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刚性变换与相似变换组合工具

刚性变换与相似变换组合工具
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2014-09-17 08:14
函数解析几何变换
所属专题 Congruence (CO) Cluster Congruence (Vol 1) Congruence (Vol 1) Over 80 Resources CCSS High School: Geometry (Congruence) Volume 1 S N ATTAR Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1 CCSS High School: Geometry (Congruence) Volume 1
该范例演示了刚性变换与相似变换的组合。刚性变换包括平移、旋转和反射，相似变换则包括这些变换加上比例变换。通过调整参数，可以观察变换组合的效果。涉及的核心数学概念包括几何变换、相似变换和比例变换。使用了TextField、Segment、Element、Polygon等GeoGebra命令进行构造。适合初中及以上学生或教师使用。

GeoGebra 命令及参数

  1. Textfield(m) → inputBox1
  2. Textfield(b) → inputBox2
  3. Segment(A, B) → a
  4. Segment(B, C) → c
  5. Segment(C, A) → d
  6. Element(A5, 1, 1) → B5
  7. Element(A5, 1, 2) → C5
  8. Element(A6, 1, 1) → B6
  9. Element(A7, 1, 1) → B7
  10. Element(A6, 1, 2) → C6
  11. Element(A7, 1, 2) → C7
  12. Element(A9, 1, 1) → B9
  13. Element(A9, 1, 2) → C9
  14. Element(A10, 1, 1) → B10
  15. Element(A11, 1, 1) → B11
  16. Element(A10, 1, 2) → C10
  17. Element(A11, 1, 2) → C11
  18. Element(A13, 1, 1) → B13
  19. Element(A14, 1, 1) → B14
  20. Element(A15, 1, 1) → B15
  21. Element(A18, 1, 1) → B18
  22. Element(A18, 1, 2) → C18
  23. Element(A19, 1, 1) → B19
  24. Element(A19, 1, 2) → C19
  25. Element(A20, 1, 1) → B20
  26. Element(A20, 1, 2) → C20
  27. Segment(D15, D14) → g
  28. Segment(D13, D14) → h
  29. Segment(D15, D13) → i
  30. Segment(D20, D19) → j
  31. Segment(D19, D18) → k
  32. Segment(D18, D20) → l
  33. Segment(D11, D9) → n
  34. Segment(D9, D10) → p
  35. Segment(D10, D11) → q
  36. Segment(D6, D7) → r
  37. Segment(D5, D7) → s
  38. Segment(D6, D5) → t
  39. Polygon(D, F, G, E) → poly1, d_1, f_1, g_1, e_1
  40. Polygon(H, I, J, K) → poly2, h_1, i_1, j_1, k_1
  41. Polygon(L, M, N, O) → poly3, l_1, m_1, n_1, o_1
  42. Element(A23, 1, 1) → B23
  43. Element(A23, 1, 2) → C23
  44. Element(A24, 1, 1) → B24
  45. Element(A24, 1, 2) → C24
  46. Element(A25, 1, 1) → B25
  47. Element(A25, 1, 2) → C25
  48. Segment(D23, D25) → a_1
  49. Segment(D24, D25) → b_1
  50. Segment(D24, D23) → c_1
  51. Segment(A28, A30) → q_1
  52. Segment(A30, A29) → r_1
  53. Segment(A29, A28) → s_1
  54. Polygon(P, Q, R, S) → poly4, p_2, q_2, r_2, s_2
  55. Shuffle({0, 0, 0, 0, 0, 0, 3 + 0 * v_1}) → A55
  56. Element(A55, 1) → A56
  57. Shuffle({1, 1, 1, 1, 0.7, 1.2, 0.4, 1.5, 0.3, 1, 1, 1, 1.1, 1.3, 1 + 0 * v_1}) → A59
  58. Element(A59, 1) → A60
  59. Shuffle({0, 0, 0, 0, 0, 0, 0, 1, 2, -1, -2, 1, 1, 4, 0, 0, 0, 0 * v_1}) → A51
  60. Segment(E64, E63) → t_1
  61. Segment(E62, E63) → a_2
  62. Segment(E62, E64) → b_2
  63. Textfield(m) → inputBox3

AI 绘图提示语参考

画一个由刚性变换（平移、旋转、反射）和相似变换（含缩放）组合而成的图形，展示不同变换参数对图形的影响。首先绘制一个基础三角形，然后通过输入参数控制变换，生成多个变换后的三角形，并用线段连接这些三角形，形成复杂的几何图案。
以上提示语为根据原始绘图命令整理而来，仅供参考。