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.
Technical Requirements:
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.
Content Quality
Rating:
Strengths:
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.
Concerns:
None.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
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.
Concerns:
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
Rating:
Strengths:
Easy, natural and fun to use.
Concerns:
None
Creative Commons:
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