Proofs Without Words III

the long version

"Proofs without words 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. The proofs in the book are intended primarily for the enjoyment of the reader, however, teachers will want to use them with students at many levels: 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"--Back cover.