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The Decomposition of Figures Into Smaller Parts

The Decomposition of Figures Into Smaller Parts

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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.
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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.
Produktdetaljer
Sprog: Engelsk
Sider: 80
ISBN-13: 9780226063577
Indbinding: Paperback
Udgave:
ISBN-10: 0226063577
Kategori: Matematik
Udg. Dato: 15 apr 1980
Længde: 9mm
Bredde: 228mm
Højde: 155mm
Forlag: The University of Chicago Press
Oplagsdato: 15 apr 1980
Forfatter(e) Izrail' Tsudikovich Gokhberg, Vladimir Grigor'evich Boltyanskii


Kategori Matematik


ISBN-13 9780226063577


Sprog Engelsk


Indbinding Paperback


Sider 80


Udgave


Længde 9mm


Bredde 228mm


Højde 155mm


Udg. Dato 15 apr 1980


Oplagsdato 15 apr 1980


Forlag The University of Chicago Press

Kategori sammenhænge