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世界闻名的穹顶

世界闻名的穹顶
几何画板及绘图内容加载中，请稍等……
2018-12-03 16:31
三角函数立体几何几何作图
这个范例展示了世界各地著名的穹顶结构。它涉及三角形、圆和立体几何等核心数学概念。通过使用Vector、OrthogonalLine、Translate等GeoGebra命令，可以构造出穹顶的几何形状。适合高中学生和数学爱好者学习和探索。

GeoGebra 命令及参数

  1. Vector(O, Y) → v
  2. Vector(O, X) → w
  3. Vector(O, Z) → u
  4. OrthogonalLine(Vues, yAxis) → a_1
  5. OrthogonalLine(Vues, xAxis) → b
  6. Translate(O, Vector[(g * u)]) → A_1
  7. Segment(O, A_1) → d
  8. Mirror(A_1, O) → E_1
  9. Segment(E_1, O) → i
  10. Sequence(CurveCartesian[x(O) + ((R * cos(j°)) * sin(i)), y(O) + ((R * sin(j°)) * sin(i)), z(O) + ((R + a) * cos(i)), j, 0, 360], i, tt, t, π / ((10 * n))) → liste1
  11. Element(liste1, 1) → aa
  12. CurveCartesian(x(O) + ((R + 0.1) * sin(i°)), y(O) - ((R + 0.1) * cos(i°)), z(O) - 0.2, i, 0, 360) → o
  13. Vector(B, C) → z
  14. Translate(aa, z) → aa'
  15. Translate(aa, Vector[(2 * z)]) → aa'_1
  16. Segment(J, K) → r
  17. Sequence(I + (((r - 0.05) * cos(i)) * u) + (((r - 0.05) * sin(i)) * v), i, 0, 6.28319, π / n) → liste6
  18. Sequence((x(C) + ((r - 0.05) * cos(i)), y(C) + ((r - 0.05) * sin(i)), z(C)), i, 0, 6.28319, π / n) → liste5
  19. Sequence(Segment[Element[liste5, i], Element[liste6, i]], i, 1, Length[liste6]) → liste7
  20. Sequence((x(I) + ((r - 0.19) * cos(i)), y(I) + ((r - 0.19) * sin(i)), z(I)), i, 0, 6.28319, π / n) → liste8
  21. Sequence((x(D) + ((r - 0.19) * cos(i)), y(D) + ((r - 0.19) * sin(i)), z(D)), i, 0, 6.28319, π / n) → liste9
  22. Sequence(Segment[Element[liste8, i], Element[liste9, i]], i, 1, Length[liste8]) → liste10
  23. Sequence((x(D) + ((r - 0.35) * cos(i)), y(D) + ((r - 0.35) * sin(i)), z(D) + 0.1), i, 0, 6.28319, π / n) → liste12
  24. Sequence(Segment[Element[liste12, i], E], i, 1, Length[liste12]) → liste11
  25. Sequence(Translate[aa, Vector[(i * z)]], i, 0, 0.75, 0.2) → liste13
  26. Circle(G, E, xOyPlane) → c_1
  27. Sequence((x(C) + ((r - 0.05) * cos(i + bb)), y(C) + ((r - 0.05) * sin(i + bb)), z(C)), i, 0, 6.28319, π / n) → liste5b
  28. Sequence((x(I) + ((r - 0.05) * cos(i + bb)), y(I) + ((r - 0.05) * sin(i + bb)), z(I)), i, 0, 6.28319, π / n) → liste6b
  29. Sequence(Segment[Element[liste5b, i], Element[liste6b, i]], i, 1, Length[liste6]) → liste7b
  30. CurveCartesian(x(C) + ((r + 0.15) * cos(i)), y(C) + ((r + 0.15) * sin(i)), z(C) - 0.2, i, 0, 6.28319) → b_1
  31. Sequence(Translate[b_1, Vector[(i * z)]], i, 0, 1.75, 0.2) → liste14
  32. Sequence(Segment[Element[liste12, i], Element[liste12, i + 1]], i, 1, Length[liste12] + 1) → liste15
  33. Sequence((x(O) + ((R + 0.1) * sin(i°)), y(O) - ((R + 0.1) * cos(i°)), z(O) - 0.75), i, 0, 360, 180 / n) → liste16
  34. Sequence((x(O) + ((R + 0.1) * sin(i°)), y(O) - ((R + 0.1) * cos(i°)), z(O) - 0.2), i, 0, 360, 180 / n) → liste17
  35. Sequence(Segment[Element[liste16, i], Element[liste17, i]], i, 1, Length[liste17]) → liste18
  36. CurveCartesian(x(O) + (R * sin(i°)), y(O) - (R * cos(i°)), z(O) - 0.75, i, 0, 360) → f_1
  37. Vector(F, O) → u_1
  38. Sequence(Translate[f_1, Vector[(u_1 * i)]], i, 0, 1, 0.075) → liste19
  39. Segment(M, N) → j_1
  40. Sequence((x(O) + ((R + 0.2) * sin(i°)), y(O) - ((R + 0.2) * cos(i°)), z(O) - 1), i, 0, 360, 90 / n) → liste21
  41. Sequence((x(O) + ((R + 0.2) * sin(i°)), y(O) - ((R + 0.2) * cos(i°)), z(O) - 0.75), i, 0, 360, 90 / n) → liste20
  42. Sequence((x(O) + ((R + 0.3) * sin(i° + kk°)), y(O) - ((R + 0.3) * cos(i° + kk°)), z(O) - 1), i, 0, 360, 90 / n) → liste23
  43. Sequence(Polygon[Element[liste21, i], Element[liste21, i + 1], Element[liste20, 1 + i], Element[liste20, i]], i, 1, Length[liste20]) → liste22
  44. Sequence((x(O) + ((R + 0.3) * sin(i° + kk°)), y(O) - ((R + 0.3) * cos(i° + kk°)), z(O) - 0.75), i, 0, 360, 90 / n) → liste24
  45. Sequence(Polygon[Element[liste23, i], Element[liste23, i + 1], Element[liste24, 1 + i], Element[liste24, i]], i, 1, Length[liste24], 2) → liste25
  46. Sequence(CurveCartesian[x(O) + ((R * cos(j°)) * sin(i)), y(O) + ((R * sin(j°)) * sin(i)), z(O) + ((R + a) * cos(i)), i, tt, t], j, 0, 360, 180 / n) → liste2
  47. Sequence(CurveCartesian[x(O) + (((R + 0.1) * cos(j°)) * sin(i)), y(O) + (((R + 0.1) * sin(j°)) * sin(i)), z(O) + ((R + 0.1 + a) * cos(i)), i, tt, t], j, 0, 360, 180 / n) → liste3
  48. Sequence(CurveCartesian[x(O) + (((R + 0.05) * cos(j°)) * sin(i)), y(O) + (((R + 0.05) * sin(j°)) * sin(i)), z(O) + ((R + a + 0.05) * cos(i)), i, tt, t], j, 0, 360, 180 / ((3 * n))) → liste4
  49. CurveCartesian(x(I) + ((r - 0.05) * cos(i)), y(I) + ((r - 0.05) * sin(i)), z(I) - 0.07, i, 0, 6.28319) → d_1
  50. CurveCartesian(x(O) + ((R + 0.2) * sin(i°)), y(O) - ((R + 0.2) * cos(i°)), z(O) - 0.75, i, 0, 360) → g_1
  51. CurveCartesian(x(O) + ((R + 0.2) * sin(i°)), y(O) - ((R + 0.2) * cos(i°)), z(O) - 1, i, 0, 360) → h_1
  52. CurveCartesian(x(O) + (R * sin(i°)), y(O) - (R * cos(i°)), z(O) - (R * sin(i°)), i, 0, 360) → e
  53. CurveCartesian(x(O) + ((R + 0.1) * sin(i°)), y(O) - ((R + 0.1) * cos(i°)), z(O) - 0.75, i, 0, 360) → e_1
  54. CurveCartesian(x(O) + (R * sin(i°)^(3)), y(O) - (R * cos(i°)^(3)), z(O) - (R * sin(i°)^(3)), i, 0, 360) → f
  55. CurveCartesian(x(O) + ((R + 0.1) * sin(i°)), y(O) - ((R + 0.1) * cos(i°)), z(O) - (((R + 0.1) * 0) * sin(i°)), i, 0, 360) → j
  56. CurveCartesian(x(O) + ((R + 0.1) * sin(i°)), y(O) - ((R + 0.1) * cos(i°)), z(O) - 0.1, i, 0, 360) → l
  57. CurveCartesian(x(O) + ((R + 0.1) * sin(i°)), y(O) - ((R + 0.1) * cos(i°)), z(O) + 0, i, 0, 360) → p
  58. CurveCartesian(x(I) + ((r - 0.05) * cos(i)), y(I) + ((r - 0.05) * sin(i)), z(I), i, 0, 6.28319) → s
  59. CurveCartesian(x(O) + (R * sin(i°)), y(O) - (R * cos(i°)), z(O) - ((R * 0) * sin(i°)), i, 0, 360) → h
  60. Segment(L, G + (0, 0, 0.125)) → i_1
  61. Surface(x(O) + ((R * cos(j°)) * sin(i)), y(O) + ((R * sin(j°)) * sin(i)), z(O) + ((R + a) * cos(i)), j, 0, 360, i, tt, t) → l_1

AI 绘图提示语参考

绘制世界著名穹顶的几何图形，展示三角形、圆形和立体几何概念。首先构建三个基本向量，然后创建垂直线，接着通过平移和镜像操作形成基本结构。使用参数方程绘制圆形曲线，并通过序列操作生成多个同心圆和曲面。最后，将所有元素组合起来，形成复杂的穹顶结构，体现立体几何的构造过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。