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Filling a Sphere

Filling a Sphere
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2018-05-11 02:27
FunctionSolid GeometryCalculusOptimizationGeometric Construction
This example demonstrates how to draw and fill a sphere using GeoGebra, involving core math concepts like solid geometry, circles, functions, derivatives, and linear programming. Key GeoGebra commands/objects used include Point, OrthogonalLine, Circle, Intersect, Ellipse, Arc, Distance, Segment, Function, and Mirror, as outlined in the construction summary. Suitable for high school and above students learning spatial geometry and related mathematical applications.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. OrthogonalLine(A, xAxis) → a_2
  3. Circle(B, r) → d
  4. OrthogonalLine(B, yAxis) → e
  5. Intersect(d, e, 1) → C
  6. Intersect(d, e, 2) → D
  7. Ellipse(E, F, D) → f_2
  8. Arc(f_2, D, C) → g
  9. Arc(f_2, C, D) → h
  10. Intersect(p, xAxis) → H, I, J
  11. OrthogonalLine(K, yAxis) → l
  12. Intersect(d, l, 1) → G
  13. Intersect(d, l, 2) → L
  14. Intersect(a_2, l) → M
  15. Intersect(g, a_2, 1) → N
  16. Distance(B, N) → m
  17. Distance(B, A) → n
  18. Distance(B, M) → o_1
  19. Distance(B, N) → w
  20. Intersect(yAxis, xAxis) → R
  21. Segment(M, A) → a_1
  22. Segment(M, L) → b_1
  23. Circle(B, A) → g_1
  24. Intersect(g_1, a_2, 2) → S
  25. Arc(f_2, C, D) → p_1
  26. Arc(f_2, D, C) → q_1
  27. Arc(d, L, G) → f_1
  28. Segment(S, M) → i_1
  29. Function(f1, 0, x(K) / 2.2) → g2
  30. Point(g_1) → A_1
  31. Mirror(Z, B) → Z'
  32. Point(g_1) → B_1
  33. Point(g_1) → C_1
  34. Ellipse(G - (0.2, 0), L + (0.2, 0), V) → c_1
  35. Ellipse(G - (0.2, 0), L + (0.2, 0), V) → d_1
  36. Ellipse(C - (0.1, 0), D + (0.1, 0), Z) → f
  37. Arc(f, D, C) → e_1
  38. Arc(f, C, D) → h_1