""Cover ""; ""copyright page ""; ""title page ""; ""Contents""; ""Preface""; ""Introduction""; ""Inequalities as a field of study""; ""Inequalities in the classroom""; ""CHAPTER 1 Representing positive numbers as lengths of segments""; ""1.1 Inequalities associated with triangles""; ""1.2 Polygonal paths""; ""1.3 n-gons inside m-gons""; ""1.4 The arithmetic mean-geometric mean inequality""; ""1.5 More inequalities for means""; ""1.6 The Ravi substitution""; ""1.7 Comparing graphs of functions""; ""1.8 Challenges""; ""CHAPTER 2 Representing positive numbers as areas or volumes""

""2.1 Three examples""""2.2 Chebyshev�s inequality""; ""2.3 The AM-GM inequality for three numbers""; ""2.4 Guha�s inequality""; ""2.5 The AM-GM inequality for n numbers""; ""2.6 The HM-AM-GM-RMS inequality for nnumbers""; ""2.7 The mediant property and Simpson�s paradox""; ""2.8 Chebyshev�s inequality revisited""; ""2.9 Schur�s inequality""; ""2.10 Challenges""; ""CHAPTER 3 Inequalities and the existence of triangles""; ""3.1 Inequalities and the altitudes of a triangle""; ""A triangle and its altitudes""; ""Existence of a triangle given a, b, and h_a""

""Existence of a triangle given a, h_b, and h_c""""More inequalities for the three altitudes""; ""Altitudes, sides and angles""; ""3.2 Inequalities and the medians of a triangle""; ""Existence of a triangle given m_a, m_b, and m_c""; ""Existence of a triangle given a, b, and m_a""; ""Existence of a triangle given a, b, and m_c""; ""Existence of a triangle given a, m_a, and m_b""; ""3.3 Inequalities and the angle-bisectors of a triangle""; ""Existence of a triangle given a, h_a, and w_a""; ""Existence of a triangle given a, h_b, and w_c""; ""Ordering of sides and angle-bisectors""

""3.4 The Steiner-Lehmus theorem""""3.5 Challenges""; ""CHAPTER 4 Using incircles and circumcircles""