Alfred S. Posamentier

Ingmar Lehmann

An innovative and appealing way for the layperson to develop math skills--while actually enjoying it Most 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.

A Treasure Trove of Unexpected Entertainments

Mathematical Curiosities

Requiring no more than a knowledge of high school mathematics and written in clear and accessible language, this book will give all readers a new insight into some of the most enjoyable and fascinating aspects of geometry. Everyone knows what a triangle is, yet very few people appreciate that the common three-sided figure holds many intriguing "secrets." For example, if a circle is inscribed in any random triangle and then three lines are drawn from the three points of tangency to the opposite vertices of the triangle, these lines will always meet at a common point-no matter what the shape of the triangle. This and many more interesting geometrical properties are revealed in this entertaining and illuminating book about geometry. Flying in the face of the common impression that mathematics is usually dry and intimidating, this book proves that this sometimes-daunting, abstract discipline can be both fun and intellectually stimulating. The authors, two veteran math educators, explore the multitude of surprising relationships connected with triangles and show some clever approaches to constructing triangles using a straightedge and a compass. Readers will learn how they can improve their problem-solving skills by performing these triangle constructions. The lines, points, and circles related to triangles harbor countless surprising relationships that are presented here in a very engaging fashion.

A Mathematical Journey

The Secrets of Triangles

The Fabulous Fibonacci Numbers

A Biography of the World's Most Mysterious Number

The Glorious Golden Ratio

PI-this seemingly mundane numer-holds a world of mystery, which has fascinated mathematicians from ancient times to the present. What is PI? What is the real value of PI? How to mathematicians determine the value of PI? In what ways is PI used? How was it calculated in ancient times? Its elusive nature has led investigators over the years to ever-closer approximations.

: A Biography Of The World's Most Mysterious Number

Afterword by Dr. Herbert A. Hauptman, Nobel LaureateThis delightful book reveals an incredibly interesting history of the development of our knowledge of this ubiquitous number in mathematics. . . . I recommend this book to anyone who remembers ever hearing about Pi!-Stanley H. Kaplan, Founder of the Kaplan Test Preparation and Admission Programs. . . Read this book and enjoy the journey through the mysteries of pi. Give it to your students and you will have aroused their appreciation of the many wonders of mathematics.-Alice F. Artzt, Professor of Mathematics Education; Director of Undergraduate and Graduate Secondary Mathematics Education, Queens College of the City University of New York. . . The history of pi and the attempts to fully understand what it represents makes for amusing, interesting and enjoyable reading.-Dr. Stephen Krulik, Professor of Mathematics Education, Temple UniversityWe all learned that the ratio of the circumference of a circle to its diameter is called p and that the value of this algebraic symbol is roughly 3.14. What we weren't told, though, is that behind this seemingly mundane fact is a world of mystery, which has fascinated mathematicians from ancient times to the present.Mathematicians call it a transcendental number because its value cannot be calculated by any combination of addition, subtraction, multiplication, division, and square root extraction. This elusive nature has led intrepid investigators over the years to attempt ever-closer approximations. In 2002, a Japanese professor using a supercomputer calculated the value to 1.24 trillion decimal places! Nonetheless, in this huge string of decimals there is no periodic repetition.In this delightful layperson's introduction to one of math's most interesting phenomena, Drs. Posamentier and Lehmann review p's history from prebiblical times to the 21st century, the many amusing and mind-boggling ways of estimating ? over the centuries, quirky examples of obsessing about p (including an attempt to legislate its exact value), and useful applications of p in everyday life, including statistics.This enlightening and stimulating approach to mathematics will entertain lay readers while improving their mathematical literacy.Alfred S. Posamentier, Ph.D. (New York, NY), is dean of the School of Education and professor of mathematics education at The City College of the City University of New York. He has published more than 40 books in the area of mathematics and mathematics education, including The Fabulous Fibonacci Numbers, Pi: A Biography of the World's Most Mysterious Number, and Math Charmers: Tantalizing Tidbits for the Mind..Ingmar Lehmann, Ph.D. (Berlin, Germany), is a mathematics educator at Humboldt University in Berlin and is the coauthor of The Fabulous Fibonacci Numbers and Pi: A Biography of the World's Most Mysterious Number.

Two 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. 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.

Magnificent Mistakes in Mathematics

What exactly is the Golden Ratio? How was it discovered? Where is it found? These questions and more are thoroughly explained in this engaging tour of one of mathematics' most interesting phenomena. The authors trace the appearance of the Golden Ratio throughout history, demonstrate a variety of ingenious techniques used to construct it, and illustrate the many surprising geometric figures in which the Golden Ratio is embedded. Requiring no more than an elementary knowledge of geometry and algebra, the authors give readers a new appreciation of the indispensable qualities and inherent beauty of mathematics.

Ingmar Lehmann

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