Research Problems in Discrete Geometry

Forsideomslag
Springer Science & Business Media, 27. jan. 2006 - 500 sider

Although discrete geometry has a rich history extending more than 150 years, it abounds in open problems that even a high-school student can understand and appreciate. Some of these problems are notoriously difficult and are intimately related to deep questions in other fields of mathematics. But many problems, even old ones, can be solved by a clever undergraduate or a high-school student equipped with an ingenious idea and the kinds of skills used in a mathematical olympiad.

Research Problems in Discrete Geometry is the result of a 25-year-old project initiated by the late Leo Moser. It is a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research.

Important features include:

* More than 500 open problems, some old, others new and never before published;

* Each chapter divided into self-contained sections, each section ending with an extensive bibliography;

* A great selection of research problems for graduate students looking for a dissertation topic;

* A comprehensive survey of discrete geometry, highlighting the frontiers and future of research;

* More than 120 figures;

* A preface to an earlier version written by the late Paul Erdos.

Peter Brass is Associate Professor of Computer Science at the City College of New York. William O. J. Moser is Professor Emeritus at McGill University. Janos Pach is Distinguished Professor at The City College of New York, Research Professor at the Courant Institute, NYU, and Senior Research Fellow at the Rényi Institute, Budapest.

 

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Indhold

I
1
II
5
III
10
IV
15
V
19
VI
23
VII
28
VIII
44
XXXVI
234
XXXVII
245
XXXVIII
248
XXXIX
259
XL
270
XLI
280
XLII
289
XLIII
302

IX
48
X
56
XI
61
XII
67
XIII
75
XIV
81
XV
88
XVI
93
XVII
106
XVIII
115
XIX
121
XX
131
XXI
136
XXII
143
XXIII
149
XXIV
160
XXVI
170
XXVII
176
XXVIII
183
XXIX
191
XXX
200
XXXI
209
XXXII
214
XXXIII
217
XXXIV
222
XXXV
230
XLIV
311
XLV
325
XLVI
329
XLVII
345
XLVIII
354
XLIX
364
L
372
LII
375
LIII
383
LIV
389
LV
396
LVI
401
LVII
408
LVIII
414
LIX
417
LX
422
LXI
430
LXII
435
LXIII
443
LXIV
451
LXV
457
LXVI
466
LXVII
473
LXVIII
491
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Side 5 - I point out the following question, related to the preceding one, and important to number theory and perhaps sometimes useful to physics and chemistry: How can one arrange most densely in space an infinite number of equal solids of given form, eg, spheres with given radii or regular tetrahedra with given edges (or in prescribed position), that is, how can one so fit them together that the ratio of the filled to the unfilled space may be as great as possible?
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Side 8 - G. Fejes Toth. New Results in the Theory of Packing and Covering. In Convexity and its applications, pages 318-359.

Om forfatteren (2006)

Pach is a distinguished researcher at NYU, his book "Combinatorial Geometry," 1995, Wiley, is considered "the bible" in the area of discrete geometry. He has also published several books with Springer-Verlag.

William O.J. Moser is a Springer author as well. He has been awarded the CMS 2003 Distinguished Service Award for his sustained and significant contributions to the Canadian mathematical community.

Bibliografiske oplysninger