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Avis sur College Geometry With Geogebra, 1st Edition de Reynolds Format Broché - Livre
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Présentation College Geometry With Geogebra, 1st Edition de Reynolds Format Broché
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Résumé : 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.
Sommaire: Preface Especially for Students Notes for Instructors Our Motivation, Philosophy, and Pedagogy Prerequisites and Chapter Dependencies Acknowledgments ONEUsing GeoGebra 1.1 Activities: Getting Started with GeoGebra 1.2 Discussion: Exploring and Conjecturing Some GeoGebra Tips Constructing ?? Exploring ?? Conjecturing: Inductive Reasoning Language of Geometry Explorations, Observations, Questions The Family of Quadrilaterals Angles Inscribed in Circles Rules of Logic 1.3 Exercises 1.4 Chapter Overview ? TWO? Constructing ? Proving ?2.1 Activities ?2.2 Discussion: Euclid's Postulates and Constructions ?Euclid's Postulates ?Congruence and Similarity ?Constructions ?Geometric Language Revisited ?Conditional Statements: Implication ?Using Robust Constructions to Develop a Proof ?Angles and Measuring Angles ?Constructing Perpendicular and Parallel Lines ?Properties of Triangles ?Euclid's Parallel Postulate ?Euclid's Constructions in the Elements ?Ideas About Betweenness ?2.3 Exercises ?2.4 Chapter Overview THREE Mathematical Arguments and Triangle Geometry 3.1 Activities 3.2 Discussion Deductive Reasoning Universal and Existential Quantifiers Negating a Quantified Statement Direct Proof and Disproof by Counterexample Step-by-Step Proofs Congruence Criteria for Triangles The Converse and the Contrapositive Concurrence Properties for Triangles Ceva's Theorem and Its Converse Brief Excursion into Circle Geometry The Circumcircle of ?ABC The Nine-Point Circle: A First Pass Menelaus' Theorem and Its Converse 3.3 Exercises 3.4 Chapter Overview FOUR Circle Geometry and Proofs ?4.1 Activities ?4.2 Discussion ?Axiom Systems: Ancient and Modern Approaches ?Language of Circles ?Inscribed Angles ?Mathematical Arguments ?Additional Methods of Proof ?Cyclic Quadrilaterals ?Incircles and Excircles ?Some Interesting Families of Circles ?The Arbelos and the Salinon ?Power of a Point ?The Radical Axis ?The Nine-Point Circle: A Second Pass ?4.3 Exercises ?4.4 Chapter Overview FIVE Analytic Geometry ?5.1 Activities ?5.2 Discussion ?Points ?Lines ?Distance ?Using Coordinates in Proofs ?Another Look at the Radical Axis ?Polar Coordinates ?The Nine-Point Circle, Revisited ?5.3 Exercises ?5.4 Chapter Overview SIX Taxicab Geometry ? 6.1 Activities ? 6.2 Discussion ? An Axiom System for Metric Geometry ? Circles ? Ellipses ? Measuring Distance from a Point to a Line ? Parabolas ? Hyperbolas ? Axiom Systems ? 6.3 Exercises ? 6.4 Chapter Overview SEVEN? Finite Geometries 7.1 Activities 7.2 Discussion An Axiom System for an Affine Plane An Axiom System for a Projective Plane Duality Relating Affine Planes to Projective Planes Coordinates for Finite Geometries 7.3 Exercises 7.4 Chapter Overview EIGHTTransformational Geometry ?8.1 Activities ?8.2 Discussion ?Transformations ?Isometries ?Other Transformations ?Composition of Isometries ?Inverse Isometries ?Using Isometries in Proofs ?Isometries in Space 8.3 Exercises 8.4 Chapter Overview NINE? Isometries a...
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