绘制圆形 by Diego Lieban

绘制圆形 by Diego Lieban
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2018-11-04 00:23
①本范例演示如何使用 GeoGebra 绘制圆形及其相关几何元素;②涉及的核心数学概念包括圆、坐标几何、几何变换和矩阵运算;③作图要点——从下方『构造摘要』提炼用到了 Polygon(多边形)、Midpoint(中点)、Circle(圆形)、Intersect(交点)、Line(直线)、Rotate(旋转)、Tangent(切线)等 GeoGebra 命令/对象;④适合高中数学教学,用于讲解圆的性质、几何变换及坐标几何应用。

GeoGebra 命令及参数

  1. Polygon(C_{c7}, C_{c10}, 3) → poly1, f, g, h, C_{c1}
  2. Midpoint(h) → D
  3. Midpoint(g) → E
  4. Midpoint(f) → F
  5. Circle(C_{c7}, 1) → c_7gray
  6. Circle(C_{c1}, 1) → c_1orange
  7. Circle(C_{c10}, 1) → c_{10}gray
  8. Intersect(c_1orange, h, 1) → G
  9. Intersect(c_1orange, g, 1) → H
  10. Intersect(c_{10}gray, g, 1) → I
  11. Intersect(c_7gray, f, 1) → J
  12. Intersect(c_7gray, h, 1) → K
  13. Intersect(c_{10}gray, f, 1) → L
  14. Midpoint(J, F) → C_{c8}
  15. Circle(C_{c8}, 1) → c_8gray
  16. Midpoint(F, L) → C_{c9}
  17. Midpoint(I, E) → C_{c6}
  18. Midpoint(E, H) → C_{c3}
  19. Midpoint(G, D) → C_{c2}
  20. Midpoint(D, K) → C_{c4}
  21. Circle(C_{c2}, 1) → c_2orange
  22. Circle(C_{c4}, 1) → c_4gray
  23. Circle(C_{c3}, 1) → c_3gray
  24. Circle(C_{c6}, 1) → c_6gray
  25. Circle(C_{c9}, 1) → c_9gray
  26. Midpoint(C_{c4}, C_{c6}) → C_{c5}
  27. Circle(C_{c5}, 1) → c_5gray
  28. Line(A, B) → i
  29. Rotate(B, 120°, C_{c10}) → B'
  30. Rotate(A, (-(120°)), C_{c7}) → A'
  31. Tangent(A', c_7gray) → j,
  32. Tangent(B', c_{10}gray) → k,
  33. Intersect(j, k) → C
  34. Intersect(i, j) → M
  35. Intersect(i, k) → N
  36. Polygon(M, N, C) → t1, c_{11}, m, n
  37. Circle(C_{laranja}, 1) → d
  38. Circle(C_{verde}, 1) → e
  39. Circle(C_{roxo}, 1) → p
  40. Circle(C_{c2}, 1) → c_2purple
  41. Circle(C_{c2}, 1) → c_2green
  42. Circle(C_{c2}, 1) → c_2gray
  43. Circle(C_{c1}, 1) → c_1gray
  44. Circle(C_{c1}, 1) → c_1purple
  45. Circle(C_{c1}, 1) → c_1green
  46. Circle(C_{c3}, 1) → c_3orange
  47. Circle(C_{c3}, 1) → c_3green
  48. Circle(C_{c3}, 1) → c_3purple
  49. Circle(C_{c4}, 1) → c_4orange
  50. Circle(C_{c4}, 1) → c_4green
  51. Circle(C_{c4}, 1) → c_4purple
  52. Circle(C_{c5}, 1) → c_5orange
  53. Circle(C_{c5}, 1) → c_5green
  54. Circle(C_{c5}, 1) → c_5purple
  55. Circle(C_{c6}, 1) → c_6green
  56. Circle(C_{c6}, 1) → c_6purple
  57. Circle(C_{c6}, 1) → c_6orange
  58. Circle(C_{c7}, 1) → c_7orange
  59. Circle(C_{c7}, 1) → c_7green
  60. Circle(C_{c7}, 1) → c_7purple
  61. Circle(C_{c8}, 1) → c_8green
  62. Circle(C_{c8}, 1) → c_8orange
  63. Circle(C_{c8}, 1) → c_8purple
  64. Circle(C_{c9}, 1) → c_9green
  65. Circle(C_{c9}, 1) → c_9purple
  66. Circle(C_{c9}, 1) → c_9orange
  67. Circle(C_{c10}, 1) → c_{10}green
  68. Circle(C_{c10}, 1) → c_{10}purple
  69. Circle(C_{c10}, 1) → c_{10}orange

AI 绘图提示语参考

画一个由三个正三角形构成的图形,每个三角形的顶点都在三个不同颜色的圆上,这些圆的圆心分别是三个正三角形的中心。在每个三角形的中点画小圆,并在相邻小圆之间画连接线。最后,在这些线上画切线,并将切线的交点连接起来形成另一个多边形。
以上提示语为根据原始绘图命令整理而来,仅供参考。