. - H.S.M. Coxeter.djvu

Non-Euclidean Geometry (Mathematical Association of America Textbooks) Harold Scott Macdonald Coxeter The Mathematical Association of America, Mathematical Association of America Textbooks, 6, 1998

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.

English [en] · DJVU · 2.7MB · 1998 · 📘 Book (non-fiction) · 🚀/lgli/lgrs/nexusstc/upload/zlib · Save

ia/regularcomplexpo0000coxe.pdf

Regular Complex Polytopes Harold Scott Macdonald Coxeter Cambridge University Press (Virtual Publishing), London, 1974 [i.e. 1975

x, 185 p. : 26 x 28 cm Includes index Bibliography: p. 180-181

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ia/mcescherartscien0000inte.pdf

M. C. Escher, art and science proceedings of the International Congress on M. C. Escher, Rome, Italy, 26 - 28 March, 1985 International Congress on M.C. Escher (1985 Rome, Italy), Interdisciplinary Congress on M. C. Escher (1985 Rome, Italy) North-Holland; Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.; Elsevier Science Ltd, Amsterdam, New York, N.Y., U.S.A., Netherlands, 1986

The work of Dutch artist Maurits Cornelis Escher (1898-1972) continues to attract wide interest. Mathematicians, physicists, crystallographers, chemists, biologists, psychologists, psychiatrists, art historians, and specialists in computer graphics and visual communications attended this congress. The papers presented here in this illustrated volume confirm that Escher's works are not only good examples of the visualization of scientific problems but also stimulate real scientific research.

English [en] · PDF · 26.3MB · 1986 · 📗 Book (unknown) · 🚀/ia · Save

ia/regularpolytopes0000coxe_q0b5.pdf

Regular polytopes. [by] H.S.M. Coxeter Harold Scott Macdonald Coxeter; Harold S M Coxeter Dover Publications, Incorporated, INscribe Digital, [N.p.], 2012

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. Polygons And Polyhedra -- Regular And Quasi-regular Solids -- Rotation Groups -- Tessellations And Honeycombs -- Kaleidoscope -- Star-polyhedra -- Ordinary Polytopes In Higher Space -- Truncation -- Poincare's Proof Of Euler's Formula -- Forms, Vectors, And Coordinates -- Generalized Kaleidoscope -- Generalized Petrie Polygon -- Sections And Projections -- Star-polytopes [by] H. S. M. Coxeter. Bibliography: P. 306-314.

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lgli/G:\!genesis\_add\!woodhead\kolxo371\M_Mathematics\MD_Geometry and topology\Coxeter H.S.M., Du Val P., Flather H.T., Petrie J.F. The fifty-nine icosahedra (2pr., Springer, 1982)(ISBN 9780387907703)(600dpi)(T)(52s)_MD_.djvu

The Fifty-Nine Icosahedra (Lecture Notes in Statistics) H. S. M. Coxeter, P. Du Val, H. T. Flather, J. F. Petrie (auth.) Springer-Verlag New York, Lecture Notes in Statistics, 1, 1982

The Fifty-Nine Icosahedra was originally published in 1938 as No. 6 of "University of Toronto Studies (Mathematical Series)". Of the four authors, only Coxeter and myself are still alive, and we two are the authors of the whole text of the book, in which any signs of immaturity may perhaps be regarded leniently on noting that both of us were still in our twenties when it was written. N either of the others was a professional mathematician. Flather died about 1950, and Petrie, tragically, in a road accident in 1972. Petrie's part in the book consisted in the extremely difficult drawings which consti tute the left half of each of the plates (the much simpler ones on the right being mine). A brief biographical note on Petrie will be found on p. 32 of Coxeter's Regular Polytopes (3rd. ed. , Dover, New York, 1973); and it may be added that he was still a schoolboy when he discovered the regular skew polygons that are named after him, and are the occasion for the note on him in Coxeter's book. (Coxeter also was a schoolboy when some of the results for which he will be most remembered were obtained; he and Petrie were schoolboy friends and used to work together on polyhedron and polytope theory. ) Flather's part in the book consisted in making a very beautiful set of miniature models of all the fifty-nine figures. These are still in existence, and in excellent preservation. Erscheinungsdatum: 04.11.1982

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lgli/H. S. M. Coxeter - Geometry Revisited.pdf

Geometry Revisited H. S. M. Coxeter; S. L. Greitzer Mathematical Association of America, American Mathematical Society, [New York], 1967

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.

English [en] · PDF · 7.5MB · 1967 · 📘 Book (non-fiction) · 🚀/lgli/zlib · Save