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Classical Topics in Discrete Geometry
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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.
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