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The book has 19 chapters. After two chapters introducing background material in linear algebra, topology, and convex geometry, two more chapters provide basic definitions of polyhedra, in their two dual versions (intersections of half-spaces and convex hulls of finite point sets), introduce Schlegel diagrams, and provide some basic examples including the cyclic polytopes.
In geometry, there was a clear need for a new set of axioms, which would be complete, and which in no way relied on pictures we draw or on our intuition of space. Such axioms, now known as Hilbert's axioms, were given by David Hilbert in 1894 in his dissertation Grundlagen der Geometrie (Foundations of Geometry).
To a system of points, straight lines, and planes, it is impossible to add other elements in such a manner that the system thus generalized shall form a new geometry obeying all of the five groups of axioms. In other words, the elements of geometry form a system which is not susceptible of extension, if we regard the five groups of axioms as valid.
ISBN 0-262-03293-7. — This book has a chapter on geometric algorithms. Frank Nielsen. Visual Computing: Graphics, Vision, and Geometry, Charles River Media, 2005. ISBN 1-58450-427-7 — This book combines graphics, vision and geometric computing and targets advanced undergraduates and professionals in game development and graphics. Includes ...
The book covers both the mathematics of polyhedra and its historical development, limiting itself only to three-dimensional geometry. [2] [3] The notion of what it means to be a polyhedron has varied over the history of the subject, as have other related definitions, an issue that the book handles largely by keeping definitions informal and flexible, and by pointing out problematic examples ...
Singmaster complains only about two pieces of mathematics in the book: the assertion in chapter 4 that the Egyptians were familiar with the 3-4-5 right triangle (still the subject of considerable scholarly debate) and the omission from chapter 7 of any discussion of why classifying constructible polygons can be reduced to the case of prime ...
The next three chapters take a step back to look at the broader history of the topics discussed in the book: geometry and its connection to human arts and architecture in chapter 3, crochet in chapter 4, and non-Euclidean geometry in chapter 5. Chapters 6, 7, and 8 cover specific geometric objects with negatively-curved surfaces, including the ...
Regular Figures is divided into two parts, "Systematology of the Regular Figures" and "Genetics of the Regular Figures", each in five chapters. [1] Although the first part represents older and standard material, much of the second part is based on a large collection of research works by Fejes Tóth, published over the course of approximately 25 years, and on his previous exposition of this ...
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