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Sphere Surface Area Visualization

Sphere Surface Area Visualization
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2017-05-25 15:10
Solid GeometryGeometric ConstructionGraphing
In collections Spheres & Cross Sections
This example demonstrates the calculation and visualization of the surface area of a sphere. It involves core mathematical concepts such as spherical geometry, surface area formulas, and 3D shape construction. GeoGebra commands like Intersect, Sphere, Line, Rotate, Circle, Center, Ray, OrthogonalPlane, CircleArc, Point, Plane, Locus, Segment, Mirror, Polygon, and Pyramid are used to construct the model. It is suitable for high school students and mathematics enthusiasts to understand spatial geometry and 3D concepts, aiding in teaching and learning.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, xOyPlane) → A
  2. Sphere(A, 1) → a
  3. Intersect(zAxis, a) → B, C
  4. Line(A, B) → i
  5. Rotate(C, 120°, xAxis) → C'
  6. Rotate(C', 120°, zAxis) → C''
  7. Circle(C, C', C'') → c_1
  8. Center(c_1) → N
  9. Ray(A, N) → f_1
  10. Intersect(f_1, a) → P, O
  11. OrthogonalPlane(O, f_1) → v
  12. Rotate(C'', 120°, zAxis) → C'''
  13. CircleArc(A, C, C') → c
  14. CircleArc(A, C, C'') → d
  15. CircleArc(A, C', C'') → e
  16. CircleArc(A, C, C''') → f
  17. CircleArc(A, C', C''') → g
  18. CircleArc(A, C'', C''') → h
  19. Circle(B, 1, i) → k
  20. Intersect(j, k) → D, E
  21. Line(D, C') → l
  22. Intersect(l, i) → F
  23. Line(F, C'') → n
  24. Intersect(n, k) → G,
  25. Ray(B, G) → j_1
  26. Line(F, C''') → m
  27. Intersect(m, k) → H,
  28. Point(g) → I
  29. Plane(I, C, A) → o
  30. Intersect(o, k) → J, K
  31. Line(J, I) → p
  32. Intersect(p, i) → L
  33. Locus(M, I) → loc1
  34. Rotate(I, 120°, zAxis) → I'
  35. Rotate(I', 120°, zAxis) → I''
  36. Rotate(M, 120°, zAxis) → M'
  37. Rotate(M', 120°, zAxis) → M''
  38. Locus(M', I) → loc2
  39. Locus(M'', I) → loc3
  40. Segment(C', D) → q
  41. Segment(C''', H) → r
  42. Segment(C'', G) → s
  43. Circle(O, 1, f_1) → d_1
  44. Rotate(d_1, (-(120°)), i) → e_1
  45. Rotate(e_1, (-(120°)), i) → g_1
  46. Ray(A, C') → h_1
  47. Rotate(C', 120°, h_1) → C''_1
  48. Circle(P, 1, f_1) → k_1
  49. Rotate(k_1, (-(120°)), i) → p_1
  50. Rotate(p_1, (-(120°)), i) → q_1
  51. Center(q_1) → Q
  52. Center(p_1) → R
  53. OrthogonalPlane(P, f_1) → u
  54. Ray(B, D) → i_1
  55. Intersect(i_1, u) → S
  56. Ray(B, H) → l_1
  57. Intersect(j_1, v) → U
  58. Intersect(j_1, u) → T
  59. Plane(A, T, U) → w
  60. Mirror(M', w) → M''_1
  61. Locus(M''_1, I) → loc4
  62. Mirror(D, w) → D'
  63. Mirror(G, w) → G'
  64. Polygon(C', C'', C''') → poly1, c''', c', c''
  65. Pyramid(poly1, C) → a_1, faceCC'C'', faceCC''C''', faceCC'C''', edgeCC', edgeCC'', edgeCC'''