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Regular Polytopes
  • Language: en
  • Pages: 368

Regular Polytopes

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.

Kaleidoscopes
  • Language: en
  • Pages: 476

Kaleidoscopes

H.S.M. Coxeter is one of the world's best-known mathematicians who wrote several papers and books on geometry, algebra and topology, and finite mathematics. This book is being published in conjunction with the 50th anniversary of the Canadian Mathematical Society and it is a collection of 26 papers written by Dr. Coxeter.

Geometry Revisited
  • Language: en
  • Pages: 193

Geometry Revisited

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.

Twelve Geometric Essays
  • Language: en
  • Pages: 300
Introduction to Geometry
  • Language: en
  • Pages: 492

Introduction to Geometry

This unabridged paperback edition contains complete coverage, ranging from topics in the Euclidean plane to affine geometry, projective geometry, differential geometry and topology.

Mathematical Recreations and Essays
  • Language: en
  • Pages: 468

Mathematical Recreations and Essays

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. "A must to add to your mathematics library" ? The Mathematics Teacher. Index. References for Further Study. Includes 150 black-and-white line illustrations.

Twisted Honeycombs
  • Language: en
  • Pages: 56

Twisted Honeycombs

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The Coxeter Legacy
  • Language: en
  • Pages: 344

The Coxeter Legacy

This collection of essays on the legacy of mathematican 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.

Projective Geometry
  • Language: en
  • Pages: 180

Projective Geometry

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 Geometric Vein
  • Language: en
  • Pages: 590

The Geometric Vein

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...