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VIBE Sphere

VIBE Sphere
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2019-04-28 23:39
FunctionSolid GeometryGeometric Construction
This example demonstrates a dynamic sphere model integrating colors and geometric shapes to illustrate concepts like volume and frequency distribution. Core mathematical concepts include sphere volume calculation, polygon construction, angle measurement, and function graphing. GeoGebra commands used in construction are Point, Angle, Sphere, and Polygon. Suitable for high school students and math enthusiasts exploring solid geometry, function graphs, and geometric constructions.

GeoGebra Commands & Parameters

  1. Point({-2, 0, 0}) → Warm
  2. Point({0, 0, 2}) → Dom
  3. Point({0, 0, -2}) → Sub
  4. Point({-1.41, 0, 1.41}) → WarmDom
  5. Point({-1.41, 0, -1.41}) → WarmSub
  6. Point({1.41, 0, -1.41}) → ColdSub
  7. Point({1.41, 0, 1.41}) → ColdDom
  8. Point({0, 0, 0}) → ZeroAxis
  9. Point({0, 1.73, 1}) → NeutDomPure
  10. Angle(ZeroAxis, WarmPure, NeutDomPure) → α
  11. Sphere(ZeroAxis, Warm) → a
  12. Polygon(Cold, ColdPure, 6, xOyPlane) → poly1, f, D, g, h, i, j, k, A, B, C
  13. Polygon(Dom, ColdDom, Cold, ColdSub, Sub, WarmSub, Warm, WarmDom) → poly2, dom, colddom, cold, coldsub, sub, warmsub, warm, warmdom
  14. Point({0, 1.73, -1}) → NeutSubPure
  15. Point({0.707, 1.73, 0.707}) → ColdDomPure
  16. Point({-0.707, 1.73, 0.707}) → WarmDomPure
  17. Point({-0.707, 1.73, -0.707}) → WarmSubPure
  18. Point({0.707, 1.73, -0.707}) → ColdSubPure
  19. Point({0, -1.73, 1}) → NeutDomDirty
  20. Point({0, -1.73, -1}) → NeutSubDirty
  21. Point({0.707, -1.73, 0.707}) → ColdDomDirty
  22. Point({-0.707, -1.73, 0.707}) → WarmDomDirty
  23. Point({-0.707, -1.73, -0.707}) → WarmSubDirty
  24. Point({0.707, -1.73, -0.707}) → ColdSubDirty
  25. Polygon(Dom, NeutDomPure, NeutSubPure, Sub, NeutSubDirty, NeutDomDirty) → poly3, l, neutdompure, neutsubpure, m, neutsubdirty, neutdomdirty
  26. Polygon(Dom, WarmDom, WarmDomPure, NeutDomPure) → q1, n, p, warmdompure, q
  27. Polygon(WarmDom, Warm, WarmPure, WarmDomPure) → q2, r, s, warmpure, t
  28. Polygon(NeutDomPure, ColdDomPure, ColdPure, ColdSubPure, NeutSubPure, WarmSubPure, WarmPure, WarmDomPure) → poly4, b, colddompure, coldpure, coldsubpure, c, warmsubpure, d, e
  29. Polygon(Dom, ColdDom, ColdDomPure, NeutDomPure) → q3, f_1, g_1, h_1, i_1
  30. Polygon(ColdDom, Cold, ColdPure, ColdDomPure) → q4, j_1, k_1, l_1, m_1
  31. Polygon(Cold, ColdPure, ColdSubPure, ColdSub) → q5, n_1, p_1, q_1, r_1
  32. Polygon(ColdSubPure, NeutSubPure, Sub, ColdSub) → q6, s_1, t_1, a_1, b_1
  33. Polygon(WarmSubPure, NeutSubPure, Sub, WarmSub) → q7, c_1, d_1, e_1, f_2
  34. Polygon(Warm, WarmSub, WarmSubPure, WarmPure) → q8, g_2, h_2, i_2, j_2
  35. Polygon(WarmDom, WarmDomDirty, WarmDirty, Warm) → q9, k_2, warmdomdirty, warmdirty, l_2
  36. Polygon(Dom, NeutDomDirty, WarmDomDirty, WarmDom) → q10, m_2, n_2, p_2, q_2
  37. Polygon(Dom, ColdDom, ColdDomDirty, NeutDomDirty) → q11, r_2, s_2, colddomdirty, t_2
  38. Polygon(D, ColdDomDirty, ColdDom, Cold) → q12, d_2, a_2, b_2, c_2
  39. Polygon(D, ColdSubDirty, ColdSub, Cold) → q13, d_3, coldsubdirty, e_2, f_3
  40. Polygon(ColdSubDirty, NeutSubDirty, Sub, ColdSub) → q14, g_3, h_3, i_3, j_3
  41. Polygon(WarmSubDirty, NeutSubDirty, Sub, WarmSub) → q15, warmsubdirty, k_3, l_3, m_3
  42. Polygon(WarmSubDirty, C, B, WarmSub) → q16, n_3, c_3, b_3, p_3

AI Drawing Prompt Reference

Draw a dynamic sphere model showcasing colors and geometric shapes to illustrate volume and frequency distribution. Include a central sphere with multiple points forming colored polygons like hexagons and pentagons around it. Connect some points to create angles, highlighting spatial relationships. Start with the sphere and base points, then build the polygons, and finally use colors to differentiate regions, showing volume and frequency distribution.
The prompt above was compiled from the original drawing commands and is for reference only.