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VIBE Sphere Structure

VIBE Sphere Structure
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2019-04-27 05:32
FunctionTrigonometrySolid GeometryGeometric Construction
This example demonstrates a complex geometric structure composed of a sphere and scalene triangles, showcasing continuity and translation transformations between polygons and the sphere. Core math concepts include sphere, scalene triangles, continuity, translation, logarithmic functions, difference, and slope. Construction highlights the use of GeoGebra commands/objects like Point, Angle, Sphere, Polygon. Suitable for high school and above learners to explore the integration of solid geometry and function graphs.

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