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Sphere + Plane Cross Section: Interactive Investigation

Sphere + Plane Cross Section: Interactive Investigation
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2019-04-07 08:34
Solid GeometryGeometric Construction
In collections GeoGebra 3D & AR: Geometry Resources & Challenges
This example demonstrates the intersection curve formed when a sphere intersects with a plane. Key math concepts include sphere, plane, intersection, normal line, rotation, scaling, etc. GeoGebra commands used in construction are Sphere, Plane, IntersectPath, Center, Point, OrthogonalLine, Rotate, CircleArc, Dilate, Segment. Suitable for high school solid geometry teaching and exploratory learning.

GeoGebra Commands & Parameters

  1. Sphere((0, 0, 0), radius) → a
  2. Plane(A, B, C) → b
  3. IntersectPath(b, a) → c
  4. Center(c) → D
  5. Point(c) → E
  6. OrthogonalLine(D, b) → f
  7. Rotate(E, If[0 < SlideMe ≤ 2, ((-π) * SlideMe), (-2 * π)], f) → E'
  8. Rotate(E, ((-π)) / 2, D, f) → E'_1
  9. CircleArc(D, E'_1, Rotate[E, π, D, f]) → h
  10. Dilate(D, If[2 < SlideMe ≤ 3, 3 - SlideMe, 0], E') → D'
  11. Segment(D, D') → g
  12. Rotate(E', If[3.5 < SlideMe ≤ 5.5, ((-(SlideMe - 3.5)) * π), (-2 * π)], D, f) → E''
  13. Segment(D, E'') → i