This is a module with an interactive Java applet illustrating the following construction of conic sections. We are given a circle with center C and radius R and another point F in the plane. As the point P goes around the circle, the perpendicular bisectors of PF define a conic as their envelope. C and F are the foci. The module includes questions for students to answer.
Type of Material:
Interactive Java animation, with several questions for students to answer.
Browser supporting Java.
Identify Major Learning Goals:
To show students an alternative definition of the conic sections.
Target Student Population:
High school students in advanced Geometry; College students in Analytic Geometry.
Prerequisite Knowledge or Skills:
The user only needs to be able to read instructions and use a mouse. The exercise is designed for students who have already seen definitions of ellipse and hyperbola, and who know what "eccentricity" means.
Illuminates a beautiful and not widely known property of the conic sections. The animation is excellent: C, F, R and P are all movable by the user. The "sweep bisector" option is impressive and satisfying.
Potential Effectiveness as a Teaching Tool
Allows students to "play" with the parameters. The transition from hyperbola to ellipse is particulaly striking. The students explorations are guided to some extent by the questions.
The last question is much harder than the rest, and would require a lead-in series of exercises for average students, unless they already had a very good grasp of analytic geometry.
Ease of Use for Both Students and Faculty
Easy, natural and fun to use.
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