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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: https://doi.org/10.1090/mawrld/016
MathSciNet review: MR1744995
MSC: Primary 00A05; Secondary 11-01, 12-01, 51-01

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Table of Contents

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Front/Back Matter

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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