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Voronoi on Sphere

Voronoi on Sphere
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2020-01-09 17:25
TrigonometrySolid GeometryProbability & StatisticsGeometric ConstructionGraphing
In collections Color 3D surfaces
This example demonstrates the generation of Voronoi diagrams on a sphere, illustrating the geometric partitioning of space around points. Key math concepts include spherical geometry, spatial partitioning, and conditional probability. Construction involves commands like Sphere and objects R, R_1, A1-A36 to define points on the sphere and create Voronoi regions. Suitable for high school students and spatial geometry enthusiasts to explore polyhedral division and spatial probability distributions.

GeoGebra Commands & Parameters

  1. Sphere(B1, r) → C1
  2. Sphere(B2, r) → C2
  3. Sphere(B3, r) → C3
  4. Sphere(B4, r) → C4
  5. Sphere(B5, r) → C5
  6. Sphere(B6, r) → C6
  7. Sphere(B7, r) → C7
  8. Sphere(B8, r) → C8
  9. Sphere(B9, r) → C9
  10. Sphere(B10, r) → C10
  11. Sphere(B11, r) → C11
  12. Sphere(B12, r) → C12
  13. Sphere(B13, r) → C13
  14. Sphere(B14, r) → C14
  15. Sphere(B15, r) → C15
  16. Sphere(B16, r) → C16
  17. Sphere(B17, r) → C17
  18. Sphere(B18, r) → C18
  19. Sphere(B19, r) → C19
  20. Sphere(B20, r) → C20
  21. Sphere(B21, r) → C21
  22. Sphere(B22, r) → C22
  23. Sphere(B23, r) → C23
  24. Sphere(B24, r) → C24
  25. Sphere(B25, r) → C25
  26. Sphere(B26, r) → C26
  27. Sphere(B27, r) → C27
  28. Sphere(B28, r) → C28
  29. Sphere(B29, r) → C29
  30. Sphere(B30, r) → C30
  31. Sphere(B31, r) → C31
  32. Sphere(B32, r) → C32
  33. Sphere(B33, r) → C33
  34. Sphere(B34, r) → C34
  35. Sphere(B35, r) → C35
  36. Sphere(B36, r) → C36
  37. Sphere(B37, r) → C37
  38. Sphere(B38, r) → C38
  39. Sphere(B39, r) → C39
  40. Sphere(B40, r) → C40
  41. Sphere(B41, r) → C41
  42. Sphere(B42, r) → C42
  43. Sphere(B43, r) → C43
  44. Sphere(B44, r) → C44
  45. Sphere(B45, r) → C45
  46. Sphere(B46, r) → C46
  47. Sphere(B47, r) → C47
  48. Sphere(B48, r) → C48
  49. Sphere(B49, r) → C49
  50. Sphere(B50, r) → C50
  51. Sphere(B51, r) → C51
  52. Sphere(B52, r) → C52
  53. Sphere(B53, r) → C53
  54. Sphere(B54, r) → C54
  55. Sphere(B55, r) → C55
  56. Sphere(B56, r) → C56
  57. Sphere(B57, r) → C57
  58. Sphere(B58, r) → C58
  59. Sphere(B59, r) → C59
  60. Sphere(B60, r) → C60
  61. Sphere(B61, r) → C61
  62. Sphere(B62, r) → C62
  63. Sphere(B63, r) → C63
  64. Sphere(B64, r) → C64
  65. Sphere(B65, r) → C65
  66. Sphere(B66, r) → C66
  67. Sphere(B67, r) → C67
  68. Sphere(B68, r) → C68
  69. Sphere(B69, r) → C69
  70. Sphere(B70, r) → C70
  71. Sphere(B71, r) → C71
  72. Sphere(B72, r) → C72
  73. Sphere(B73, r) → C73
  74. Sphere(B74, r) → C74
  75. Sphere(B75, r) → C75
  76. Sphere(B76, r) → C76
  77. Sphere(B77, r) → C77
  78. Sphere(B78, r) → C78
  79. Sphere(B79, r) → C79
  80. Sphere(B80, r) → C80
  81. Sphere(B81, r) → C81
  82. Sphere(B82, r) → C82
  83. Sphere(B83, r) → C83
  84. Sphere(B84, r) → C84
  85. Sphere(B85, r) → C85
  86. Sphere(B86, r) → C86
  87. Sphere(B87, r) → C87
  88. Sphere(B88, r) → C88
  89. Sphere(B89, r) → C89
  90. Sphere(B90, r) → C90
  91. Sphere(B91, r) → C91
  92. Sphere(B92, r) → C92
  93. Sphere(B93, r) → C93
  94. Sphere(B94, r) → C94
  95. Sphere(B95, r) → C95
  96. Sphere(B96, r) → C96
  97. Sphere(B97, r) → C97
  98. Sphere(B98, r) → C98
  99. Sphere(B99, r) → C99
  100. Sphere(B100, r) → C100
  101. Sphere(B101, r) → C101
  102. Sphere(O, R_1 + r) → a

AI Drawing Prompt Reference

Draw a Voronoi diagram on a sphere by placing 36 points randomly on the sphere and generating Voronoi regions based on these points. First, create 36 spheres with the same radius, each centered at one of these 36 points.
The prompt above was compiled from the original drawing commands and is for reference only.