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| Author | : Hugo Hadwiger |
| Publisher | : |
| Total Pages | : 113 |
| Release | : 1964 |
| Genre | : Combinatorial geometry |
| ISBN | : |
| Author | : Hugo Hadwiger |
| Publisher | : Courier Corporation |
| Total Pages | : 129 |
| Release | : 2015-01-15 |
| Genre | : Mathematics |
| ISBN | : 0486789969 |
Advanced undergraduate-level text discusses theorems on topics restricted to the plane, such as convexity, coverings, and graphs. Two-part treatment begins with specific topics followed by an extensive selection of short proofs. 1964 edition.
| Author | : Hugo Hadwiger |
| Publisher | : |
| Total Pages | : 122 |
| Release | : 1964 |
| Genre | : |
| ISBN | : |
| Author | : Hugo Hadwiger |
| Publisher | : |
| Total Pages | : 113 |
| Release | : 1964 |
| Genre | : |
| ISBN | : |
| Author | : Hugo Hadwiger |
| Publisher | : |
| Total Pages | : 113 |
| Release | : 1964 |
| Genre | : |
| ISBN | : |
| Author | : Hugo HADWIGER (and DEBRUNNER (Hans) of Bern University.) |
| Publisher | : |
| Total Pages | : 113 |
| Release | : 1964 |
| Genre | : |
| ISBN | : |
| Author | : Vladimir Grigorʹevich Bolti︠a︡nskiĭ |
| Publisher | : University of Chicago Press |
| Total Pages | : 80 |
| Release | : 1980 |
| Genre | : Combinatorial geometry |
| ISBN | : 0226063577 |
In contrast to the vast literature on Euclidean geometry as a whole, little has been published on the relatively recent developments in the field of combinatorial geometry. Boltyanskii and Gohberg's book investigates this area, which has undergone particularly rapid growth in the last thirty years. By restricting themselves to two dimensions, the authors make the book uniquely accessible to interested high school students while maintaining a high level of rigor. They discuss a variety of problems on figures of constant width, convex figures, coverings, and illumination. The book offers a thorough exposition of the problem of cutting figures into smaller pieces. The central theorem gives the minimum number of pieces into which a figure can be divided so that all the pieces are of smaller diameter than the original figure. This theorem, which serves as a basis for the rest of the material, is proved for both the Euclidean plane and Minkowski's plane.
| Author | : Martin Gardner |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 278 |
| Release | : 2020-10-06 |
| Genre | : Mathematics |
| ISBN | : 1470463644 |
Martin Gardner's Mathematical Games columns in Scientific American inspired and entertained several generations of mathematicians and scientists. Gardner in his crystal-clear prose illuminated corners of mathematics, especially recreational mathematics, that most people had no idea existed. His playful spirit and inquisitive nature invite the reader into an exploration of beautiful mathematical ideas along with him. These columns were both a revelation and a gift when he wrote them; no one--before Gardner--had written about mathematics like this. They continue to be a marvel. This is the original 1986 edition and contains columns published from 1972-1974.
| Author | : Eugene Fink |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 104 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 3642188494 |
Restricted-orientation convexity is the study of geometric objects whose intersections with lines from some fixed set are connected. This notion generalizes standard convexity and several types of nontraditional convexity. The authors explore the properties of this generalized convexity in multidimensional Euclidean space, and describ restricted-orientation analogs of lines, hyperplanes, flats, halfspaces, and identify major properties of standard convex sets that also hold for restricted-orientation convexity. They then introduce the notion of strong restricted-orientation convexity, which is an alternative generalization of convexity, and show that its properties are also similar to that of standard convexity.
| Author | : Bettina Richmond |
| Publisher | : American Mathematical Society |
| Total Pages | : 540 |
| Release | : 2023-08-25 |
| Genre | : Mathematics |
| ISBN | : 147047204X |
This textbook bridges the gap between lower-division mathematics courses and advanced mathematical thinking. Featuring clear writing and appealing topics, the book introduces techniques for writing proofs in the context of discrete mathematics. By illuminating the concepts behind techniques, the authors create opportunities for readers to sharpen critical thinking skills and develop mathematical maturity. Beginning with an introduction to sets and logic, the book goes on to establish the basics of proof techniques. From here, chapters explore proofs in the context of number theory, combinatorics, functions and cardinality, and graph theory. A selection of extension topics concludes the book, including continued fractions, infinite arithmetic, and the interplay among Fibonacci numbers, Pascal's triangle, and the golden ratio. A Discrete Transition to Advanced Mathematics is suitable for an introduction to proof course or a course in discrete mathematics. Abundant examples and exercises invite readers to get involved, and the wealth of topics allows for course customization and further reading. This new edition has been expanded and modernized throughout. New features include a chapter on combinatorial geometry, a more in-depth treatment of counting, and over 365 new exercises.
