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Magnificent Mistakes in Mathematics

by Alfred S. Posamentier Ingmar Lehmann

Requiring no more than high-school-level math competency, this playful excursion through the nuances of math will give you a better grasp of this fundamental, all-important science. Veteran math educators demonstrate how some "magnificent mistakes" had profound consequences for our understanding of mathematics' key concepts. In the nineteenth century, English mathematician William Shanks spent fifteen years calculating the value of pi, setting a record for the number of decimal places. Later, his calculation was reproduced using large wooden numerals to decorate the cupola of a hall in the Palais de la Découverte in Paris. However, in 1946, with the aid of a mechanical desk calculator that ran for seventy hours, it was discovered that there was a mistake in the 528th decimal place. Today, supercomputers have determined the value of pi to trillions of decimal places. This is just one of the amusing and intriguing stories about mistakes in mathematics in this layperson's guide to mathematical principles. In another example, the authors show that when we "prove" that every triangle is isosceles, we are violating a concept not even known to Euclid-that of "betweenness." And if we disregard the time-honored Pythagorean theorem, this is a misuse of the concept of infinity. Even using correct procedures can sometimes lead to absurd-but enlightening-results.

Mathematical Curiosities

by Alfred S. Posamentier Ingmar Lehmann

An innovative and appealing way for the layperson to develop math skills--while actually enjoying itMost people agree that math is important, but few would say it's fun. This book will show you that the subject you learned to hate in high school can be as entertaining as a witty remark, as engrossing as the mystery novel you can't put down--in short, fun! As veteran math educators Posamentier and Lehmann demonstrate, when you realize that doing math can be enjoyable, you open a door into a world of unexpected insights while learning an important skill.The authors illustrate the point with many easily understandable examples. One of these is what mathematicians call the "Ruth-Aaron pair" (714 and 715), named after the respective career home runs of Babe Ruth and Hank Aaron. These two consecutive integers contain a host of interesting features, one of which is that their prime factors when added together have the same sum. The authors also explore the unusual aspects of such numbers as 11 and 18, which have intriguing properties usually overlooked by standard math curriculums. And to make you a better all-around problem solver, a variety of problems is presented that appear simple but have surprisingly clever solutions.If math has frustrated you over the years, this delightful approach will teach you many things you thought were beyond your reach, while conveying the key message that math can and should be anything but boring.

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