Proofs without Words III: Further Exercises in Visual Thinking

Proofs without words (PWWs) are figures or diagrams that help the reader see why a particular mathematical statement is true, and how one might begin to formally prove it true. Many PWWs date back to classical Greece, ancient China, and medieval Europe and the Middle East. This third collection of PWWs follows a coherent structure, with proofs being arranged by topic into five chapters: geometry and algebra; trigonometry, calculus and analytic geometry; inequalities; integers and integer sums; and infinite series and other topics. They are intended primarily for the enjoyment of the reader; however, teachers will want to use them with students at many levels, including high school courses from algebra through precalculus and calculus, college level courses in number theory, combinatorics, and discrete mathematics, and pre-service and in-service courses for teachers.