Although the triangle has a limited number of parameters (sides, angles, altitudes, etc.), the range of inequalities among these entities is surprisingly large. Bottema, Djordjević, Janić, Mitrinović, and Vasić (1969), in their book Geometric Inequalities, have collected approx- imately 400 inequalities for the triangle. It is shown in this chapter 5 that majorization provides a unified approach to obtaining many known geometric inequalities. This unification also has the advantage of suggesting new inequalities.
KeywordsGreat Area Isoperimetric Inequality Isosceles Triangle Middle Term Plane Figure
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