Alfred S. Posamentier

In this delightful layperson's introduction to one of math's most interesting phenomena, Drs Posamentier and Lehmann review p's history from pre-biblical times to the 21st century, the many amusing and mind-boggling ways of estimating p 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.

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.

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.

It is no secret that most people avoid mathematics, in large measure because elementary school teachers have never done much to motivate a love of the subject matter. In his latest book, mathematician Alfred S. Posamentier provides easily understandable, easily presentable and easily replicated tricks that one can do with mathematics. All that is required is the ability to do arithmetic, understand the very basics of algebra and geometry and have an open mind for probability. From geometrical puzzles to numerical quirks, Math Tricks will give readers that "aha!" moment they may never have received at school.

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. ,

An innovative and appealing way for the layperson to develop math skillswhile actually enjoying it Most people agree that math is important, but few would say its 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 cant put downin 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.

Did you grow up thinking math is boring? Its time to reconsider. This book will teach you everything you ever wondered about numbers-and more. How and why did human beings first start using numbers at the dawn of history? Would numbers exist if we Homo sapiens werent around to discover them? Whats 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. Youll never look at those squiggles on your calculator the same again.

In this delightful laypersons introduction to one of maths most interesting phenomena, Drs. Posamentier and Lehmann review pis history from prebiblical times to the 21st century, the many amusing and mind-boggling ways of estimating pi over the centuries, quirky examples of obsessing about pi, and useful applications of pi in everyday life, including statistics.

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 laypersons 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.

El número Pi reina en un mundo de misterio, ¿Que ha fascinado el valor real de Pi? ¿Cómo determinan los matemáticos el valor de Pi? ¿Cómo se utiliza Pi? ¿Cómo se calculaba Pi antaño? Su esquiva naturaleza ha conducido a los investigadores con el paso de los años a aproximaciones cada vez mas exactas. Este ubicuo numero aparece cuando menos te lo esperas, por ejemplo, en el calculo de probabilidades o en los estudios biblicos. Ademas, presentan algunos ejemplos peculiares de la obsesion con Pi durante siglos, incluido el intento por legislar su valor exacto e incluso una cancion sobre Pi, ademas de aplicaciones muy utiles de Pi en la vida cotidiana. Los matematicos denominan a Pi “numero trascendental” porque su curioso valor no puede ser calculado a traves de ninguna combinacion de sumas, restas, multiplicaciones, divisiones o raices cuadradas. Aun mas curioso, al margen del numero de decimales que se quieran calcular del valor de Pi, el decimal jamas se repite. En el año 2002, un profesor japones calculo con ayuda de un supercomputador el valor de Pi ¡con mil doscientos cuarenta mil millones de decimales!. Sin embargo, en esta ingente cadena de decimales no hay ninguna repeticion periodica. “Un libro esclarecedor sobre uno de los grandes misterios de

The circle has fascinated mathematicians since ancient times. This entertaining book describes in laypersons 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 circles place on the sphere bring "full circle" this presentation of a key element of geometry.

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 calculushe 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 studentshe is remembered for her work on Fermats Last Theorem and on elasticity theory; Emmy Noether (1882 - 1935), whom Albert Einstein described as the most important woman in the history of mathematicsshe 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.

Two experienced math educators help the average reader discover not only the everyday usefulness of math but the fun that comes from mastering the basics of arithmetic, algebra, geometry, and more. If you think of mathematics as a series of pointless classroom exercises without much relevance to real life, this book will change your mind. As the authors show, math is deeply embedded in almost every aspect of daily life--from managing your personal finances, making consumer purchases, and sharpening your computational skills, to learning to apply mathematical concepts that will give you a better grasp of both ordinary and extraordinary events and help you better appreciate the world we live in. With some basic geometry under your belt, youll discover that there is an optimal point on a soccer field from which to shoot a goal. And youll be more clever with the gears of a bike. If you like to play cards or go to the casino, knowing something about probability will give you an edge. Youll also have an enhanced understanding of the "whispering effect" inside the Capitol rotunda, why a cars headlights are so bright, and even why sewer covers are round. After reading this entertaining and instructive book, youll come away with a whole new awareness of how elegantly mathematics explains everyday experiences and observations--from present day items to classical art and architecture.