This second edition of Alexander Sofier's How Does One Cut a Triangle? demonstrates how different areas of mathematics can be juxtaposed in the solution of a given problem. To develop a clear "mini-model" of mathematical research, Sofier employs geometry, algebra, trigonometry, linear algebra, and rings. The author brings mathematics alive by giving the audience, primarily high school students, a taste of what mathematicians do. His book presents open problems which invite the reader to actively play the role of the mathematician. By doing so, the author skillfully inspires the reader to discover uncharted solutions while using his analytical proofs and counter-examples as a guide.