Essays on Numbers and Figures
About this Title
V. V. Prasolov, Independent University of Moscow, Moscow, Russia. Translated by A. B. Sossinski
Publication: Mathematical World
Publication Year 2000: Volume 16
ISBNs: 978-0-8218-1944-9 (print); 978-1-4704-2479-4 (online)
MathSciNet review: MR1744995
MSC: Primary 00A05; Secondary 11-01, 12-01, 51-01
This is the English translation of the book originally published in Russian. It contains 20 essays, each dealing with a separate mathematical topic. The topics range from brilliant mathematical statements with interesting proofs, to simple and effective methods of problem-solving, to interesting properties of polynomials, to exceptional points of the triangle. Many of the topics have a long and interesting history. The author has lectured on them to students worldwide.
The essays are independent of one another for the most part, and each presents a vivid mathematical result that led to current research in number theory, geometry, polynomial algebra, or topology.
Advanced high school and undergraduate students, mathematics educators at secondary and university level; general mathematical audience.
Table of Contents
- Chapter 1. Conjugate numbers
- Chapter 2. Rational parametrizations of the circle
- Chapter 3. Sums of squares of polynomials
- Chapter 4. Representing numbers as the sum of two squares
- Chapter 5. Can any knot be unraveled?
- Chapter 6. Construction of a regular 17-gon
- Chapter 7. The Markov equation
- Chapter 8. Integer-valued polynomials
- Chapter 9. Chebyshev polynomials
- Chapter 10. Vectors in geometry
- Chapter 11. The averaging method and geometric inequalities
- Chapter 12. Intersection points of the diagonals of regular polygons
- Chapter 13. The chromatic polynomial of a graph
- Chapter 14. Brocard points
- Chapter 15. Diophantine equations for polynomials
- Chapter 16. The Pascal lines
- Chapter 17. One butterfly and two butterflies theorems
- Chapter 18. The Van der Waerden theorem on arithmetical progressions
- Chapter 19. Isogonal conjugate points
- Chapter 20. Cubic curves related to the triangle