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Field name	Details
Dewey Class	516
Title	Strange Phenomena in Convex and Discrete Geometry ([EBook]) / by Chuanming Zong ; edited by James J. Dudziak.
Author	Zong, Chuanming
Added Personal Name	Dudziak, James Joseph , 1955-
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 1996.
Physical Details	VI, 158 pages. 6 illus. : online resource.
Series	Universitext 0172-5939
ISBN	9781461384816
Summary Note	Convex and discrete geometry is one of the most intuitive subjects in mathematics. One can explain many of its problems, even the most difficult - such as the sphere-packing problem (what is the densest possible arrangement of spheres in an n-dimensional space?) and the Borsuk problem (is it possible to partition any bounded set in an n-dimensional space into n+1 subsets, each of which is strictly smaller in "extent" than the full set?) - in terms that a layman can understand; and one can reasonably make conjectures about their solutions with little training in mathematics.:
Contents note	1 Borsuk’s Problem -- §1 Introduction -- §2 The Perkal-Eggleston Theorem -- §3 Some Remarks -- §4 Larman’s Problem -- §5 The Kahn-Kalai Phenomenon -- 2 Finite Packing Problems -- §1 Introduction -- §2 Supporting Functions, Area Functions, Minkowski Sums, Mixed Volumes, and Quermassintegrals -- §3 The Optimal Finite Packings Regarding Quermassintegrals -- §4 The L. Fejes Tóth-Betke-Henk-Wills Phenomenon -- §5 Some Historical Remarks -- 3 The Venkov-McMullen Theorem and Stein’s Phenomenon -- §1 Introduction -- §2 Convex Bodies and Their Area Functions -- §3 The Venkov-McMullen Theorem -- §4 Stein’s Phenomenon -- §5 Some Remarks -- 4 Local Packing Phenomena -- §1 Introduction -- §2 A Phenomenon Concerning Blocking Numbers and Kissing Numbers -- §3 A Basic Approximation Result -- §4 Minkowski’s Criteria for Packing Lattices and the Densest Packing Lattices -- §5 A Phenomenon Concerning Kissing Numbers and Packing Densities -- §6 Remarks and Open Problems -- 5 Category Phenomena -- §1 Introduction -- §2 Gruber’s Phenomenon -- §3 The Aleksandrov-Busemann-Feller Theorem -- §4 A Theorem of Zamfirescu -- §5 The Schneider-Zamfirescu Phenomenon -- §6 Some Remarks -- 6 The Busemann-Petty Problem -- §1 Introduction -- §2 Steiner Symmetrization -- §3 A Theorem of Busemann -- §4 The Larman-Rogers Phenomenon -- §5 Schneider’s Phenomenon -- §6 Some Historical Remarks -- 7 Dvoretzky’s Theorem -- §1 Introduction -- §2 Preliminaries -- §3 Technical Introduction -- §4 A Lemma of Dvoretzky and Rogers -- §5 An Estimate for ?V(AV) -- §6 ?-nets and ?-spheres -- §7 A Proof of Dvoretzky’s Theorem -- §8 An Upper Bound for M (n, ?) -- §9 Some Historical Remarks -- Inedx.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4613-8481-6
Links to Related Works	Subject References: Geometry . Mathematics . Authors: Dudziak, James Joseph 1955- . editor . Zong, Chuanming . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 516 . 516 (DDC 22) .

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Strange Phenomena in Convex and Discrete Geometry

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