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Sphere and Polygon Intersection Demo

Sphere and Polygon Intersection Demo
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2017-08-19 14:44
VectorCoordinate GeometrySolid GeometryCalculusGeometric Construction
This example demonstrates the intersection points between a sphere and polygons (e.g., scalene triangles), involving core math concepts like solid geometry, coordinate geometry, vector operations, and differential calculus. Construction highlights include using GeoGebra commands like Textfield, Segment, Rotate, CircleArc, Distance, Intersect, Point, Mirror, Line, Vector, and Translate to create geometric objects and calculate intersections. Suitable for high school students and math enthusiasts exploring spatial geometry and calculus applications.

GeoGebra Commands & Parameters

  1. Textfield(a) → InputBox1
  2. Segment(A, B) → f
  3. Rotate(A, 32°, A) → A'
  4. Rotate(B, 32°, A) → B'
  5. CircleArc(C, H, I) → h
  6. Segment(H, I) → g_Π
  7. Distance(K, L) → distanceKL
  8. Distance(M, N) → distanceMN
  9. Segment(N, M) → i
  10. Segment(L, K) → j
  11. Segment(K, N) → k_Φ
  12. Segment(M, L) → l
  13. Intersect(i, j) → O
  14. Segment(F, G_2) → m
  15. Segment(D, E) → p
  16. Point(j) → R
  17. Segment(M, R) → q
  18. Mirror(M, j) → M'
  19. Mirror(R, j) → R'
  20. Mirror(M, i) → M'_1
  21. Mirror(R, i) → R'_1
  22. Segment(M'_1, R'_1) → q'_1
  23. Segment(R', N) → s
  24. Segment(N, R'_1) → t
  25. Point(j) → S
  26. Segment(R'_1, S) → r
  27. Point(r) → T
  28. Segment(R, T) → a_1
  29. Distance(T, R'_1) → distanceTR'1
  30. Line(R'_1, t) → b_1
  31. Line(T, a_1) → c_1
  32. Segment(R'_1, T) → d_1
  33. Intersect(i, q) → U
  34. Segment(T, U) → e_1
  35. Segment(C, B) → f_1
  36. Segment(C, A) → g_1
  37. Segment(R', U) → h_1
  38. Intersect(i, j) → V
  39. Line(V, h_1) → i_1
  40. Mirror(R', i_1) → R''
  41. Mirror(U, i_1) → U'
  42. Segment(R'', U') → j_1
  43. Line(V, s) → k_1
  44. Mirror(R', k_1) → R''_1
  45. Mirror(N, k_1) → N'
  46. Segment(R''_1, N') → s'
  47. Vector(W, Z) → u
  48. Translate(R''_1, u) → A_1
  49. Translate(N', u) → N''
  50. Segment(A_1, N'') → s''
  51. Mirror(A_1, k_1) → B_1
  52. Mirror(N'', k_1) → N'''
  53. Segment(B_1, N''') → s'''
  54. Vector(C_1, D_1) → v
  55. Translate(B_1, v) → E_1
  56. Translate(N''', v) → F_1
  57. Vector(G_1, H_1) → w
  58. Translate(R'', w) → R'''
  59. Translate(U', w) → U''
  60. Segment(R''', U'') → l_1
  61. Point(j) → K_1
  62. Point(p) → L_1
  63. Segment(K_1, L_1) → m_1
  64. Point(p) → N_1
  65. Point(j) → O_1
  66. Segment(N_1, O_1) → q_1
  67. Point(i) → P_1
  68. Point(j) → Q_1
  69. Segment(P_1, Q_1) → r_1
  70. Point(f) → M_1
  71. Segment(M_1, R_1) → n_1
  72. Segment(M_1, S_1) → p_1
  73. Point(p) → T_1
  74. Segment(S_1, T_1) → s_1
  75. Segment(S_1, U_1) → t_1
  76. Segment(U_1, R_1) → a_2
  77. Segment(N_1, U_1) → b_2
  78. Segment(V_1, W_1) → c_2
  79. Segment(Z_1, A_2) → d_2
  80. Segment(N, B) → f_2
  81. Segment(B, A) → g_2
  82. Segment(N, A) → h_2
  83. Segment(Q, B_2) → i_2
  84. Segment(C_2, D_2) → j_2
  85. Segment(E_2, F_2) → k_2