Charming Proofs: A Journey Into Elegant MathematicsMAA, 2010 - 295 páginas "Theorems and their proofs lie at the heart of mathematics. In speaking of the purely aesthetic qualities of theorems and proofs, G. H. Hardy wrote that in beautiful proofs 'there is a very high degree of unexpectedness, combined with inevitability and economy'. Charming Proofs present a collection of remarkable proofs in elementary mathematics that are exceptionally elegant, full of ingenuity, and succinct. By means of a surprising argument or a powerful visual representation, the proofs in this collection will invite readers to enjoy the beauty of mathematics, to share their discoveries with others, and to become involved in the process of creating new proofs. Charming Proofs is organized as follows. Following a short introduction about proofs and the process of creating proofs, the authors present, in twelve chapters, a wide and varied selection of proofs they consider charming, Topics include the integers, selected real numbers, points in the plane, triangles, squares, and other polygons, curves, inequalities, plane tilings, origami, colorful proofs, three-dimensional geometry, etc. At the end of each chapter are some challenges that will draw the reader into the process of creating charming proofs. There are over 130 such challenges. Charming Proofs concludes with solutions to all of the challenges, references, and a complete index. As in the authors' previous books with the MAA (Math Made Visual and When Less Is More), secondary school and college and university teachers may wish to use some of the charming proofs in their classrooms to introduce their students to mathematical elegance. Some may wish to use the book as a supplement in an introductory course on proofs, mathematical reasoning, or problem solving."--Publisher's description. |
Otras ediciones - Ver todo
Charming Proofs: A Journey Into Elegant Mathematics Claudi Alsina,Roger B. Nelsen Vista previa restringida - 2010 |
Charming Proofs: A Journey into Elegant Mathematics Claudi Alsina,Roger B. Nelsen Vista previa restringida - 2010 |
Términos y frases comunes
Additional angles appear base begin Book called Challenges CHAPTER circle color complete consequence consider construct convex count create cube curve cyclic dark gray denote diagonals distance divides draw edge Elements equal equilateral triangle example exists faces figure first fold formula four functional equation geometry given golden hence hexagon illustrated in Figure inequality infinite inscribed integer intersection irrational isosceles joining known lattice least Lemma length limit line segments lunes Mathematical mean median midpoint n-gon opposite original pair parallel parallelogram partition pentagon perpendicular plane points polygon positive integers present prime problem proof properties Prove Pythagorean theorem quadrilateral radius ratio rectangle regions regular result right triangle rotation sequence shaded shown in Figure sides similar Similarly simple solution sphere square tiling triangular true vertex vertices yields