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VIBE球体结构

VIBE球体结构
几何画板及绘图内容加载中，请稍等……
2019-04-27 05:32
函数三角函数立体几何几何作图
①本范例演示了一个由球体和不等边三角形构成的复杂几何结构，展示了多边形与球体的连续性和平移变换；②涉及的核心数学概念包括球体、不等边三角形、连续性、平移、对数函数、差值与斜率；③作图要点——从下方『构造摘要』提炼用到了Point（点）、Angle（角）、Sphere（球体）、Polygon（多边形）等GeoGebra命令/对象；④适合高中及以上数学学习者，用于理解立体几何与函数图像的结合应用。

GeoGebra 命令及参数

  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