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Charming Proofs : a Journey into Elegant Mathematics.

Author: Claudi Alsina; Roger B Nelsen
Publisher: Washington : Mathematical Association of America, 2014.
Series: Dolciani mathematical expositions.
Edition/Format:   Print book : Document   Computer File : EnglishView all editions and formats
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Genre/Form: Electronic books
Material Type: Document
Document Type: Book, Computer File
All Authors / Contributors: Claudi Alsina; Roger B Nelsen
ISBN: 0883853485 9780883853481
OCLC Number: 952752973
Notes: ""8.3 Three-square theorems""
Description: 1 online resource (320 pages).
Contents: ""Cover ""; ""copyright page ""; ""title page ""; ""Preface""; ""Contents""; ""Introduction""; ""CHAPTER 1 A Garden of Integers""; ""1.1 Figurate numbers""; ""1.2 Sums of squares, triangular numbers, and cubes""; ""1.3 There are infinitely many primes""; ""1.4 Fibonacci numbers""; ""1.5 Fermat�s theorem""; ""1.6 Wilson�s theorem""; ""1.7 Perfect numbers""; ""1.8 Challenges""; ""CHAPTER 2 Distinguished Numbers""; ""2.1 The irrationality of sqrt2""; ""2.2 The irrationality of sqrt{k} for non-square k""; ""2.3 The golden ratio""; ""2.4 pi and the circle""; ""2.5 The irrationality of pi"" ""2.6 The Comte de Buffon and his needle""""2.7 e as a limit""; ""2.8 An infinite series for e""; ""2.9 The irrationality of e""; ""2.10 Steiner�s problem on the number e""; ""2.11 The Euler-Mascheroni constant""; ""2.12 Exponents, rational and irrational""; ""2.13 Challenges""; ""CHAPTER 3 Points in the Plane""; ""3.1 Pick�s theorem""; ""3.2 Circles and sums of two squares""; ""3.3 The Sylvester-Gallai theorem""; ""3.4 Bisecting a set of 100,000 points""; ""3.5 Pigeons and pigeonholes""; ""3.6 Assigning numbers to points in the plane""; ""3.7 Challenges"" ""CHAPTER 4 The Polygonal Playground""""4.1 Polygonal combinatorics""; ""4.2 Drawing an n-gon with given side lengths""; ""4.3 The theorems of Maekawa and Kawasaki""; ""4.4 Squaring polygons""; ""4.5 The stars of the polygonal playground""; ""4.6 Guards in art galleries""; ""4.7 Triangulation of convex polygons""; ""4.8 Cycloids, cyclogons, and polygonal cycloids""; ""4.9 Challenges""; ""CHAPTER 5 A Treasury of TriangleTheorems""; ""5.1 The Pythagorean theorem""; ""5.2 Pythagorean relatives""; ""5.3 The inradius of a right triangle"" ""5.4 Pappus� generalization of the Pythagorean theorem""""5.5 The incircle and Heron�s formula""; ""5.6 The circumcircle and Euler�s triangle inequality""; ""5.7 The orthic triangle""; ""5.8 The Erdos-Mordell inequality""; ""5.9 The Steiner-Lehmus theorem""; ""5.10 The medians of a triangle""; ""5.11 Are most triangles obtuse?""; ""5.12 Challenges""; ""CHAPTER 6 The Enchantment of the Equilateral Triangle""; ""6.1 Pythagorean-like theorems""; ""6.2 The Fermat point of a triangle""; ""6.3 Viviani�s theorem""; ""6.4 A triangular tiling of the plane and Weitzenböck�s inequality"" ""6.5 Napoleon�s theorem""""6.6 Morley�s miracle""; ""6.7 Van Schooten�s theorem""; ""6.8 The equilateral triangle and the golden ratio""; ""6.9 Challenges""; ""CHAPTER 7 The Quadrilaterals� Corner""; ""7.1 Midpoints in quadrilaterals""; ""7.2 Cyclic quadrilaterals""; ""7.3 Quadrilateral equalities and inequalities""; ""7.4 Tangential and bicentric quadrilaterals""; ""7.5 Anne�s and Newton�s theorems""; ""7.6 Pythagoras with a parallelogram andequilateral triangles""; ""7.7 Challenges""; ""CHAPTER 8 Squares Everywhere""; ""8.1 One-square theorems""; ""8.2 Two-square theorems""
Series Title: Dolciani mathematical expositions.
Other Titles: Dolciani Mathematical Expositions, Volume 42

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