Geometry Turned On

Geometry Turned On : Dynamic Software in Learning, Teaching, and Research

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This volume is a collection of articles about dynamic geometry: active, exploratory geometry carried out with interactive computer software. This software has had a profound effect on classroom teaching wherever it has been introduced. Unconstrained parts of the configurations are moveable - they can literally be grabbed with a cursor (using a mouse) and be dragged or stretched - and as they move, all other objects in the configuration automatically self-adjust, preserving all dependent relationships and constraints. The software has also become an indispensable research tool for mathematicians and scientists. This book gives many examples of the ways in which it can be used, and some of the effects it can have. It raises various questions for teaching and research. Some articles address the basic question, 'What is dynamic geometry good for?' as they discuss: accuracy of construction, visualization, exploration and discovery, motivating proof, transformations, tracing loci, simulation, and creating microworlds.

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Product details

  • Paperback | 220 pages
  • 210.8 x 274.3 x 15.2mm | 498.96g
  • Mathematical Association of America
  • Washington, United States
  • English
  • 0883850990
  • 9780883850992

Table of contents

Part I. Personal Reflections On Investigation, Discovery, and Proof: 1. Discovery and dissection of a geometric gem Douglas R. Hofstadter; 2. The role and function of proof in dynamic geometry: some personal reflections Michael de Villiers; 3. Dynamic geometry renews interest in an old problem Dan Bennett; 4. Dynamic geometry as a bridge from Euclidean geometry to analysis Albert A. Cuoco and E. Paul Goldenberg; Part II. Dynamic Geometry In The Classroom: 5. Dynamic visualization from middle school through College James Morrow; 6. Geometer's sketchpad in the classroom Tim Garry; 7. Students discovering geometry using dynamic geometry software Michael Keyton; 8. Moving triangles; 9. Experiences with geometer's sketchpad in the classroom Kathryn W. Boehm; 10. Beyond elementary constructions: selected exercises Arnold Perham and Bernadette H. Perham; 11. Interactive generation, manipulation, and application of loci Heinz Schumann; 12. Calculus with dynamic geometry Catherine A. Gorini; 13. Beginning geometry at college Tony Hampson; 14. Identifying transformations by their orbits James M. Parks; 15. Dynamic proofs that use similarities James King; 16. Visualization of group theory concepts through dynamic geometry Doris Schattschneider; 17. Using the geometer's sketchpad with preservice teachers Zhonghong Jian and Edwin McClintock; 18. Fish in the pond: inquiry with dynamic geometry Fadia Harik; Part III. Dynamic Visualization In History, Perception, Optics and Aerodynamics: 19. Drawing logarithmic curves with geometer's sketchpad: a method inspired by historical sources David Dennis and Jere Confrey; 20. Lost in the funhouse: an application of dynamic projective geometry Susan Addington and Stuart Levy; 21. The use of dynamic geometry software in teaching and research in optometry and vision science Benjamin T. Backus; 22. Creating airfoils from circles: the Joukowski transformation John Olive; Part IV. The Worlds Of Dynamic Geometry: Issues In Design And Use: 23. Drawing worlds: scripted exploration environments in the geometer's sketchpad R. Nicholas Jackiw; 24. Dynamic geometry and declarative geometric programming Richard J. Allen and Laurent Trilling.

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