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Five Point Sphere

Five Point Sphere
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2019-06-15 04:44
TrigonometryCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the geometric construction and properties of a five-point sphere. It involves core mathematical concepts such as sphere, trigonometry, median value, fractions, Pythagorean theorem, and ellipse. The construction utilizes GeoGebra commands/objects like Intersect, Point, Sphere, PointIn, Midpoint, CircleArc, Segment, OrthogonalPlane, and OrthogonalLine. It is suitable for high school and above, particularly for teaching and exploring solid geometry and coordinate geometry.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, zAxis) → A
  2. Point(zAxis) → B
  3. Sphere(A, B) → a
  4. PointIn(a) → C
  5. PointIn(a) → E
  6. PointIn(a) → F
  7. PointIn(a) → D
  8. Midpoint(B, F) → G
  9. Midpoint(B, D) → H
  10. Midpoint(B, C) → I
  11. Midpoint(B, E) → J
  12. Midpoint(C, D) → K
  13. Midpoint(C, E) → L
  14. Midpoint(C, F) → M
  15. Midpoint(D, E) → N
  16. Midpoint(D, F) → O
  17. CircleArc(A, B, C) → c
  18. CircleArc(A, B, D) → d
  19. CircleArc(A, B, E) → e
  20. CircleArc(A, B, F) → f
  21. CircleArc(A, C, D) → g
  22. CircleArc(A, C, E) → h
  23. CircleArc(A, C, F) → k
  24. CircleArc(A, D, E) → p
  25. CircleArc(A, D, F) → q
  26. CircleArc(A, E, F) → r
  27. Point(c) → P
  28. Point(d) → Q
  29. Point(e) → R
  30. Point(f) → S
  31. Point(g) → T
  32. Point(h) → U
  33. Point(k) → V
  34. Point(p) → W
  35. Point(q) → Z
  36. Point(r) → A_1
  37. Segment(B, D) → i
  38. Segment(B, F) → j
  39. Segment(B, E) → l
  40. Segment(B, C) → m
  41. Segment(C, D) → n
  42. Segment(C, E) → s
  43. Segment(C, F) → t
  44. Segment(D, E) → b
  45. Segment(D, F) → f_1
  46. Segment(F, E) → g_1
  47. OrthogonalPlane(P, m) → p_1
  48. OrthogonalPlane(Q, i) → q_1
  49. OrthogonalPlane(R, l) → r_1
  50. OrthogonalPlane(S, j) → p_2
  51. OrthogonalPlane(T, n) → q_2
  52. OrthogonalPlane(U, s) → r_2
  53. OrthogonalPlane(V, t) → p_3
  54. OrthogonalPlane(W, b) → q_3
  55. OrthogonalPlane(Z, f_1) → r_3
  56. OrthogonalPlane(A_1, g_1) → p_4
  57. OrthogonalLine(A, p_1) → h_1
  58. Circle(h_1, P) → c_1
  59. OrthogonalLine(A, q_1) → i_1
  60. Circle(i_1, Q) → d_1
  61. OrthogonalLine(A, r_1) → j_1
  62. Circle(j_1, R) → e_1
  63. OrthogonalLine(A, p_2) → k_1
  64. Circle(k_1, S) → s_1
  65. OrthogonalLine(A, q_2) → l_1
  66. Circle(l_1, T) → t_1
  67. OrthogonalLine(A, r_2) → m_1
  68. OrthogonalLine(A, p_3) → n_1
  69. Circle(n_1, V) → e_2
  70. OrthogonalLine(A, q_3) → a_1
  71. Circle(a_1, W) → f_2
  72. OrthogonalLine(A, r_3) → b_1
  73. Circle(b_1, Z) → g_2
  74. OrthogonalLine(A, r_2) → h_2
  75. Circle(h_2, U) → k_2
  76. OrthogonalLine(A, p_4) → i_2
  77. Circle(i_2, A_1) → s_2