Author: Claudi Alsina
Publisher: American Mathematical Soc.
ISBN: 1614442010
Category : Mathematics
Languages : en
Pages : 321
Get Book Here
Book Description
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, threedimensional 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, 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.
Author: Claudi Alsina
Publisher: MAA
ISBN: 0883853485
Category : Mathematics
Languages : en
Pages : 321
Get Book Here
Book Description
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 presents 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, and to develop the ability to create proofs themselves. The authors consider proofs from topics such as geometry, number theory, inequalities, plane tilings, origami and polyhedra. Secondary school and university teachers can use this book to introduce their students to mathematical elegance. More than 130 exercises for the reader (with solutions) are also included.
Author: Claudi Alsina
Publisher: MAA
ISBN: 0883853523
Category : Mathematics
Languages : en
Pages : 348
Get Book Here
Book Description
An exploration of the mathematics of twenty geometric diagrams that play a crucial role in visualizing mathematical proofs. Those teaching undergraduate mathematics will find material here for problem solving sessions, as well as enrichment material for courses on proofs and mathematical reasoning.
Author:
Publisher: Bloomsbury Publishing USA
ISBN: 0802714315
Category : Mathematics
Languages : en
Pages : 65
Get Book Here
Book Description
Q.E.D. presents some of the most famous mathematical proofs in a charming book that will appeal to nonmathematicians and math experts alike. Grasp in an instant why Pythagoras's theorem must be correct. Follow the ancient Chinese proof of the volume formula for the frustrating frustum, and Archimedes' method for finding the volume of a sphere. Discover the secrets of pi and why, contrary to popular belief, squaring the circle really is possible. Study the subtle art of mathematical domino tumbling, and find out how slicing cones helped save a city and put a man on the moon.
Author: Roger B. Nelsen
Publisher: MAA
ISBN: 9780883857007
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 166
Get Book Here
Book Description
Author: Arthur T. Benjamin
Publisher: American Mathematical Society
ISBN: 1470472597
Category : Mathematics
Languages : en
Pages : 210
Get Book Here
Book Description
Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.
Author: Philip Ording
Publisher: Princeton University Press
ISBN: 0691218978
Category : Mathematics
Languages : en
Pages : 272
Get Book Here
Book Description
An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo—whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp—Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau’s Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird’s-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.
Author: Bierbaum
Publisher:
ISBN:
Category :
Languages : en
Pages : 282
Get Book Here
Book Description
Author: Friedrich Julius Bierbaum
Publisher:
ISBN:
Category :
Languages : en
Pages : 342
Get Book Here
Book Description
Author: Friedrich Julius Bierbaum
Publisher:
ISBN:
Category : English language
Languages : en
Pages : 344
Get Book Here
Book Description
