Sphere Cross Sections Investigation
- Edward Knote
1. What is the shape of the cross section formed by slicing the sphere above with the single plane through all three points A, B, and C? (Use the initial positions of points A, B, and C if you moved the points reset the GeoGebra file)
2. What cross section shapes can be formed by moving points A, B, and C anywhere along the surface of the sphere, being sure the 3 points are not collinear?
3. Which of the following statements is TRUE about the cross sections of a sphere?
4. Can you position the points so that the cross section created is an ellipse, parabola, and/or a polygon? (add a comment and explain why, or why not?)