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3D Ellipse Connection

3D Ellipse Connection
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2016-12-07 10:28
Coordinate GeometrySolid GeometryLimit
This example demonstrates the connection between ellipses and planes in three-dimensional space, including limit distributions. Key math concepts involve ellipses, planes, limits, distributions, squares, and incircles. Construction highlights include using GeoGebra commands like Point, Intersect, IntersectPath, Cone, Corner, OrthogonalLine, Distance, Midpoint, Ellipse, Segment, Circle, Line, and Mirror. Suitable for high school and above students studying solid geometry and spatial relationships.

GeoGebra Commands & Parameters

  1. Point(zAxis) → A
  2. Intersect(yAxis, xAxis) → B
  3. IntersectPath(d, xOyPlane) → g
  4. Cone(A, B, 8) → c_1, c_2, c_3
  5. IntersectPath(d, c_1) → e
  6. Corner(e) → C, D, E, F
  7. Intersect(zAxis, e) → G,
  8. Intersect(zAxis, d) → H
  9. OrthogonalLine(H, g, space) → f
  10. Intersect(f, e) → I, J
  11. Distance(J, I) → distanceJI
  12. OrthogonalLine(I, xOyPlane) → h
  13. OrthogonalLine(J, xOyPlane) → i
  14. Intersect(h, xOyPlane) → K
  15. Intersect(i, xOyPlane) → L
  16. Midpoint(K, L) → M
  17. Distance(L, K) → distanceLK
  18. Ellipse(F_2, F_1, N) → k
  19. Point(k) → O
  20. Segment(F_2, O) → j
  21. Segment(F_1, O) → l
  22. Circle(F_1, r, xOyPlane) → p
  23. Line(F_1, O) → m
  24. Intersect(m, p) → P, Q
  25. Segment(F_1, P) → n
  26. Mirror(g, M) → g'
  27. Point(p) → R
  28. Segment(R, F_1) → q
  29. Intersect(q, k) → S, T
  30. Segment(F_1, T) → s
  31. Segment(F_2, T) → t