Exploring Advanced Euclidean Geometry With Geogebra
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Exploring Advanced Euclidean Geometry With Geogebra
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Author : Gerard A. Venema
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-12-31
Exploring Advanced Euclidean Geometry With Geogebra written by Gerard A. Venema and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-31 with Mathematics categories.
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 Poincare 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.
Exploring Advanced Euclidean Geometry With Geogebra
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Author : Gerard A. Venema
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-12-31
Exploring Advanced Euclidean Geometry With Geogebra written by Gerard A. Venema and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-31 with Mathematics categories.
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 Poincare 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.
Foundations Of Geometry
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Author : Gerard Venema
language : en
Publisher:
Release Date : 2012
Foundations Of Geometry written by Gerard Venema and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Geometry categories.
Normal 0 false false false Foundations of Geometry, Second Edition is written to help enrich the education of all mathematics majors and facilitate a smooth transition into more advanced mathematics courses. The text also implements the latest national standards and recommendations regarding geometry for the preparation of high school mathematics teachers--and encourages students to make connections between their college courses and classes they will later teach. This text's coverage begins with Euclid's Elements, lays out a system of axioms for geometry, and then moves on to neutral geometry, Euclidian and hyperbolic geometries from an axiomatic point of view, and then non-Euclidean geometry. Good proof-writing skills are emphasized, along with a historical development of geometry. The Second Edition streamlines and reorganizes material in order to reach coverage of neutral geometry as early as possible, adds more exercises throughout, and facilitates use of the open-source software Geogebra. This text is ideal for an undergraduate course in axiomatic geometry for future high school geometry teachers, or for any student who has not yet encountered upper-level math, such as real analysis or abstract algebra. It assumes calculus and linear algebra as prerequisites.
College Geometry With Geogebra
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Author : Barbara E. Reynolds
language : en
Publisher: John Wiley & Sons
Release Date : 2021-01-20
College Geometry With Geogebra written by Barbara E. Reynolds and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-20 with Education categories.
From two authors who embrace technology in the classroom and value the role of collaborative learning comes College Geometry Using GeoGebra, a book that is ideal for geometry courses for both mathematics and math education majors. The book's discovery-based approach guides students to explore geometric worlds through computer-based activities, enabling students to make observations, develop conjectures, and write mathematical proofs. This unique textbook helps students understand the underlying concepts of geometry while learning to use GeoGebra software—constructing various geometric figures and investigating their properties, relationships, and interactions. The text allows students to gradually build upon their knowledge as they move from fundamental concepts of circle and triangle geometry to more advanced topics such as isometries and matrices, symmetry in the plane, and hyperbolic and projective geometry. Emphasizing active collaborative learning, the text contains numerous fully-integrated computer lab activities that visualize difficult geometric concepts and facilitate both small-group and whole-class discussions. Each chapter begins with engaging activities that draw students into the subject matter, followed by detailed discussions that solidify the student conjectures made in the activities and exercises that test comprehension of the material. Written to support students and instructors in active-learning classrooms that incorporate computer technology, College Geometry with GeoGebra is an ideal resource for geometry courses for both mathematics and math education majors.
Digital Education For The 21st Century
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Author : Souvik Pal
language : en
Publisher: CRC Press
Release Date : 2021-12-23
Digital Education For The 21st Century written by Souvik Pal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-23 with Science categories.
This new volume highlights the evolution of digital education related issues by reporting on effective IoT-based technologies for the teaching-learning process. It brings together a selection of leading academic policymakers, researchers, educationalists, and education scholars to share their experiences and research on many aspects of digital pedagogy in the Education of Things. The volume discusses recent innovations, trends, and concerns as well as the practical challenges encountered and solutions adopted in the fields of digital pedagogies and educational design.The chapters cover the concepts of IoT-based digital technologies regarding teacher and teaching education, IoT-based education, flipped learning, assessment process, and more. Key features: Introduces the integration of technology with digital education Explains the functional framework workflow in the Education of Things and networked learning Explores basic and high-level concepts of teaching-learning pedagogy in IoT-based education Covers the major challenges, issues, and advances in flipped and blended learning based on IoT technologies Looks at digital education pedagogy collaborations with organizations outside academia Explores teaching education and the process of assessment, testing, and evaluation Digital Education for the 21st Century: Technologies and Protocols provides a rich resource for academic and administrative policymakers, academicians, researchers, educationalists and experts who are concerned with educational research.
Advanced Euclidean Geometry
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Author : Roger A. Johnson
language : en
Publisher: Dover Publications
Release Date : 2013-12-20
Advanced Euclidean Geometry written by Roger A. Johnson and has been published by Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-20 with categories.
This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.
Discovering Discrete Dynamical Systems
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Author : Aimee Johnson
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-12-31
Discovering Discrete Dynamical Systems written by Aimee Johnson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-31 with Mathematics categories.
Discovering Discrete Dynamical Systems is a mathematics textbook designed for use in a student-led, inquiry-based course for advanced mathematics majors. Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-discovery on topics such as fixed points and their classifications, chaos and fractals, Julia and Mandelbrot sets in the complex plane, and symbolic dynamics. Topics have been carefully chosen as a means for developing student persistence and skill in exploration, conjecture, and generalization while at the same time providing a coherent introduction to the fundamentals of discrete dynamical systems. This book is written for undergraduate students with the prerequisites for a first analysis course, and it can easily be used by any faculty member in a mathematics department, regardless of area of expertise. Each module starts with an exploration in which the students are asked an open-ended question. This allows the students to make discoveries which lead them to formulate the questions that will be addressed in the exposition and exercises of the module. The exposition is brief and has been written with the intent that a student who has taken, or is ready to take, a course in analysis can read the material independently. The exposition concludes with exercises which have been designed to both illustrate and explore in more depth the ideas covered in the exposition. Each module concludes with a project in which students bring the ideas from the module to bear on a more challenging or in-depth problem. A section entitled "To the Instructor" includes suggestions on how to structure a course in order to realize the inquiry-based intent of the book. The book has also been used successfully as the basis for an independent study course and as a supplementary text for an analysis course with traditional content.
Perspective And Projective Geometry
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Author : Annalisa Crannell
language : en
Publisher: Princeton University Press
Release Date : 2019-12-10
Perspective And Projective Geometry written by Annalisa Crannell and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-10 with Mathematics categories.
Frontmatter -- Contents -- 0. Introduction and First Action -- 1. Window Taping -- 2. Drawing ART -- 3. What's the Image of a Line? -- 4. The Geometry of R2 and R3 -- 5. Extended Euclidean Space -- 6. Of Meshes and Maps -- 7. Desargues's Theorem -- 8. Collineations -- 9. Dynamic Cubes and Viewing Distance -- 10. Drawing Boxes and Cubes in Two-Point Perspective -- 11. Perspective by the Numbers -- 12. Coordinate Geometry -- 13. The Shape of Extended Space -- Appendix G. Introduction to GEOGEBRA -- Appendix R. Reference Manual -- Appendix W. Writing Mathematical Prose -- Acknowledgments -- Bibliography -- Index
Glimpses Into The World Of Mathematics
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Author : Szymon Chlebowski
language : en
Publisher: LIT Verlag Münster
Release Date :
Glimpses Into The World Of Mathematics written by Szymon Chlebowski and has been published by LIT Verlag Münster this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Essays collected in this volume deal with various problems from the philosophy of mathematics. What connects them are two questions: how mathematics is created and how it is acquired. In 'Three Worlds of Mathematics' we are familiarized with David Tall's ideas pertaining to the embodied, symbolic and formal worlds of mathematics. In 'Basic Ideas of Intuitionism', we focus on an epistemological approach to mathematics which is distinctive to constructive mathematics. The author focuses on the computational content of intuitionistic logic and shows how it relates to functional programming. 'The Brave Mathematical Ant' carefully selects mathematical puzzles related to teaching experiences in a way that the solution requires creativity and is not obtainable by following an algorithm. Moreover the solution gives us some new insight into the underlying idea. 'Degrees Of Accessibility Of Mathematical Objects' discusses various criteria which can be used to judge accessibility of mathematical objects. We find logical complexity, range of applications, existence of a physical model as well as aesthetic values.
Arithmetical Wonderland
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Author : Andy Liu
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-12-31
Arithmetical Wonderland written by Andy Liu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-31 with Mathematics categories.
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.