2007;
463 pp;
Hardcover

Print ISBN: 978-0-8218-4316-1

Product Code: MBK/46

List Price: $65.00

Individual Member Price: $52.00

**Electronic ISBN: 978-1-4704-1812-0
Product Code: MBK/46.E**

List Price: $65.00

Individual Member Price: $52.00

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#### Supplemental Materials

# Mathematical Omnibus: Thirty Lectures on Classic Mathematics

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*Dmitry Fuchs; Serge Tabachnikov*

The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader's effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an award-winning artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher.

#### Table of Contents

# Table of Contents

## Mathematical Omnibus: Thirty Lectures on Classic Mathematics

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface ix10 free
- Credits xiii14 free
- Part 1. Algebra and arithmetics 118 free
- Chapter 1. Arithmetic and combinatorics 320
- Can a number be approximately rational? 522
- Arithmetical properties of binomial coefficients 2744
- On collecting like terms, on Euler, Gauss, and MacDonald, and on missed opportunities 4562
- Chapter 2. Equations 6582
- Equations of degree three and four 6784
- Equations of degree five 7996
- How many roots does a polynomial have? 93110
- Chebyshev polynomials 101118
- Geometry of equations 109126
- Part 2. Geometry and topology 121138
- Chapter 3. Envelopes and singularities 123140
- Cusps 125142
- Around four vertices 141158
- Segments of equal areas 159176
- On plane curves 171188
- Chapter 4. Developable surfaces 187204
- Paper sheet geometry 189206
- Paper Möbius band 203220
- More on paper folding 213230
- Chapter 5. Straight lines 223240
- Straight lines on curved surfaces 225242
- Twenty-seven lines 239256
- Web geometry 253270
- The Crofton formula 269286
- Chapter 6. Polyhedra 283300
- Curvature and polyhedra 285302
- Non-inscribable polyhedra 301318
- Can one make a tetrahedron out of a cube? 307324
- Impossible tilings 319336
- Rigidity of polyhedra 335352
- Flexible polyhedra 345362
- Chapter 7. Two surprising topological constructions 359376
- Alexander’s horned sphere 361378
- Cone eversion 373390
- Chapter 8. On ellipses and ellipsoids 381398
- Billiards in ellipses and geodesics on ellipsoids 383400
- The Poncelet porism and other closure theorems 403420
- Gravitational attraction of ellipsoids 415432
- Solutions to selected exercises 425442
- Bibliography 457474
- Index 461478 free
- Back Cover Back Cover1482

#### Readership

Undergraduates, graduate students, and research mathematicians interested in mathematics.

#### Reviews

The authors manage to breathe new life into topics that at first glance appear to be old hat.