Bøger af Alfred S. Posamentier

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.

We see numbers on automobile license plates, addresses, weather reports, and, of course, on our smartphones. Yet we look at these numbers for their role as descriptors, not as an entity in and unto themselves. Each number has its own history of meaning, usage, and connotation in the larger world. The Secret Lives of Numbers takes readers on a journey through integers, considering their numerological assignments as well as their significance beyond mathematics and in the realm of popular culture. Of course we all know that the number 13 carries a certain value of unluckiness with it. The phobia of the number is called Triskaidekaphobia; Franklin Delano Roosevelt was known to invite and disinvite guests to parties to avoid having 13 people in attendance; high-rise buildings often skip the 13th floor out of superstition. There are many explanations as to how the number 13 received this negative honor, but from a mathematical point of view, the number 13 is also the smallest prime number that when its digits are reversed is also a prime number. It is honored with a place among the Fibonacci numbers and integral Pythagorean triples, as well as many other interesting and lesser-known occurrences. In The Secret Lives of Numbers, popular mathematician Alfred S. Posamentier provides short and engaging mini-biographies of more than 100 numbers, starting with 1 and featuring some especially interesting numbers -like 6,174, a number with most unusual properties -to provide readers with a more comprehensive picture of the lives of numbers both mathematically and socially.

A veteran math educator reveals the hidden fascinations of geometry and why this staple of math education is important.If you remember anything about high school geometry class, it's probably doing proofs. But geometry is more than axioms, postulates, theorems, and proofs. It's the science of beautiful and extraordinary geometric relationships--most of which is lost in high school classrooms where the focus is on the rigor of logically proving those relationships. This book will awaken readers to the appeal of geometry by placing the focus squarely on geometry's visually compelling features and intrinsic elegance. Who knew that straight lines, circles, and area could be so interesting? Not to mention optical illusions. So get out the rulers, compasses, or even a software program, and discover geometry for the first time.

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 École 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.

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 promises to help teachers and all readers do just that by revealing some wonders of mathematics often missing from classrooms. Here's your chance to catch up with the math gems you may have missed in your school years.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 a grasp of math you never thought possible and a true appreciation for this "queen of the sciences."

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 geometryleading 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 "e;full circle"e; this presentation of a key element of geometry.

Did you grow up thinking math is boring? It's time to reconsider. This book will teach you everything you ever wondered about numbersand more.How and why did human beings first start using numbers at the dawn of history? Would numbers exist if we Homo sapiens weren't around to discover them? What's so special about weird numbers like pi and the Fibonacci sequence? What about rational, irrational, real, and imaginary numbers? Why do we need them?Two veteran math educators explain it all in ways even the most math phobic will find appealing and understandable.You'll never look at those squiggles on your calculator the same again.

Two veteran math educators demonstrate how some "e;magnificent mistakes"e; 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 "e;prove"e; that every triangle is isosceles, we are violating a concept not even known to Euclid - that of "e;betweenness."e; 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.

What Successful Math Teachers Do is a powerful portal to what the best research looks like in practice, strategy by strategy-now aligned to both the Common Core and the NCTM Standards.

Anticipate common math questions, eliminate pat responses, and provide explanations that are certain to engage and motivate students. Al Posamentier and his coauthors have all the answers.

All the basics of geometry in a motivating new format, from Ptolemy to Napoleon, from the Arbelos to the billiard table!

This easy-to-use reference tool translates the latest research results and provides tips for K-12 math teachers.

Crammed with strategies, ideas, and techniques to help you boost your students' math SAT I scores.

Number Theory, Geometry, Topology, Binary and Exponential Arithmetic, and much, much more!

We should all be having fun with math and helping our kids to do better in life by encouraging them to appreciate not only its usefulness but especially its charm. This book is intended for adults looking for a way to turn their kids on to an important subject or discover for themselves what they might have missed in their own math education.

What are the odds of finding two people who share the same birth date in a room of thirty-five? Most people would guess they're pretty low. In actuality, the probability is better than 80 percent. This book features examples of mathematical curiosities.

This updated edition presents ten strategies for solving a wide range of mathematics problems, plus new sample problems.

Algebraic Identities, the Fibonacci Sequence, Patterns in Mathematics, Odds, Means, Averages . . . and that's only the beginning!

Invigorate instruction and engage students with this updated treasure trove of 114 ready-to-use techniques compiled by two of the greatest minds in mathematics.