Softcover ISBN:  9780821819449 
Product Code:  MAWRLD/16 
List Price:  $21.00 
MAA Member Price:  $18.90 
AMS Member Price:  $16.80 
Electronic ISBN:  9781470424794 
Product Code:  MAWRLD/16.E 
List Price:  $19.00 
MAA Member Price:  $17.10 
AMS Member Price:  $15.20 

Book DetailsMathematical WorldVolume: 16; 2000; 75 ppMSC: Primary 00;
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 problemsolving, 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.ReadershipAdvanced high school and undergraduate students, mathematics educators at secondary and university level; general mathematical audience.

Table of Contents

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 17gon

Chapter 7. The Markov equation

Chapter 8. Integervalued 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


Additional Material

Reviews

This volume is quite delightful … Each essay … engages the reader's interest in an immediate and lively manner … can be highly recommended for wellprepared students aspiring to a toplevel mathematics degree and will prove a marvelous source for teachers … a good bedtime read for Putnam competitors … a pleasure indeed for the general lover of mathematics.
Mathematical Reviews 
A worthwhile resource for mathematics departments to have on hand … this collection serves as a nice resource for accessible topics beyond the standard curriculum around the level of calculus.
MAA Online


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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 problemsolving, 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.

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 17gon

Chapter 7. The Markov equation

Chapter 8. Integervalued 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

This volume is quite delightful … Each essay … engages the reader's interest in an immediate and lively manner … can be highly recommended for wellprepared students aspiring to a toplevel mathematics degree and will prove a marvelous source for teachers … a good bedtime read for Putnam competitors … a pleasure indeed for the general lover of mathematics.
Mathematical Reviews 
A worthwhile resource for mathematics departments to have on hand … this collection serves as a nice resource for accessible topics beyond the standard curriculum around the level of calculus.
MAA Online