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Mathematical Omnibus: Thirty Lectures on Classic Mathematics
About this Title
Dmitry Fuchs, University of California, Davis, CA and Serge Tabachnikov, Pennsylvania State University, University Park, PA
Publication: Miscellaneous Books
Publication Year:
2007; Volume 46
ISBNs: 978-0-8218-4316-1 (print); 978-1-4704-1812-0 (online)
DOI: https://doi.org/10.1090/mbk/046
MathSciNet review: MR2350979
MSC: Primary 00A05; Secondary 00A08, 51-02
ReadershipTable of Contents
Front/Back Matter
Algebra and arithmetics
Chapter 1. Arithmetic and combinatorics
- Lecture 1. Can a number be approximately rational?
- Lecture 2. Arithmetical properties of binomial coefficients
- Lecture 3. On collecting like terms, on Euler, Gauss, and MacDonald, and on missed opportunities
Chapter 2. Equations
- Lecture 4. Equations of degree three and four
- Lecture 5. Equations of degree five
- Lecture 6. How many roots does a polynomial have?
- Lecture 7. Chebyshev polynomials
- Lecture 8. Geometry of equations
Geometry and topology
Chapter 3. Envelopes and singularities
- Lecture 9. Cusps
- Lecture 10. Around four vertices
- Lecture 11. Segments of equal areas
- Lecture 12. On plane curves
Chapter 4. Developable surfaces
- Lecture 13. Paper sheet geometry
- Lecture 14. Paper Möbius band
- Lecture 15. More on paper folding
Chapter 5. Straight lines
- Lecture 16. Straight lines on curved surfaces
- Lecture 17. Twenty-seven lines
- Lecture 18. Web geometry
- Lecture 19. The Crofton formula
Chapter 6. Polyhedra
- Lecture 20. Curvature and polyhedra
- Lecture 21. Non-inscribable polyhedra
- Lecture 22. Can one make a tetrahedron out of a cube?
- Lecture 23. Impossible tilings
- Lecture 24. Rigidity of polyhedra
- Lecture 25. Flexible polyhedra
Chapter 7. Two surprising topological constructions
- Lecture 26. Alexander’s horned sphere
- Lecture 27. Cone eversion
Chapter 8. On ellipses and ellipsoids
- Lecture 28. Billiards in ellipses and geodesics on ellipsoids
- Lecture 29. The Poncelet porism and other closure theorems
- Lecture 30. Gravitational attraction of ellipsoids
- Lecture 31. Solutions to selected exercises