LEADER 05100nam 22007095 450 001 9910338254903321 005 20200629120102.0 010 $a3-030-03868-8 024 7 $a10.1007/978-3-030-03868-7 035 $a(CKB)4100000007810218 035 $a(DE-He213)978-3-030-03868-7 035 $a(MiAaPQ)EBC5926908 035 $a(PPN)235233943 035 $a(EXLCZ)994100000007810218 100 $a20190316d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBodies of Constant Width$b[electronic resource] $eAn Introduction to Convex Geometry with Applications /$fby Horst Martini, Luis Montejano, Déborah Oliveros 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2019. 215 $a1 online resource (XI, 486 p. 163 illus., 32 illus. in color.) 311 $a3-030-03866-1 327 $aIntroduction -- Convex Geometry -- Basic Properties of Bodies of Constant Width -- Figures of Constant Width -- Systems of Lines in the Plane -- Spindle Convexity -- Complete and Reduced Convex Bodies -- Examples and Constructions -- Sections of Bodies of Constant Width -- Bodies of Constant Width in Mikowski Spaces -- Bodies of Constant Width in Differential Geometry -- Mixed Volumes -- Bodies of Constant Width in Analysis -- Geometric Inequalities -- Bodies of Constant Width in Discrete Geometry -- Bodies of Constant Width in Topology -- Concepts Related to Constant Width -- Bodies of Constant Width in Art, Design, and Engineering. 330 $aThis is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry. It examines bodies of constant width from several points of view, and, in doing so, shows surprising connections between various areas of mathematics. Concise explanations and detailed proofs demonstrate the many interesting properties and applications of these bodies. Numerous instructive diagrams are provided throughout to illustrate these concepts. An introduction to convexity theory is first provided, and the basic properties of constant width bodies are then presented. The book then delves into a number of related topics, which include Constant width bodies in convexity (sections and projections, complete and reduced sets, mixed volumes, and further partial fields) Sets of constant width in non-Euclidean geometries (in real Banach spaces, and in hyperbolic, spherical, and further non-Euclidean spaces) The concept of constant width in analysis (using Fourier series, spherical integration, and other related methods) Sets of constant width in differential geometry (using systems of lines and discussing notions like curvature, evolutes, etc.) Bodies of constant width in topology (hyperspaces, transnormal manifolds, fiber bundles, and related topics) The notion of constant width in discrete geometry (referring to geometric inequalities, packings and coverings, etc.) Technical applications, such as film projectors, the square-hole drill, and rotary engines Bodies of Constant Width: An Introduction to Convex Geometry with Applications will be a valuable resource for graduate and advanced undergraduate students studying convex geometry and related fields. Additionally, it will appeal to any mathematicians with a general interest in geometry. 606 $aConvex geometry  606 $aDiscrete geometry 606 $aDifferential geometry 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aCombinatorics 606 $aTopology 606 $aConvex and Discrete Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21014 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 606 $aTopology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28000 615 0$aConvex geometry . 615 0$aDiscrete geometry. 615 0$aDifferential geometry. 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aCombinatorics. 615 0$aTopology. 615 14$aConvex and Discrete Geometry. 615 24$aDifferential Geometry. 615 24$aAnalysis. 615 24$aCombinatorics. 615 24$aTopology. 676 $a516.08 700 $aMartini$b Horst$4aut$4http://id.loc.gov/vocabulary/relators/aut$060948 702 $aMontejano$b Luis$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aOliveros$b Déborah$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910338254903321 996 $aBodies of Constant Width$92517368 997 $aUNINA