Eight topics about the unit cubes are introduced within this textbook: cross sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture. In particular Chuanming Zong demonstrates how deep analysis like log concave measure and the Brascamp-Lieb inequality can deal with the cross section problem, how Hyperbolic Geometry helps with the triangulation problem, how group rings can deal with Minkowski's conjecture and Furtwangler's conjecture, and how Graph Theory handles Keller's conjecture.
The Cube-A Window to Convex and Discrete Geometry
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Editorial Reviews
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"Because this book is a love letter to the unity of mathematics, readers can hardly but come to share Zong's undisguised enthusiasm...Highly recommended." -- Choice
Book Description
This tract has two purposes: to show what is known about the n-dimensional unit cubes and to demonstrate how Analysis, Algebra, Combinatorics, Graph Theory, Hyperbolic Geometry, Number Theory, can be applied to the study of them. The unit cubes, from any point of view, are among the most important and fascinating objects in an n-dimensional Euclidean space. In this Tract eight topics about the unit cubes are introduced: cross sections, projections, inscribed simplices, triangulations, 0/1 polytopes, Minkowski's conjecture, Furtwangler's conjecture, and Keller's conjecture.
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Inside This Book
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First Sentence:
Let En denote the n-dimensional Euclidean space over the real number field R and with an orthonormal basis {e1, e2,..., en}. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
simplex inscribed, relative interior point, primitive solution, combinatorial equivalence, cyclic sets, vertex simplex, binary matrices, more peaked, centrally symmetric, unit cube, algebraic version, inductive assumption Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof of Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Let En denote the n-dimensional Euclidean space over the real number field R and with an orthonormal basis {e1, e2,..., en}. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
simplex inscribed, relative interior point, primitive solution, combinatorial equivalence, cyclic sets, vertex simplex, binary matrices, more peaked, centrally symmetric, unit cube, algebraic version, inductive assumption Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof of Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
This book cites 12
books:
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- Hadamard matrices and their applications (Lecture notes in mathematics) by S. S Agaian in Back Matter
- Abelian Groups (Lecture Notes in Pure and Applied Mathematics) by Laszlo Fuchs in Back Matter
- Convex Bodies: The Brunn-Minkowski Theory (Encyclopedia of Mathematics and its Applications) by Rolf Schneider in Back Matter
- Proofs from THE BOOK by Martin Aigner in Back Matter
- Combinatorial Theory (Wiley Classics Library) by Marshall Hall in Back Matter
See all 12 books this book cites
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