Alfred S. Posamentier – författare

State curriculum standards are mandating more coverage of geometry, as are the curricula for pre-service mathematics education and in-service teaching. Yet many secondary teachers know just enough geometry to stay one chapter ahead of their students! What’s more, most college-level geometry texts don’t address their specific needs. Advanced Euclidean Geometry fills this void by providing a thorough review of the essentials of the high school geometry course and then expanding those concepts to advanced Euclidean geometry, to give teachers more confidence in guiding student explorations and questions.  The text contains hundreds of illustrations created in The Geometer’s Sketchpad Dynamic Geometry® software, and it is packaged with a CD-ROM (for Windows®/Macintosh® formats) containing over 100 interactive sketches using Sketchpad™ (assumes that the user has access to the program).

Stimulating collection of over 300 unusual problems involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms and more. Problems range from easy to difficult. Detailed solutions, as well as brief answers, for all problems are provided.

Activities in Pre-Algebra is a set of versatile enrichment exercises that covers a very broad range of mathematical topics and applications-from the Moebius strip to the googol. Several criteria have been used in developing the activities and in selecting the topics that are included. All of them bear heavily, and equally, on our concerns for curriculum goals and classroom management. Each activity is presented as a reproducible student investigation. It is followed by guidelines and notes for the teacher. Each activity is keyed to the National Council of Teachers of Mathematics (NCTM) Standards, Revised. This link to the NCTM standards allows teachers to facilitate linking classroom activities to specific state and school district content standards. First and foremost, the activities are meant to be motivational. As much as possible, we want this book to achieve the goal of being attractive to people who thought they didn′t like mathematics. To accomplish this, it is necessary for the activities to be quite different from what students encounter in their basal texts-different in both substance and form. This seems especially critical; no matter how excellent a basal text is being used, nearly every class experiences the "blahs." Unfortunately, this sort of boredom is often well entrenched long before the teacher and perhaps even the students are aware of it. Presenting activities on a regular basis gives the variety and change of pace needed to sustain interest in any subject.

Activities in Pre-Algebra is a set of versatile enrichment exercises that covers a very broad range of mathematical topics and applications-from the Moebius strip to the googol. Several criteria have been used in developing the activities and in selecting the topics that are included. All of them bear heavily, and equally, on our concerns for curriculum goals and classroom management. Each activity is presented as a reproducible student investigation. It is followed by guidelines and notes for the teacher. Each activity is keyed to the National Council of Teachers of Mathematics (NCTM) Standards, Revised. This link to the NCTM standards allows teachers to facilitate linking classroom activities to specific state and school district content standards. First and foremost, the activities are meant to be motivational. As much as possible, we want this book to achieve the goal of being attractive to people who thought they didn′t like mathematics. To accomplish this, it is necessary for the activities to be quite different from what students encounter in their basal texts-different in both substance and form. This seems especially critical; no matter how excellent a basal text is being used, nearly every class experiences the "blahs." Unfortunately, this sort of boredom is often well entrenched long before the teacher and perhaps even the students are aware of it. Presenting activities on a regular basis gives the variety and change of pace needed to sustain interest in any subject.

Activities in Algebra is a set of versatile enrichment exercises that covers a very broad range of mathematical topics and applications-from the Moebius strip to the googol. Several criteria have been used in developing the activities and in selecting the topics that are included. All of them bear heavily, and equally, on our concerns for curriculum goals and classroom management. Each activity is presented as a reproducible student investigation. It is followed by guidelines and notes for the teacher. Each activity is keyed to the National Council of Teachers of Mathematics (NCTM) Standards, Revised. This link to the NCTM standards allows teachers to facilitate linking classroom activities to specific state and school district content standards. First and foremost, the activities are meant to be motivational. As much as possible, we want this book to achieve the goal of being attractive to people who thought they didn′t like mathematics. To accomplish this, it is necessary for the activities to be quite different from what students encounter in their basal texts-different in both substance and form. This seems especially critical; no matter how excellent a basal text is being used, nearly every class experiences the "blahs." Unfortunately, this sort of boredom is often well entrenched long before the teacher and perhaps even the students are aware of it. Presenting activities on a regular basis gives the variety and change of pace needed to sustain interest in any subject.

Activities in Algebra is a set of versatile enrichment exercises that covers a very broad range of mathematical topics and applications-from the Moebius strip to the googol. Several criteria have been used in developing the activities and in selecting the topics that are included. All of them bear heavily, and equally, on our concerns for curriculum goals and classroom management. Each activity is presented as a reproducible student investigation. It is followed by guidelines and notes for the teacher. Each activity is keyed to the National Council of Teachers of Mathematics (NCTM) Standards, Revised. This link to the NCTM standards allows teachers to facilitate linking classroom activities to specific state and school district content standards. First and foremost, the activities are meant to be motivational. As much as possible, we want this book to achieve the goal of being attractive to people who thought they didn′t like mathematics. To accomplish this, it is necessary for the activities to be quite different from what students encounter in their basal texts-different in both substance and form. This seems especially critical; no matter how excellent a basal text is being used, nearly every class experiences the "blahs." Unfortunately, this sort of boredom is often well entrenched long before the teacher and perhaps even the students are aware of it. Presenting activities on a regular basis gives the variety and change of pace needed to sustain interest in any subject.

Activities in Geometry is a set of versatile enrichment exercises that covers a very broad range of topics in geometry-Euclidean, post-Euclidean, and non-Euclidean. Several criteria have been used in developing the activities and in selecting the topics that are included. All of them bear heavily, and equally, on our concerns for curriculum goals and classroom management. Each activity is presented as a reproducible student investigation. It is followed by guidelines and notes for the teacher. Each activity is keyed to the National Council of Teachers of Mathematics (NCTM) Standards, Revised. This link to the NCTM standards allows teachers to facilitate linking classroom activities to specific state and school district content standards. First and foremost, the activities are meant to be motivational. As much as possible, we want this book to achieve the goal of being attractive to students and show them that there is much more to geometry that proving theorems. To demonstrate this aspect of geometry, it is necessary for the investigation to be quite different from what students encounter in their basal texts-different in both substance and form. Presenting activities on a regular basis gives the variety and change of pace needed to sustain interest in any subject

As a mathematics teacher, you know how hard it can be for your students to understand and solve math problems. The old ways of problem solving don′t always work. Even the most innovative teachers need some fresh ideas to make mathematics something students comprehend and enjoy. Problem solving is the main theme of this new, idea-filled handbook. The chapter authors look at the subject in a completely new light, and the result is an enticing, entertaining, and useful resource. The editors of this guidebook present a host of interesting ideas that range from practical to theoretical, from common to glitzy, that you can adapt for use in your classroom. With margin notes identifying subject matter and strategy type, this book is as easy to read as it is valuable. Full of important ideas on: * Interest grabbers * The pigeonhole approach * Combinatorics, or counting without really counting * Symmetry * Graph theory * Using game strategies Mathematics professionals from all over the world bring you their personal favorite strategies for problem solving. The chapters are independent of each other, and the editors encourage you to use the chapters in whatever order suits your needs. If you have ever despaired of making mathematics into a favorite subject for yourself and your class, this is the book you need. These passionate professionals give you new insight into the art of problem solving.

If you're a teacher or administrator who wants to give your students the best chances possible on the Math SAT, or if you're a parent of a student facing the test, here is the advantage you're looking for. Designed as a companion book to Students! Get Ready for the Mathematics for SAT I, this workbook is crammed with strategies and ideas. Show your students techniques that can make a big difference in their college chances--teach them techniques that will really boost their Math SAT I scores. This information-packed teacher's volume gives you: * An overview of the SAT I, including a description of its format, content, and the use of a calculator on the test * A selective review of the mathematics taught through elementary algebra and geometry, with particular attention to problem solving. * Less-well-known mathematics "facts" and problem-solving tools * Ways to advise students on strategies for taking the SAT I, including when and how to guess on unfamiliar items * A detailed presentation of specific problem-solving strategies Follow the step-by-step plan in this book, and you will help to signicantly increase your students' scores. Hand your students these tools and they'll be prepared to face the SAT I.

If you′re a teacher or administrator who wants to give your students the best chances possible on the Math SAT, or if you′re a parent of a student facing the test, here is the advantage you′re looking for. Designed as a companion book to Students! Get Ready for the Mathematics for SAT I, this workbook is crammed with strategies and ideas. Show your students techniques that can make a big difference in their college chances--teach them techniques that will really boost their Math SAT I scores. This information-packed teacher′s volume gives you: * An overview of the SAT I, including a description of its format, content, and the use of a calculator on the test * A selective review of the mathematics taught through elementary algebra and geometry, with particular attention to problem solving. * Less-well-known mathematics "facts" and problem-solving tools * Ways to advise students on strategies for taking the SAT I, including when and how to guess on unfamiliar items * A detailed presentation of specific problem-solving strategies Follow the step-by-step plan in this book, and you will help to signicantly increase your students′ scores. Hand your students these tools and they′ll be prepared to face the SAT I.

Here is an organized, easy-to-use reference that provides the latest research results and practical tips for K-12 math teachers. Each of the chapters presents a collection of tips on different aspects of mathematics teaching in a user-friendly manner. For each tip, the authors give you: * The teaching tip * A discussion of the research project that led to the tip * Practical applications for using the tip * Ways to avoid common difficulties associated with each tip * Resources for details on process and findings Foster questioning and independent thinking - challenge students with stimulating problems. Get higher levels of achievement. You'll find ideas for improving students' poor mathematics self-concepts, and for building students' confidence in their skills and abilities.

"The book is very easy to follow, with practical, research-based strategies for the teacher to use. It also provides insight to better remediate students who are struggling." -Allen Stevens, Math/Science Teacher Mooresville Middle School, NC "The ′Precautions and Pitfalls′ section is such a welcome feature! This is a powerful book for beginning teachers or seasoned teachers who want to improve their practice to ensure student learning." -Rhonda Naylor, Math Teacher/Coordinator Campus Middle School, Englewood, CO "The research and vignettes that follow each strategy clearly support why the strategy is important and how it can be effective." -Trish Guinee, Mathematics Coordinator Peoria Public Schools, IL Facilitate learning in PreK-5 mathematics and maximize student achievement with research-based teaching strategies! This easy-to-navigate guide offers research-based teaching strategies for introducing prekindergarten and elementary school students to the content and skills recommended by the NCTM principles and standards for mathematics. Using the popular format of the What Successful Teachers Do books, the authors present 47 dynamic learning activities, each including: A concise statement of the teaching strategy Research-based validations for the strategy How the strategy aligns with NCTM standards Grade-specific classroom applications and vignettes Precautions and possible pitfalls Primary sources for further reading This insightful resource allows teachers to increase students′ confidence in math-and their enthusiasm-with practical and engaging activities, while responding effectively to NCTM standards.

"The book is very easy to follow, with practical, research-based strategies for the teacher to use. It also provides insight to better remediate students who are struggling." -Allen Stevens, Math/Science Teacher Mooresville Middle School, NC "The 'Precautions and Pitfalls' section is such a welcome feature! This is a powerful book for beginning teachers or seasoned teachers who want to improve their practice to ensure student learning." -Rhonda Naylor, Math Teacher/Coordinator Campus Middle School, Englewood, CO "The research and vignettes that follow each strategy clearly support why the strategy is important and how it can be effective." -Trish Guinee, Mathematics Coordinator Peoria Public Schools, IL Facilitate learning in PreK-5 mathematics and maximize student achievement with research-based teaching strategies! This easy-to-navigate guide offers research-based teaching strategies for introducing prekindergarten and elementary school students to the content and skills recommended by the NCTM principles and standards for mathematics. Using the popular format of the What Successful Teachers Do books, the authors present 47 dynamic learning activities, each including:

A concise statement of the teaching strategy Research-based validations for the strategy How the strategy aligns with NCTM standards Grade-specific classroom applications and vignettes Precautions and possible pitfalls Primary sources for further reading

This insightful resource allows teachers to increase students' confidence in math-and their enthusiasm-with practical and engaging activities, while responding effectively to NCTM standards.

Multiply math mastery and interest with these inspired teaching tactics! Invigorate instruction and engage students with this treasure trove of "Great Ideas" compiled by two of the greatest minds in mathematics. From commonly taught topics in algebra, geometry, trigonometry, and statistics, to more advanced explorations into indirect proofs, binomial theorem, irrationality, relativity, and more, this guide outlines concepts and techniques that will inspire veteran and new educators alike. This updated second edition offers more proven practices for bringing math concepts to life in the classroom, including: 114 innovative strategies organized by subject area User-friendly content identifying "objective," "materials," and "procedure" for each technique A range of teaching models, including hands-on and computer-based methods Specific and straightforward examples with step-by-step lessonsWritten by two distinguished leaders in the field-mathematician, author, professor, university dean, and popular commentator Alfred S. Posamentier, along with mathematical pioneer and Nobel Prize recipient Herbert A. Hauptman-this guide brings a refreshing perspective to secondary math instruction to spark renewed interest and success among students and teachers.

Multiply math mastery and interest with these inspired teaching tactics! Invigorate instruction and engage students with this treasure trove of "Great Ideas" compiled by two of the greatest minds in mathematics. From commonly taught topics in algebra, geometry, trigonometry, and statistics, to more advanced explorations into indirect proofs, binomial theorem, irrationality, relativity, and more, this guide outlines concepts and techniques that will inspire veteran and new educators alike. This updated second edition offers more proven practices for bringing math concepts to life in the classroom, including: 114 innovative strategies organized by subject area User-friendly content identifying "objective," "materials," and "procedure" for each technique A range of teaching models, including hands-on and computer-based methods Specific and straightforward examples with step-by-step lessonsWritten by two distinguished leaders in the field-mathematician, author, professor, university dean, and popular commentator Alfred S. Posamentier, along with mathematical pioneer and Nobel Prize recipient Herbert A. Hauptman-this guide brings a refreshing perspective to secondary math instruction to spark renewed interest and success among students and teachers.

"The authors have provided a unique, strategy-focused resource supported by a wealth of engaging examples that mathematics teachers can readily use to help students develop a more purposeful, systematic, and successful approach to problem solving."—Howard W. Smith, Superintendent Public Schools of the Tarrytowns, Sleepy Hollow, NY"Helps both new and veteran teachers better understand the nature of problem solving as a critical mathematics process. The authors present in very simple terms the strategies that are the backbone of mathematics instruction. This indispensable material is useful at all levels, from basic stages to advanced student work to the development of top problem solvers."—Daniel Jaye, Principal Bergen County Academies, Hackensack, NJHelp students become skilled and confident problem solvers!Demonstrating there is always more than one approach to solving a problem, well-known authors and educators Alfred S. Posamentier and Stephen Krulik present ten basic strategies that are effective for finding solutions to a wide range of mathematics problems. These tried-and-true methods—including working backwards, finding a pattern, adopting a different point of view, solving a simpler analogous problem, and making a visual representation—make problem solving easier, neater, and more understandable for students as well as teachers. Providing numerous sample problems that illustrate how mathematics teachers and specialists can incorporate these techniques into their mathematics curriculum, this updated edition also includes:A variety of new problems that show how to use the strategiesReferences to current NCTM standards Solutions to the problems in each chapterExtensive discussions of the empowering strategies used to solve sample problemsThe second edition of Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6–12 helps teachers develop students′ creative problem-solving skills for success in and out of school.

"Demonstrates problem solving strategies with solutions and teaching notes and allows the teacher to create a collection of problems to fit a particular grade level."—Janice L. Richardson, Associate Professor and Education Coordinator, Department of MathematicsElon University

Help students succeed as problem solvers in and out of the classroom!

Problem solving skills are critical to students' success in mathematics, but the techniques can't be caught; they must be taught. Based on the premise that educators must take a deliberate approach to the teaching of problem solving skills, this book helps teachers engage students in the process.

Problem Solving in Mathematics, Grades 3–6 stresses the importance of problem solving in mathematics and presents nine strategies that students can use to solve problems, such as working backwards, finding a pattern, making a drawing, or solving a simpler equivalent problem. Each chapter demonstrates how teachers can:

Apply the strategies to problems at different grade levels Incorporate these strategies into a mathematics program Understand how each strategy can be applied to real-life situations Make each strategy an integral part of students' thinking processes

With helpful teaching notes, sample problems for students that fit into any mathematics curriculum, and step-by-step solutions to sample problems, this book is perfect for teachers who want their students to succeed in mathematics!

"Demonstrates problem solving strategies with solutions and teaching notes and allows the teacher to create a collection of problems to fit a particular grade level."—Janice L. Richardson, Associate Professor and Education Coordinator, Department of MathematicsElon University

Help students succeed as problem solvers in and out of the classroom!

Problem solving skills are critical to students' success in mathematics, but the techniques can't be caught; they must be taught. Based on the premise that educators must take a deliberate approach to the teaching of problem solving skills, this book helps teachers engage students in the process.

Problem Solving in Mathematics, Grades 3–6 stresses the importance of problem solving in mathematics and presents nine strategies that students can use to solve problems, such as working backwards, finding a pattern, making a drawing, or solving a simpler equivalent problem. Each chapter demonstrates how teachers can:

Apply the strategies to problems at different grade levels Incorporate these strategies into a mathematics program Understand how each strategy can be applied to real-life situations Make each strategy an integral part of students' thinking processes

With helpful teaching notes, sample problems for students that fit into any mathematics curriculum, and step-by-step solutions to sample problems, this book is perfect for teachers who want their students to succeed in mathematics!

100 ways to get students hooked on math!It happens to the best of us: that one question that’s got you stumped. Or maybe you have the answer, but it’s not all that compelling or convincing. Al Posamentier and his coauthors to the rescue with this handy reference containing fun answers to students’ 100 most frequently asked math questions. Even if you already have the answers, Al’s explanations are certain to keep kids hooked—and that’s what it’s all about.The questions are all organized around the Common Core’s math content standards and relate directly to Numbers and Quantity, Functions, Algebra, Geometry, and Statistics and Probability. The big benefits? You’ll discover high-interest ways to:• Teach inquiry and process in mathematical thinking• Encourage flexibility in problem solving• Emphasize efficient test-taking strategies • Provide practical applications from mathematics, education, and human development research• Build students’ procedural skills and conceptual understanding Use this complete resource to save time, anticipate questions, promote process and thinking, and present yourself as the math expert we know you are.

The math teacher’s go-to resource—now updated for the Common Core!What works in math and why has never been the issue; the research is all out there. Where teachers struggle is the "how"—something the research rarely manages to tackle. That’s the big service What Successful Math Teachers Do provides. It’s a powerful portal to what the best research looks like in practice, strategy by strategy—aligned in this new edition to both the Common Core and the NCTM Standards. How exactly does What Successful Math Teachers Do work? It couldn’t be easier to navigate. The book’s eleven chapters organize clusters of strategies around a single aspect of a typical instructional program. For each of the 80 strategies, the authors present:• A brief description of that strategy• A summary of supporting research• The NCTM and Common Core Standards it meets--and how• Classroom applications, with examples• Precautions and possible pitfalls• Primary sources for further reading and researchWhether you’re a newly minted math teacher or veteran looking to fine-tune your teaching, What Successful Math Teachers Do is your best resource for successful standards-based instruction.

Professional mathematicians often speak of the beauty of mathematics and the elegance of its solutions. Yet the esthetic appeal of math is rarely conveyed to students at the elementary, secondary, or even college level. Instead, most of us develop phobias in school about math's elusive logic and then pass these negative impressions on to our children. 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. That's just what veteran math educator Alfred Posamentier sets out to do in this delightful exploration of math's many intriguing, interesting, and fun qualities. Beginning with the beauty of the number system, thr author doesn't just talk mathematics; he entices readers to do math and discover for themselves just how stimulating the process can be! Brief and entertaining introductions to each chapter invite readers to try their hands at arithmetic marvels, surprising solutions, algebraic entertainments, geometric wonders, and fun mathematical paradoxes, among other topics. Presented in a reader-friendly, conversational tone, the text is very accessible and the examples are geared to a beginner's level, so that even the most math-phobic individual will discover the hidden joy and inherent appeal of doing math. This is the ideal book 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.

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 - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a 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." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few.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.

If you've been waiting for a book that will evoke the delight and intrigue that mathematics has to offer, this is the book for you. 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. Two veteran math educators 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. As you marvel at the many unusual relationships and novelties revealed in this ingenious and delightful presentation, you'll be learning more math than you ever thought possible - and will be relishing every moment of it!

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!

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.

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.

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.