Gal 3: 圆链几何演示

Gal 3: 圆链几何演示
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2019-07-30 04:23
①本范例演示了通过动态圆链构建复杂几何图形的现象;②涉及的核心数学概念包括圆、几何作图、不等式、向量与三维空间;③作图要点提炼自构造摘要,使用了Point(点)、Segment(线段)、Circle(圆)、Intersect(交点)、CircleSector(圆扇形)等GeoGebra命令与对象;④适合高中及以上数学学习者,用于理解空间几何与参数化作图的原理与技巧。

GeoGebra 命令及参数

  1. Point(yAxis) → A_0
  2. Point(Circle[A_0, (2 * r)]) → A_1
  3. Segment(A_0, A_1) → f
  4. Point(Circle[A_1, (2 * r)]) → A_2
  5. Segment(A_1, A_2) → g
  6. Point(Circle[A_2, (2 * r)]) → A_3
  7. Segment(A_2, A_3) → h
  8. Point(Circle[A_3, (2 * r)]) → A_4
  9. Segment(A_3, A_4) → i
  10. Point(Circle[A_4, (2 * r)]) → A_5
  11. Segment(A_4, A_5) → j
  12. Point(Circle[A_5, (2 * r)]) → A_6
  13. Segment(A_5, A_6) → k
  14. Point(Circle[A_6, (2 * r)]) → A_7
  15. Segment(A_6, A_7) → l
  16. Point(Circle[A_7, (2 * r)]) → A_8
  17. Segment(A_7, A_8) → m
  18. Point(Circle[A_8, (2 * r)]) → A_9
  19. Segment(A_8, A_9) → n
  20. Point(Circle[A_9, (2 * r)]) → A_{10}
  21. Segment(A_9, A_{10}) → p
  22. Point(Circle[A_{10}, (2 * r)]) → A_{11}
  23. Segment(A_{10}, A_{11}) → q
  24. Point(Circle[A_{11}, (2 * r)]) → A_{12}
  25. Segment(A_{11}, A_{12}) → s
  26. Point(Circle[A_{12}, (2 * r)]) → A_{13}
  27. Segment(A_{12}, A_{13}) → t
  28. Point(Circle[A_{13}, (2 * r)]) → A_{14}
  29. Segment(A_{13}, A_{14}) → a
  30. Circle(A_0, (2 * r)) → d
  31. Circle(A_{14}, (2 * r)) → e
  32. Intersect(d, e) → B, A_{15}, ,
  33. Segment(A_{15}, A_{14}) → b
  34. Segment(A_{15}, A_0) → c
  35. Circle(A_0, r) → c_1
  36. Circle(A_1, r) → d_1
  37. Circle(A_2, r) → e_1
  38. Circle(A_3, r) → f_1
  39. Circle(A_4, r) → g_1
  40. Circle(A_5, r) → h_1
  41. Circle(A_6, r) → k_1
  42. Circle(A_7, r) → p_1
  43. Circle(A_8, r) → q_1
  44. Circle(A_9, r) → r_1
  45. Circle(A_{11}, r) → s_1
  46. Circle(A_{10}, r) → t_1
  47. Circle(A_{12}, r) → c_2
  48. Circle(A_{13}, r) → d_2
  49. Circle(A_{14}, r) → e_2
  50. Circle(A_{15}, r) → f_2
  51. Intersect(e_1, g) → A,
  52. Intersect(d_1, f) → C,
  53. Intersect(c_1, c) → D,
  54. Intersect(f_2, b) → E,
  55. Intersect(e_2, a) → F,
  56. Intersect(d_2, t) → G,
  57. Intersect(c_2, s) → H,
  58. Intersect(s_1, q) → I,
  59. Intersect(t_1, p) → J,
  60. Intersect(r_1, n) → K,
  61. Intersect(q_1, m) → L,
  62. Intersect(p_1, l) → M,
  63. Intersect(k_1, k) → N,
  64. Intersect(h_1, j) → O,
  65. Intersect(f_1, i) → P,
  66. Intersect(f_1, h) → Q,
  67. CircleSector(A_0, C, D) → g_2
  68. CircleSector(A_1, A, C) → h_2
  69. CircleSector(A_2, Q, A) → k_2
  70. CircleSector(A_3, P, Q) → p_2
  71. CircleSector(A_4, O, P) → q_2
  72. CircleSector(A_5, N, O) → r_2
  73. CircleSector(A_6, M, N) → s_2
  74. CircleSector(A_7, L, M) → t_2
  75. CircleSector(A_8, K, L) → c_3
  76. CircleSector(A_9, J, K) → d_3
  77. CircleSector(A_{10}, I, J) → e_3
  78. CircleSector(A_{11}, H, I) → f_3
  79. CircleSector(A_{12}, G, H) → g_3
  80. CircleSector(A_{13}, F, G) → h_3
  81. CircleSector(A_{14}, E, F) → k_3
  82. CircleSector(A_{15}, D, E) → p_3

AI 绘图提示语参考

在三维空间中,从y轴上的一个点开始,依次以该点为圆心、以两倍半径作圆,并在每个圆上取一点作为下一个圆心,重复此过程,形成一条由十五个点组成的链。连接相邻点得到一系列线段,构成一条折线。首尾两个点分别以两倍半径作圆,两圆相交于两个点,取其中一个点与首尾点相连,形成闭合三角形。再以每个链上的点为圆心、以单倍半径作小圆,形成一串相切的小圆链,整体呈现几何构造的链条与闭合结构。
以上提示语为根据原始绘图命令整理而来,仅供参考。