# 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)

DOI: http://dx.doi.org/10.1090/mawrld/016

MathSciNet review: MR1744995

MSC: Primary 00A05; Secondary 11-01, 12-01, 51-01

### Table of Contents

**Front/Back Matter**

**Chapters**

- 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