exploring advanced euclidean geometry with geogebra classroom resource materials

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Exploring Advanced Euclidean Geometry With Geogebra

Author : Gerard A. Venema
ISBN : 9780883857847
Genre : Mathematics
File Size : 81. 16 MB
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This book provides an inquiry-based introduction to advanced Euclidean geometry. It utilizes dynamic geometry software, specifically GeoGebra, to explore the statements and proofs of many of the most interesting theorems in the subject. Topics covered include triangle centers, inscribed, circumscribed, and escribed circles, medial and orthic triangles, the nine-point circle, duality, and the theorems of Ceva and Menelaus, as well as numerous applications of those theorems. The final chapter explores constructions in the Poincaré disk model for hyperbolic geometry. The book can be used either as a computer laboratory manual to supplement an undergraduate course in geometry or as a stand-alone introduction to advanced topics in Euclidean geometry. The text consists almost entirely of exercises (with hints) that guide students as they discover the geometric relationships for themselves. First the ideas are explored at the computer and then those ideas are assembled into a proof of the result under investigation. The goals are for the reader to experience the joy of discovering geometric relationships, to develop a deeper understanding of geometry, and to encourage an appreciation for the beauty of Euclidean geometry.

Mathematical Modeling

Author : Jonas Hall
ISBN : 9781119102847
Genre : Mathematics
File Size : 49. 66 MB
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A logical problem-based introduction to the use of GeoGebra for mathematical modeling and problem solving within various areas of mathematics A well-organized guide to mathematical modeling techniques for evaluating and solving problems in the diverse field of mathematics, Mathematical Modeling: Applications with GeoGebra presents a unique approach to software applications in GeoGebra and WolframAlpha. The software is well suited for modeling problems in numerous areas of mathematics including algebra, symbolic algebra, dynamic geometry, three-dimensional geometry, and statistics. Featuring detailed information on how GeoGebra can be used as a guide to mathematical modeling, the book provides comprehensive modeling examples that correspond to different levels of mathematical experience, from simple linear relations to differential equations. Each chapter builds on the previous chapter with practical examples in order to illustrate the mathematical modeling skills necessary for problem solving. Addressing methods for evaluating models including relative error, correlation, square sum of errors, regression, and confidence interval, Mathematical Modeling: Applications with GeoGebra also includes: Over 400 diagrams and 300 GeoGebra examples with practical approaches to mathematical modeling that help the reader develop a full understanding of the content Numerous real-world exercises with solutions to help readers learn mathematical modeling techniques A companion website with GeoGebra constructions and screencasts Mathematical Modeling: Applications with GeoGebrais ideal for upper-undergraduate and graduate-level courses in mathematical modeling, applied mathematics, modeling and simulation, operations research, and optimization. The book is also an excellent reference for undergraduate and high school instructors in mathematics.

Proofs Without Words

Author : Malcolm Scott MacKenzie
ISBN : 0883857006
Genre : Mathematics
File Size : 54. 13 MB
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Proofs without words are generally pictures or diagrams that help the reader see why a particular mathematical statement may be true, and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into five chapters: Geometry and algebra; Trigonometry, calculus and analytic geometry; Inequalities; Integer sums; and Sequences and series. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.

The Calculus Collection

Author : Caren L. Diefenderfer
ISBN : 0883857618
Genre : Juvenile Nonfiction
File Size : 52. 10 MB
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The Calculus Collection is a useful resource for everyone who teaches calculus, in high school or in a 2- or 4-year college or university. It consists of 123 articles, selected by a panel of six veteran high school teachers, each of which was originally published in Math Horizons, MAA Focus, The American Mathematical Monthly, The College Mathematics Journal, or Mathematics Magazine. The articles focus on engaging students who are meeting the core ideas of calculus for the first time. The Calculus Collection is filled with insights, alternate explanations of difficult ideas, and suggestions for how to take a standard problem and open it up to the rich mathematical explorations available when you encourage students to dig a little deeper. Some of the articles reflect an enthusiasm for bringing calculators and computers into the classroom, while others consciously address themes from the calculus reform movement. But most of the articles are simply interesting and timeless explorations of the mathematics encountered in a first course in calculus.The MAA has twice previously issued a calculus reader, collecting articles on calculus from its journals: Selected Papers in Calculus, published in 1969 and reprinted as Part I of A Century of Calculus, and Part II published in 1992. In a sense The Calculus Collection is the third volume in that series, but different in that it is a collection chosen for its usefulness to those who teach first-year calculus in high schools as well as colleges and universities.

Advanced Euclidean Geometry

Author : Alfred S. Posamentier
ISBN : 1930190859
Genre : Mathematics
File Size : 26. 83 MB
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CD-ROM contains: Interactive sketches using The geometer's sketchpad (not included).

Model Centered Learning

Author : Lingguo Bu
ISBN : 9789460916182
Genre : Education
File Size : 82. 37 MB
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Model-Centered Learning: Pathways to Mathematical Understanding Using GeoGebra is the first book to report on the international use of GeoGebra and its growing impact on mathematics teaching and learning. Supported by new developments in model-centered learning and instruction, the chapters in this book move beyond the traditional views of mathematics and mathematics teaching, providing theoretical perspectives and examples of practice for enhancing students’ mathematical understanding through mathematical and didactical modeling. Designed specifically for teaching mathematics, GeoGebra integrates dynamic multiple representations in a conceptually rich learning environment that supports the exploration, construction, and evaluation of mathematical models and simulations. The open source nature of GeoGebra has led to a growing international community of mathematicians, teacher educators, and classroom teachers who seek to tackle the challenges and complexity of mathematics education through a grassroots initiative using instructional innovations. The chapters cover six themes: 1) the history, philosophy, and theory behind GeoGebra, 2) dynamic models and simulations, 3) problem solving and attitude change, 4) GeoGebra as a cognitive and didactical tool, 5) curricular challenges and initiatives, 6) equity and sustainability in technology use. This book should be of interest to mathematics educators, mathematicians, and graduate students in STEM education and instructional technologies.

Discovering Discrete Dynamical Systems

Author : Aimee S. A. Johnson
ISBN : 9780883857939
Genre : Mathematics
File Size : 68. 28 MB
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A dynamical system is a collection of possible states and a rule (or rules) that describes evolution of these states over time. The main purpose of this book is to introduce important concepts in dynamical systems - including fixed and periodic points, attractors and repellers, chaos and fractals - in a way that encourages readers to explore, discover , and learn independently. The book differs from other dynamical system textbooks in that topics have been carefully chosen both to give a coherent introduction to dynamical systems and to support inquiry-based learning.

Cameos For Calculus

Author : Roger B. Nelsen
ISBN : 9780883857885
Genre : Mathematics
File Size : 82. 20 MB
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A thespian or cinematographer might define a cameo as “a brief appearance of a known figure,” while a gemologist or lapidary might define it as “a precious or semiprecious stone.” This book presents fifty short enhancements or supplements (the Cameos) for the first-year calculus course in which a geometric figure briefly appears. Some of the Cameos illustrate mainstream topics such as the derivative, combinatorial formulas used to compute Riemann sums, or the geometry behind many geometric series. Other Cameos present topics accessible to students at the calculus level but not usually encountered in the course, such as the Cauchy-Schwarz inequality, the arithmetic mean-geometric mean inequality, and the Euler-Mascheroni constant. There are fifty Cameos in the book, grouped into five sections: Part I Limits and Differentiation; Part II Integration; Part III Infinite Series; Part IV Additional Topics, and Part V Appendix: Some Precalculus Topics. Many of the Cameos include exercises, so Solutions to all the Exercises follows Part V. The book concludes with References and an Index. Many of the Cameos are adapted from articles published in journals of the MAA, such as The American Mathematical Monthly, Mathematics Magazine, and The College Mathematics Journal. Some come from other mathematical journals, and some were created for this book. By gathering the Cameos into a book we hope that they will be more accessible to teachers of calculus, both for use in the classroom and as supplementary explorations for students.

The Heart Of Calculus

Author : Philip M. Anselone
ISBN : 9780883857878
Genre : Mathematics
File Size : 42. 46 MB
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This book contains enrichment material for courses in first and second year calculus, differential equations, modeling, and introductory real analysis. It targets talented students who seek a deeper understanding of calculus and its applications. The book can be used in honors courses, undergraduate seminars, independent study, capstone courses taking a fresh look at calculus, and summer enrichment programs. The book develops topics from novel and/or unifying perspectives. Hence, it is also a valuable resource for graduate teaching assistants developing their academic and pedagogical skills and for seasoned veterans who appreciate fresh perspectives. The explorations, problems, and projects in the book impart a deeper understanding of and facility with the mathematical reasoning that lies at the heart of calculus and conveys something of its beauty and depth. A high level of rigor is maintained. However, with few exceptions, proofs depend only on tools from calculus and earlier. Analytical arguments are carefully structured to avoid epsilons and deltas. Geometric and/or physical reasoning motivates challenging analytical discussions. Consequently, the presentation is friendly and accessible to students at various levels of mathematical maturity. Logical reasoning skills at the level of proof in Euclidean geometry suffice for a productive use of the book.

Arithmetical Wonderland

Author : Andy Liu
ISBN : 9780883857892
Genre : Mathematics
File Size : 51. 10 MB
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Arithmetical Wonderland is intended as an unorthodox mathematics textbook for students in elementary education, in a contents course offered by a mathematics department. The scope is deliberately restricted to cover only arithmetic, even though geometric elements are introduced whenever warranted. For example, what the Euclidean Algorithm for finding the greatest common divisors of two numbers has to do with Euclid is showcased. Many students find mathematics somewhat daunting. It is the author's belief that much of that is caused not by the subject itself, but by the language of mathematics. In this book, much of the discussion is in dialogues between Alice, of Wonderland fame, and the twins Tweedledum and Tweedledee who hailed from Through the Looking Glass. The boys are learning High Arithmetic or Elementary Number Theory from Alice, and the reader is carried along in this academic exploration. Thus many formal proofs are converted to soothing everyday language. Nevertheless, the book has considerable depth. It examines many arcane corners of the subject, and raises rather unorthodox questions. For instance, Alice tells the twins that six divided by three is two only because of an implicit assumption that division is supposed to be fair, whereas fairness does not come into addition, subtraction or multiplication. Some topics often not covered are introduced rather early, such as the concepts of divisibility and congruence.

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