Geometry turned on: dynamic software in learning, teaching, and research

Copyright
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Contents vii
Preface: Making Geometry Dynamic ix

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I. Personal Reflections on Investigation, Discovery, and Proof 1
-Discovery and Dissection of a Geometric Gem, Douglas R. Hofstadter 3
-The Role of Proof in Investigative, Computer-based Geometry: Some Personal Reflections, Michael de Villiers 15
-Dynamic Geometry Renews Interest in an Old Problem, Dan Bennett 25
-Quadrilaterals Formed by Perpendicular Bisectors, James King 29
-Dynamic Geometry as a Bridge from Euclidean Geometry to Analysis, Albert A. Cuoco and E. Paul Goldenberg 33

II. Making Geometry Dynamic in the Classroom 45
-Dynamic Visualization from Middle School through College, James Morrow 47
-Geometer\'s Sketchpad in the Classroom, Tim Garry 55
-Students Discovering Geometry using Dynamic Geometry Software, Michael Keyton 63
-Moving Triangles, Douglas K. Brumbaugh 69
-Experiences with The Geometer\'s Sketchpad in the Classroom, Kathryn  Boehm 71
-Beyond Elementary Constructions: Selected Exercises, Arnold Perham and Bernadette H. Perham 75
-Producing and using Loci with Dynamic Geometry Software, Heinz Schumann and David Green 79
-Dynamic Visualization in Calculus, Catherine A. Gorini 89
-Beginning Geometry at College, Tony Hampson 95
-Identifying Transformations by their Orbits, James M. Parks 105
-An Eye for Similarity Transformations, James R. King 109
-Visualization of Group Theory Concepts With Dynamic Geometry Software, Doris Schattschneider 121
-Using The Geometer\'s Sketchpad with Preservice Teachers, Zhonghong Jiang and Edwin McClintock 129
-Fish in the Pond: Inquiry with Interactive Geometry Software, Fadia Harik 137

III. Dynamic Visualization in History, Perception, Optics, and Aerodynamics 145
-Drawing Logarithmic Curves with Geometer\'s Sketchpad: A Method Inspired by Historical Sources, David Dennis and Jere Confrey 147
-Lost in the Fun House: An Application of Dynamic Projective Geometry, Susan Addington and Stuart Levy 157
-The Use of Dynamic Geometry Software in Teaching and Research in Optometry and Vision Science, Benjamin T. Backus 161
-Creating Airfoils from Circles: The loukowski Transformation, John Olive 169

IV. The Worlds of Dynamic Geometry: Issues in Design and Use 177
-Drawing Worlds: Scripted Exploration Environments in The Geometer\'s Sketchpad, R. Nicholas Jackiw 179
-Exploring Non-Euclidean Geometry in a Dynamic Geometry Environment like Cabri-geometre, Jean-Marie Laborde 185
-Dynamic Geometry and Declarative Geometric Programming, Richard J. Allen and Laurent Trilling 193

About the Authors 199
Information on Software and Interactive Sketches 205