This second edition of Alexander Soifer’s How Does One Cut a Triangle? demonstrates how different areas of mathematics can be juxtaposed in the solution ofa given problem. The author employs geometry, algebra, trigonometry, linear algebra, and rings to develop a miniature model of mathematical research. How Does One Cut a Triangle? contains dozens of proofs and counterexamples to a variety of problems, such as a pool table problem, a fifty-dollar problem, a five-point problem, and a joint problem. By proving these examples, the author demonstrates that research is a collection of mathematical ideas that have been developed throughout the course of history. The author brings mathematics aliveby giving the reader a taste of what mathematicians do. His book presents open problems that invite the reader to play the role of the mathematician. By doing so, the author skillfully inspires the discovery of uncharted solutions using his solutions as a guide. INDICE: Forewords.- Preface.- Part I: The Original Book.- Pool Table, Irrational Numbers, and Integral Independence.- How does One Cut a Triangle? I.- Excursions in Algebra.- How Does One Cut a Triangle? II.- Excursion in Trigonometry.- Is There Anything Beyond the Solution?.- Pursuit of the Best Result.- Convex Figures and the Function S(F).- Faul Erdos: Our Joint Problems.- Convex Figures and Erdos' Function.- Part II: Developments of the Subsequent 20 Years.- An Alternative Proof of the Grand Problem II.- Miklos Lasckovich on CuttingTriangles.- Soifer's $50 Problem and Mitya Karabash.- Conway-Soifer's Cover-Up.- Appendices.- References.- Notation.-Index.
- ISBN: 978-0-387-74650-0
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 174
- Fecha Publicación: 01/09/2009
- Nº Volúmenes: 1
- Idioma: Inglés