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Classical Topics in Discrete Geometry (CMS Books in Mathematics)

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Classical Topics in Discrete Geometry (CMS Books in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

About the Author - Karoly Bezdek received his Dr.rer.nat.(1980) and Habilitation (1997) degrees in mathematics from the Eötvös Loránd University, in Budapest and his Candidate of Mathematical Sciences (1985) and Doctor of Mathematical Sciences (1994) degrees from the Hungarian Academy of Sciences. He is the author of more than 100 research papers and currently he is professor and Canada Research Chair of mathematics at the University of Calgary. About the book: This multipurpose book can serve as a textbook for a semester long graduate level course giving a brief introduction to Discrete Geometry. It also can serve as a research monograph that leads the reader to the frontiers of the most recent research developments in the classical core part of discrete geometry. Finally, the forty-some selected research problems offer a great chance to use the book as a short problem book aimed at advanced undergraduate and graduate students as well as researchers. The text is centered around four major and by now classical problems in discrete geometry. The first is the problem of densest sphere packings, which has more than 100 years of mathematically rich history. The second major problem is typically quoted under the approximately 50 years old illumination conjecture of V. Boltyanski and H. Hadwiger. The third topic is on covering by planks and cylinders with emphases on the affine invariant version of Tarski's plank problem, which was raised by T. Bang more than 50 years ago. The fourth topic is centered around the Kneser-Poulsen Conjecture, which also is approximately 50 years old. All four topics witnessed very recent breakthrough results, explaining their major role in this book.

Synopsis:

The goal of this book is to provide focused material for a semester long graduate level course, which can be regarded as a brief introduction to Discrete Geometry. There are a large number of exercises and the book can also act as a short problem book aimed at advanced undergraduate and graduate students as well as researchers. This text is centered around three major problems of Discrete Geometry. The first is the problem of Densest Sphere Packings, which has more than 100 years of mathematically rich history. The second major problem is typically quoted under the roughly 50 years old Illumination Conjecture of V. Boltyanski and H. Hadwiger, and the third topic is centered around another nearly 50 years old conjecture called the Kneser-Poulsen Conjecture. All three topics witnessed very recent breakthrough results, explaining their major role in this book.

Synopsis:

This monograph leads the reader to the frontiers of the very latest research developments in what is regarded as the central zone of discrete geometry. It is constructed around four classic problems in the subject, including the Kneser-Poulsen Conjecture.

Synopsis:

This multipurpose book can serve as a textbook for a semester long graduate level course giving a brief introduction to Discrete Geometry. It also can serve as a research monograph that leads the reader to the frontiers of the most recent research developments in the classical core part of discrete geometry. Finally, the forty-some selected research problems offer a great chance to use the book as a short problem book aimed at advanced undergraduate and graduate students as well as researchers. The text is centered around four major and by now classical problems in discrete geometry. The first is the problem of densest sphere packings, which has more than 100 years of mathematically rich history. The second major problem is typically quoted under the approximately 50 years old illumination conjecture of V. Boltyanski and H. Hadwiger. The third topic is on covering by planks and cylinders with emphases on the affine invariant version of Tarski's plank problem, which was raised by T. Bang more than 50 years ago. The fourth topic is centered around the Kneser-Poulsen Conjecture, which also is approximately 50 years old. All four topics witnessed very recent breakthrough results, explaining their major role in this book.

Table of Contents

Preface.- Part I.- Sphere Packings.- Finite Packings by Translates of Convex Bodies.- Coverings by Homothetic Bodies - Illumination and Related Topics.- Coverings by Planks and Cylinders.- On the Volume of Finie Arrangements of Spheres.- Ball-Polyhedra as Interesctions of Congruent Balls.- Part II.- Selected Proofs on Sphere Packagings.- Selected Proofs on Finite Packagings of Translates of Convex Bodies.- Selected Proofs on Illumination and Related Topics.- Selected Proofs on Coverings by Planks and Cylinders.- Selected Proofs on the Kesner-Poulsen Conjecture.- Selected Proofs on Ball-Polyhedra.- References.

Product Details

ISBN:
9781441905994
Author:
Bezdek, Karoly
Publisher:
Springer
Author:
Bezdek, Kroly
Author:
Bezdek
Author:
Károly
Subject:
Geometry - General
Subject:
Geometry
Subject:
Mathematics-Geometry and Trigonometry
Copyright:
Edition Description:
2010
Series:
CMS Books in Mathematics
Publication Date:
20100707
Binding:
HARDCOVER
Language:
English
Pages:
180
Dimensions:
235 x 155 mm 950 gr

Related Subjects

History and Social Science » World History » General
Humanities » Philosophy » General
Religion » Comparative Religion » General
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry

Classical Topics in Discrete Geometry (CMS Books in Mathematics) New Hardcover
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$50.25 In Stock
Product details 180 pages Springer - English 9781441905994 Reviews:
"Synopsis" by , The goal of this book is to provide focused material for a semester long graduate level course, which can be regarded as a brief introduction to Discrete Geometry. There are a large number of exercises and the book can also act as a short problem book aimed at advanced undergraduate and graduate students as well as researchers. This text is centered around three major problems of Discrete Geometry. The first is the problem of Densest Sphere Packings, which has more than 100 years of mathematically rich history. The second major problem is typically quoted under the roughly 50 years old Illumination Conjecture of V. Boltyanski and H. Hadwiger, and the third topic is centered around another nearly 50 years old conjecture called the Kneser-Poulsen Conjecture. All three topics witnessed very recent breakthrough results, explaining their major role in this book.
"Synopsis" by , This monograph leads the reader to the frontiers of the very latest research developments in what is regarded as the central zone of discrete geometry. It is constructed around four classic problems in the subject, including the Kneser-Poulsen Conjecture.
"Synopsis" by , This multipurpose book can serve as a textbook for a semester long graduate level course giving a brief introduction to Discrete Geometry. It also can serve as a research monograph that leads the reader to the frontiers of the most recent research developments in the classical core part of discrete geometry. Finally, the forty-some selected research problems offer a great chance to use the book as a short problem book aimed at advanced undergraduate and graduate students as well as researchers. The text is centered around four major and by now classical problems in discrete geometry. The first is the problem of densest sphere packings, which has more than 100 years of mathematically rich history. The second major problem is typically quoted under the approximately 50 years old illumination conjecture of V. Boltyanski and H. Hadwiger. The third topic is on covering by planks and cylinders with emphases on the affine invariant version of Tarski's plank problem, which was raised by T. Bang more than 50 years ago. The fourth topic is centered around the Kneser-Poulsen Conjecture, which also is approximately 50 years old. All four topics witnessed very recent breakthrough results, explaining their major role in this book.
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