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Archimedes Sphere Surface Area Diagram

Archimedes Sphere Surface Area Diagram
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2016-01-08 22:13
Solid GeometryGeometric ConstructionSlider Animation
This example demonstrates the calculation of the surface area of a sphere, involving geometric concepts. Construction uses GeoGebra commands like Segment, Circle, and Rotate. Suitable for high school mathematics teaching. Key points include the sphere surface area formula and construction steps.

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. Midpoint(K, D) →
  33. Distance(M, E) → distanceME
  34. Midpoint(M, E) →
  35. Distance(N, F) → distanceNF
  36. Midpoint(N, F) →
  37. Distance(Q, B) → distanceQB
  38. Midpoint(Q, B) →
  39. Distance(A, K) → distanceAK
  40. Midpoint(A, K) →
  41. Distance(L, M) → distanceLM
  42. Midpoint(L, M) →
  43. Distance(O, N) → distanceON
  44. Midpoint(O, N) →
  45. Distance(P, Q) → distancePQ
  46. Midpoint(P, Q) →
  47. Intersect(e_1, h_1) → R
  48. Distance(A, D) → distanceAD
  49. Midpoint(A, D) →
  50. Distance(A, B) → distanceAB
  51. Midpoint(A, B) →
  52. Segment(D, K) → r_1
  53. Segment(K, J) → p_1
  54. Segment(I, M) → q_1
  55. Segment(M, E) → r_2
  56. Segment(F, N) → r_3
  57. Segment(N, H) → t_1
  58. Segment(G, Q) → a_4
  59. Segment(Q, B) → r_4
  60. Segment(A, K) → a_11
  61. Segment(K, L) → a_2
  62. Segment(L, M) → b_2
  63. Segment(M, O) → c_2
  64. Segment(O, N) → d_2
  65. Segment(N, P) → e_2
  66. Segment(P, Q) → f_2
  67. Segment(Q, C) → g_2

AI Drawing Prompt Reference

Draw a sphere and calculate its surface area. Start by drawing a circle, then rotate the circle around its center to form the sphere's surface. Next, draw a polygon on the sphere's surface and connect its vertices to form the polygon's sides. Finally, calculate and mark the midpoints of the polygon's sides and the distances between the midpoints and the vertices.
The prompt above was compiled from the original drawing commands and is for reference only.