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With admirable clarity, math educators Alfred Posamentier and Ingmar Lehmann take us on a fascinating tour of the many ramifications of the Fibonacci numbers. The authors begin with a brief history of their distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West.
Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms pineapples, sunflowers, and daisies are just a few examples. In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio.
Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings. Sold by: Amazon. Designed for high-school students and teachers with an interest in mathematical problem-solving, this stimulating collection includes more than problems that are "off the beaten path" — i.
With few exceptions, their solution requires little more than some knowledge of elementary algebra, though a dash of ingenuity may help. Readers will find here thought-provoking posers involving equations and inequalities, diophantine equations, number theory, quadratic equations, logarithms, combinations and probability, and much more. The problems range from fairly easy to difficult, and many have extensions or variations the author calls "challenges.
That one question got you stumped? Skip to main content Alfred S. Something went wrong. Please try your request again later. Alfred S. He is the author and co-author of more than 60 mathematics books for teachers, secondary and elementary school students, and the general readership.
Posamentier is also a frequent commentator in newspapers and journals on topics relating to education. Posamentier has a B. In recognition of his outstanding teaching, the City College Alumni Association named him Educator of the Year in , and in In , he was also awarded the Grand Medal of Honor from the Republic of Austria, and in , upon approval of Parliament, the President of the Republic of Austria awarded him the title of University Professor of Austria.
He has taken on numerous important leadership positions in mathematics education locally. Are you an author? Help us improve our Author Pages by updating your bibliography and submitting a new or current image and biography. Learn more at Author Central. Previous page. Kindle Edition. Next page. There's a problem loading this menu right now.
Learn more about Amazon Prime. Get free delivery with Amazon Prime. Books By Alfred S. The Fabulous Fibonacci Numbers Jun 21, Posamentier , Ingmar Lehmann. The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence.
In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it 1, 1, 2, 3, 5, 8, 13, 21, ad infinitum. Far from being just a curiosity, this sequence recurs in structures found throughout nature? All of which is astounding evidence for the deep mathematical basis of the natural world.
Other Formats: Hardcover. Posamentier , Spreitzer, Christian,. 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 , 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 - , 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 - , 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 , 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. Posamentier , Charles T. Designed for high school students and teachers with an interest in mathematical problem-solving, this volume offers a wealth of nonroutine problems in geometry that stimulate students to explore unfamiliar or little-known aspects of mathematics.
Included are nearly problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency, and many other subjects.
Within each topic, the problems are arranged in approximate order of difficulty. Detailed solutions as well as hints are provided for all problems, and specific answers for most. Invaluable as a supplement to a basic geometry textbook, this volume offers both further explorations on specific topics and practice in developing problem-solving techniques. Other Formats: Paperback. Magnificent Mistakes in Mathematics Aug 13, 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 , with the aid of a mechanical desk calculator that ran for seventy hours, it was discovered that there was a mistake in the th 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.
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.
Posamentier , Robert L. With its coverage of plane, solid, coordinate, vector, and non-Euclidean geometry, this text is suitable for high school, college, and continuing education courses as well as independent study. Each new topic is carefully developed and clarified with many examples. More than 2, illustrations help students visualize the problems. Every set of exercises is preceded by numerous examples with detailed solutions. Chapters include a vocabulary list, set of review exercises, chapter test, and topics for suggested research.
Periodic cumulative reviews offer the opportunity for self-evaluation. Co-written by Alfred S. Posamentier, a bestselling author of high school and university textbooks and pioneer of educational standards, this volume is geared toward high school geometry classes and contains standard material for numerous state competencies.
An electronic solutions manual is available upon request. Posamentier , William L. Farber , Terri L. Germain-Williams , Elaine S.
Paris , Bernd Thaller , Ingmar H. The big benefits? 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 is just one of many entertaining examples of mathematical curiosities presented in this book. If you have been waiting for a book that will evoke the delight and intrigue that mathematics has to offer, this is the book for you.
Mathematics educators Alfred S Posamentier and Ingmar Lehmann have created the perfect introduction to the wonders of mathematics for the general reader, requiring only a high school background in the subject. Among the entertaining and useful tricks they teach are shortcuts in arithmetic, such as ways to determine at a glance the exact divisors of any given number.
They also demonstrate how the properties of certain numbers can lead to infinite loops. What is particularly exciting is how many correct answers turn out to be counterintuitive.
Exploring all these features will instill insights into the nature of numbers, improve your ability to manipulate them, and give you an appreciation for the inherent elegance of mathematics. Posamentier and Lehmann evoke the beauty of mathematics through the visual aspect of geometry. Enjoy with them the riches of the aesthetic and surprising properties to be found in triangles, quadrilaterals, and circles.
As you marvel at the many unusual relationships and novelties revealed in this ingenious and delightful presentation, you will be learning more maths than you ever thought possible - and will be relishing every moment of it!
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. 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. The Glorious Golden Ratio Dec 20, What exactly is the Golden Ratio? How was it discovered?
Alfred S. Posamentier
Alfred S. Posamentier born October 18, is an American educator and a lead commentator on American math and science education , regularly contributing to The New York Times and other news publications. Posamentier earned a Ph. He resides in River Vale , New Jersey. He is professor emeritus of mathematics education and former dean of the School of Education at The City College of the City University of New York, where he spent over 40 years. In , he was also awarded the Grand Medal of Honor from the Republic of Austria , [ citation needed ] and in , upon approval of Parliament, the President of the Republic of Austria awarded him the title of University Professor of Austria.
Challenging Problems in Geometry
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Books by Alfred S. Posamentier
With admirable clarity, math educators Alfred Posamentier and Ingmar Lehmann take us on a fascinating tour of the many ramifications of the Fibonacci numbers. The authors begin with a brief history of their distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms pineapples, sunflowers, and daisies are just a few examples. In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio. Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings. Sold by: Amazon.