Alfred S Posamentier

'The physical form of this new title is pleasing, including good paper, readable font, and durable binding … The book is not a collection of practical ideas. Rather, it is intended for those curious about pure mathematical tidbits. The flavor is light, as opposed to pedantic. Among the numerous books of this type, this title is significantly better than most. It should be considered for private collections and for libraries that can afford to serve a small, unique readership. Summing Up: Recommended. General readers.'CHOICEThis book demonstrates to the general audience that mathematics can be entertaining and fun, rather than the sad reputation it has gained over decades from uninspired school instruction that is often devoid of enrichment or motivational considerations. The book is designed in such a way that a reader will need almost no special preparation in mathematics, but to recall some of the most basic concepts that were taught at the lower-secondary-grade level. Yet, by the same token, the book will hopefully open up doors for those less motivated in mathematics — to interest readers to investigate some of the topics presented and thereby enhance their knowledge of mathematics — something most general readers will not initially find possible, but we hope will be an end product of this book.

This book will present a collection of mathematical problems — lighthearted in nature — intended to entertain the general readership. Problems will be selected largely for the unusual and unexpected solutions to which they lend themselves. Some interesting contents included: All in all, the book is meant to entertain the general readership and to convince them about the power and beauty of mathematics.

This book will present a collection of mathematical problems — lighthearted in nature — intended to entertain the general readership. Problems will be selected largely for the unusual and unexpected solutions to which they lend themselves. Some interesting contents included: All in all, the book is meant to entertain the general readership and to convince them about the power and beauty of mathematics.

An entertaining history of mathematics as chronicled through fifty short biographies. Mathematics today is the fruit of centuries of brilliant insights by men and women whose personalities and life experiences were often as extraordinary as their mathematical achievements. This entertaining history of mathematics chronicles those achievements through fifty short biographies that bring these great thinkers to life while making their contributions understandable to readers with little math background. Among the fascinating characters profiled are Isaac Newton (1642-1727), the founder of classical physics and infinitesimal calculus--he frequently quarreled with fellow scientists and was obsessed by alchemy and arcane Bible interpretation; Sophie Germain (1776 - 1831), who studied secretly at the Ecole Polytechnique in Paris, using the name of a previously enrolled male student--she is remembered for her work on Fermat's Last Theorem and on elasticity theory; Emmy Noether (1882 - 1935), whom Albert Einstein described as the most important woman in the history of mathematics--she made important contributions to abstract algebra and in physics she clarified the connection between conservation laws and symmetry; and Srinivasa Ramanujan (1887-1920), who came from humble origins in India and had almost no formal training, yet made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions. The unusual behavior and life circumstances of these and many other intriguing personalities make for fascinating reading and a highly enjoyable introduction to mathematics.

The art or skill of problem solving in mathematics is mostly relegated to the strategies one can use to solve problems in the field. Although this book addresses that issue, it delves deeply into the psychological aspects that affect successful problem-solving. Such topics as decision-making, judgment, and reasoning as well as using memory effectively and a discussion of the thought processes that could help address certain problem-solving situations. Most books that address problem-solving and mathematics focus on the various skills. This book goes beyond that and investigates the psychological aspects to solving problems in mathematics.

'The reference list is excellent. This is a worthwhile (though 'niche') book that will be attractive to a particular sector of the general reading public interested in mathematical riddles and puzzles. Professional educators might well employ it in integrated learning settings. Summing Up: Recommended. All readers.'CHOICEImmerse yourself in the fascinating world of geometry and spatial ability — either individually or in small groups, either as challenges or play problems! Here are four reasons why you should work with this book:This book offers a very unique opportunity to enhance your spatial ability, your mathematical competence, and your logical thinking. The authors arranged 45 problems — including more than 120 tasks — in a well-balanced order, which have been tested with a variety of populations.

'The reference list is excellent. This is a worthwhile (though 'niche') book that will be attractive to a particular sector of the general reading public interested in mathematical riddles and puzzles. Professional educators might well employ it in integrated learning settings. Summing Up: Recommended. All readers.'CHOICEImmerse yourself in the fascinating world of geometry and spatial ability — either individually or in small groups, either as challenges or play problems! Here are four reasons why you should work with this book:This book offers a very unique opportunity to enhance your spatial ability, your mathematical competence, and your logical thinking. The authors arranged 45 problems — including more than 120 tasks — in a well-balanced order, which have been tested with a variety of populations.

Parents need to take an ever-increasing role in their child's learning experience. However, what to do and how to do it is often not prescribed to the parents. This book offers a wide variety of aspects related to the parent's role as a support to their child's learning of mathematics, and above all appreciation for the subject. The uniqueness of this book is that we provide the parent the information they need about how mathematics is taught in today's early grades. We then provide a plethora of ideas that can motivate children with information beyond that which is taught in the classroom.

Parents need to take an ever-increasing role in their child's learning experience. However, what to do and how to do it is often not prescribed to the parents. This book offers a wide variety of aspects related to the parent's role as a support to their child's learning of mathematics, and above all appreciation for the subject. The uniqueness of this book is that we provide the parent the information they need about how mathematics is taught in today's early grades. We then provide a plethora of ideas that can motivate children with information beyond that which is taught in the classroom.

Many schools throughout the United States are now employing coaches to support teachers in the teaching of mathematics. Very often, these are professionals selected from the current teaching ranks who did not receive any special training to serve as a coach. This book provides the skills, knowledge, and lessons from experience that lead such a mentor to function effectively. Aside from describing the basic duties of an effective math coach, we also provide a plethora of resources to enrich instruction, improve problem-solving direction, and provide teachers with a wide variety of techniques to enhance their teaching effectiveness.

Wouldn't it be great if all school teachers (from kindergarten through high school) would share the joy of mathematics with their students, rather than focus only on the prescribed curriculum that will subsequently be tested? This book reveals some of the wonders of mathematics that are often missing from classrooms. Here's your chance to catch up with the math gems you may have missed. Using jargon-free language and many illustrations, the authors--all veteran math educators--explore five areas--arithmetic, algebra, geometry, probability, and the ways in which mathematics can reinforce common sense. Among other things, you'll learn "the rule of 72," which enables you to quickly determine how long it will take your bank account to double its value at a specific interest rate. Other handy techniques include an automatic algorithm for multiplying numbers mentally and a clever application that will allow you to convert from miles to kilometers (or the reverse) mentally. A delightful presentation of geometric novelties reveals relationships that could have made your study of geometry more fun and enlightening. In the area of probability there is a host of interesting examples: from the famous Monty-Hall problem to the counterintuitive probability of two people having the same birthday in a crowded room. Finally, the authors demonstrate how math will make you a better thinker by improving your organizing abilities and providing useful and surprising solutions to common mathematics problems. You'll come away with an appreciation for math you never thought possible and a true appreciation for this "queen of the sciences."

Games are seen only for recreation. However, this book shows that games can be used to strengthen problem-solving skills and beyond. This book presents strategy games and discusses for each one solutions towards a winning position in the game. In most cases, these strategies are analogous to problem-solving strategies in mathematics. Readers are also exposed to a wide variety of games from several different cultures, which will broaden the perspective of the readers.

Games are seen only for recreation. However, this book shows that games can be used to strengthen problem-solving skills and beyond. This book presents strategy games and discusses for each one solutions towards a winning position in the game. In most cases, these strategies are analogous to problem-solving strategies in mathematics. Readers are also exposed to a wide variety of games from several different cultures, which will broaden the perspective of the readers.

The circle has fascinated mathematicians since ancient times. This entertaining book describes in layperson's terms the many intriguing properties of this fundamental shape. If math has intimidated you, this may be the ideal book to help you appreciate the discipline through one of its most important elements. The authors begin with a brief review of the basic properties of the circle and related figures. They then show the many ways in which the circle manifests itself in the field of geometry--leading to some amazing relationships and truly important geometric theorems. In addition, they explore remarkable circle constructions and demonstrate how all constructions in geometry that usually require an unmarked straightedge and a compass can also be done with the compass alone. Among other things, the reader will learn that circles can generate some unusual curves - many even quite artistic. Finally, the role of circles in art and architecture and a discussion of the circle's place on the sphere bring "full circle" this presentation of a key element of geometry.

This book introduces ten problem-solving strategies by first presenting the strategy and then applying it to problems in elementary mathematics. In doing so, first the common approach is shown, and then a more elegant strategy is provided. Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics.

This book introduces ten problem-solving strategies by first presenting the strategy and then applying it to problems in elementary mathematics. In doing so, first the common approach is shown, and then a more elegant strategy is provided. Elementary mathematics is used so that the reader can focus on the strategy and not be distracted by some more sophisticated mathematics.

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.

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 Decouverte 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.

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. 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.

The Pythagorean theorem may be the best-known equation in mathematics. Its origins reach back to the beginnings of civilization, and today every student continues to study it. What most nonmathematicians don't understand or appreciate is why this simply stated theorem has fascinated countless generations. In this entertaining and informative book, a veteran math educator makes the importance of the Pythagorean theorem delightfully clear. He begins with a brief history of Pythagoras and the early use of his theorem by the ancient Egyptians, Babylonians, Indians, and Chinese, who used it intuitively long before Pythagoras's name was attached to it. He then shows the many ingenious ways in which the theorem has been proved visually using highly imaginative diagrams. Some of these go back to ancient mathematicians; others are comparatively recent proofs, including one by the twentieth president of the United States, James A. Garfield. After demonstrating some curious applications of the theorem, the author then explores the Pythagorean triples, pointing out the many hidden surprises of the three numbers that can represent the sides of the right triangle (e.g, 3, 4, 5 and 5, 12, 13). And many will truly amaze the reader. He then turns to the "Pythagorean means" (the arithmetic, geometric, and harmonic means). By comparing their magnitudes in a variety of ways, he gives the reader a true appreciation for these mathematical concepts. The final two chapters view the Pythagorean theorem from an artistic point of view - namely, how Pythagoras's work manifests itself in music and how the Pythagorean theorem can influence fractals. The author's lucid presentation and gift for conveying the significance of this key equation to those with little math background will inform, entertain, and inspire the reader, once again demonstrating the power and beauty of mathematics!