Titlebook: Bodies of Constant Width; An Introduction to C Horst Martini,Luis Montejano,Déborah Oliveros Textbook 2019 Springer Nature Switzerland AG 2

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https://doi.org/10.1007/b138658it can be completed to a body of constant width. These results are known as the Theorems of Meissner and Pál, respectively. Section . will be devoted to the study of reduced convex bodies, a notion somehow “dual” to completeness, and in Section . we complete convex bodies preserving some of their original characteristics, such as symmetries.

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Bodies of Constant Width in Topology,bic dodecahedron circumscribing the sphere of diameter 1 is a universal cover in .. Finally, in Section . the topology and the geometry of Grassmannian spaces are used to see how big or complicated a collection of constant width sections should be such that the original body is of constant width.

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Basic Properties of Bodies of Constant Width,rds of a convex body that have maximum length, and it is their behavior which gives constant width bodies their basic properties. Unlike the diameters of a ball, those of a body of constant width do not always meet at a single point, but when they do so, it is because the body is indeed a ball.

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Systems of Lines in the Plane,nes, in particular those which are combined with a given convex set by a certain property. For example, the system of lines that leave a fixed proportion of area, or a fixed proportion of perimeter, in one side of the convex set for every direction. Consider, for instance, the collection of tangent

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