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Archimedes Surface Area of a Sphere Diagram

Archimedes Surface Area of a Sphere Diagram
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2016-01-09 01:42
Solid GeometryTransformationGeometric Construction
This example demonstrates Archimedes' diagram for the surface area of a sphere. Key mathematical concepts include spheres, area, and rotation. Using GeoGebra commands such as Segment, Circle, Point, Rotate, and Polygon, a dynamic surface area diagram of a sphere is constructed. Suitable for high school mathematics education and learning solid geometry.

GeoGebra Commands & Parameters

  1. Segment(A_1, B_1) → a
  2. Circle(O, a) → c
  3. Point(c) → A
  4. Rotate(A, α, O) → J
  5. Polygon(A, J, n) → poly1, b, l, I, H, G, C, B, F, E, D, d, e, f, g, h, i, j, k
  6. Segment(A, D) → m
  7. Segment(D, E) → p
  8. Segment(E, F) → q
  9. Segment(F, B) → r
  10. Segment(B, C) → s
  11. Segment(C, G) → t
  12. Segment(G, H) → a_3
  13. Segment(H, I) → b_1
  14. Segment(I, J) → c_1
  15. Segment(J, A) → d_1
  16. Segment(A, C) → e_1
  17. Segment(J, D) → f_1
  18. Segment(I, E) → g_1
  19. Segment(H, F) → h_1
  20. Segment(G, B) → i_1
  21. Segment(H, B) → j_1
  22. Segment(I, F) → k_1
  23. Segment(J, E) → l_1
  24. Segment(A, B) → m_1
  25. Intersect(e_1, f_1) → K
  26. Intersect(e_1, l_1) → L
  27. Intersect(e_1, g_1) → M
  28. Intersect(e_1, h_1) → N
  29. Intersect(e_1, j_1) → P
  30. Intersect(e_1, i_1) → Q
  31. Distance(K, D) → distanceKD
  32. Distance(M, E) → distanceME
  33. Distance(N, F) → distanceNF
  34. Distance(Q, B) → distanceQB
  35. Distance(A, K) → distanceAK
  36. Distance(L, M) → distanceLM
  37. Distance(O, N) → distanceON
  38. Distance(P, Q) → distancePQ
  39. Intersect(e_1, h_1) → R
  40. Distance(A, D) → distanceAD
  41. Distance(A, B) → distanceAB
  42. Segment(D, K) → r_1
  43. Segment(K, J) → p_1
  44. Segment(I, M) → q_1
  45. Segment(M, E) → r_2
  46. Segment(F, N) → r_3
  47. Segment(N, H) → t_1
  48. Segment(G, Q) → a_4
  49. Segment(Q, B) → r_4
  50. Segment(A, K) → a_11
  51. Segment(K, L) → a_2
  52. Segment(L, M) → b_2
  53. Segment(M, O) → c_2
  54. Segment(O, N) → d_2
  55. Segment(N, P) → e_2
  56. Segment(P, Q) → f_2
  57. Segment(Q, C) → g_2
  58. Line(H, G) → a_1
  59. Line(G, C) → n_1
  60. Line(I, H) → s_1
  61. Surface(t, (a_1(t) * cos(u)), (a_1(t) * sin(u)), t, x(H), x(G), u, 0, (2 * π)) → w
  62. Surface(t, (s_1(t) * cos(u)), (s_1(t) * sin(u)), t, x(I), x(H), u, 0, (2 * π)) → u_1
  63. Surface(t, (n_1(t) * cos(u)), (n_1(t) * sin(u)), t, x(G), x(C), u, 0, (2 * π)) → o_1
  64. Line(J, I) → h_2
  65. Surface(t, (h_2(t) * cos(u)), (h_2(t) * sin(u)), t, x(J), x(I), u, 0, (2 * π)) → v_1
  66. Line(A, J) → i_2
  67. Surface(t, (i_2(t) * cos(u)), (i_2(t) * sin(u)), t, x(A), x(J), u, 0, (2 * π)) → w_1
  68. Circle(K, distanceKD, y = y(K)) → k_2
  69. Circle(M, distanceME, y = y(M)) → p_2
  70. Circle(N, distanceNF, y = y(N)) → q_2
  71. Circle(Q, distanceQB, y = y(Q)) → s_2