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Essays on numbers and figures / V.V. Prasolov ; [translated from the Russian by A.B. Sossinski].

By: Material type: TextTextLanguage: English Original language: Russian Series: Mathematical world ; v. 16.Publisher: Providence, R.I. : American Mathematical Society, [2000]Copyright date: ©2000Description: ix, 75 pages : illustrations ; 26 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 0821819445
  • 9780821819449
Uniform titles:
  • Rasskazy o chislakh, mnogochlenakh, i figurakh. English
Subject(s): DDC classification:
  • 510 22
LOC classification:
  • QA7 .P713 2000
Contents:
Conjugate numbers -- Rational parametrizations of the circle -- Sums of squares of polynomials -- Representing numbers as the sum of two squares -- Can any knot be unraveled? -- Construction of a regular 17-gon -- The Markov equation -- Integer-valued polynomials -- Chebyshev polynomials -- Vectors in geometry -- The averaging method and geometric inequalities -- Intersection points of the diagonals of regular polygons -- The chromatic polynomial of a graph -- Brocard points -- Diophantine equations for polynomials -- The Pascal lines -- One butterfly and two butterflies theorems -- The Van der Waerden theorem on arithmetical progressions -- Isogonal conjugate points -- Cubic curves related to the triangle.
Summary: "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."--Book jacket.
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Includes bibliographical references.

Conjugate numbers -- Rational parametrizations of the circle -- Sums of squares of polynomials -- Representing numbers as the sum of two squares -- Can any knot be unraveled? -- Construction of a regular 17-gon -- The Markov equation -- Integer-valued polynomials -- Chebyshev polynomials -- Vectors in geometry -- The averaging method and geometric inequalities -- Intersection points of the diagonals of regular polygons -- The chromatic polynomial of a graph -- Brocard points -- Diophantine equations for polynomials -- The Pascal lines -- One butterfly and two butterflies theorems -- The Van der Waerden theorem on arithmetical progressions -- Isogonal conjugate points -- Cubic curves related to the triangle.

"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."--Book jacket.

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