积极 AI Logo 积极 AI

等腰直角三角形反射与多项式函数动画231

等腰直角三角形反射与多项式函数动画231
几何画板及绘图内容加载中，请稍等……
2017-04-06 08:05
测试改名0函数变换几何作图滑块动画
该范例演示了一个由等腰直角三角形、反射变换与多项式函数曲线共同构成的动态几何动画。核心数学概念包括等腰三角形、直角三角形、反射（镜像）变换、线段、圆弧、圆与扇形，以及多项式函数图像。作图要点：利用GeoGebra的Rotate（旋转）、Dilate（缩放）、Mirror（反射）等变换命令构造基本图形；通过Polygon（多边形）、Midpoint（中点）、CircleArc（圆弧）、Circle（圆）、CircleSector（扇形）等命令生成几何元素；使用Point（点）、Segment（线段）、Intersect（交点）、Ray（射线）、Line（直线）、Angle（角）、Vector（向量）、Translate（平移）等命令丰富图形结构；最终以滑块或动画形式展示动态变化。适合中学几何教学、数学实验或动态几何探究，帮助学生直观理解反射对称、三角形性质与函数图像的结合。

GeoGebra 命令及参数

  1. Rotate(A, If[1 < e ≤ 2, ((-(e - 1)) * π / 2), -1.5707963267948966], B_2) → A'_1
  2. Dilate(A, If[0 < e ≤ 1, 1 - e, 0], B_2) → A'
  3. Rotate(A', If[1 < e ≤ 2, ((-(e - 1)) * π / 2), -1.5707963267948966], B_2) → A''
  4. Polygon(A, B_2, 4) → poly1, a, b, c, d, C, D
  5. Midpoint(A, C) → V
  6. CircleArc(V, C, D) → g_2
  7. Point(g_2) → B
  8. Segment(C, B) → j_1
  9. Segment(A, B) → n
  10. Rotate(A'', If[2 < e ≤ 3, ((-(e - 2)) * π / 2), -1.5707963267948966], C) → A'''
  11. Rotate(A'_1, If[2 < e ≤ 3, ((-(e - 2)) * π / 2), -1.5707963267948966], C) → R
  12. Segment(R, A''') → f''
  13. Intersect(n, f'') → Z
  14. Segment(B, Z) → l_1
  15. Segment(A, A') → f
  16. Segment(A'_1, A'') → f'
  17. Segment(A, B_2) → g
  18. Segment(B_2, C) → h
  19. Segment(C, D) → i
  20. Segment(D, A) → j
  21. Circle(B_2, (0.5 * Min[j_1, l_1])) → p
  22. Circle(C, (0.1 * j)) → k
  23. Circle(A, (0.1 * j)) → q
  24. Circle(D, (0.1 * j)) → r
  25. Segment(A, C) → l
  26. Segment(D, B_2) → m
  27. Intersect(r, j, 1) → F
  28. Intersect(r, m, 1) → G
  29. Intersect(r, i, 1) → H
  30. Intersect(k, i, 1) → I
  31. Intersect(k, l, 1) → J
  32. Intersect(k, h, 1) → K
  33. Intersect(p, h, 1) → L
  34. Intersect(p, m, 1) → M
  35. Intersect(p, g, 1) → N
  36. Intersect(q, g, 1) → O
  37. Intersect(q, l, 1) → P
  38. Intersect(q, j, 1) → Q
  39. CircleSector(B_2, L, N) → s
  40. Rotate(R, If[3 < e ≤ 4, ((-(e - 3)) * π / 2), -1.5707963267948966], D) → R'
  41. Rotate(A''', If[3 < e ≤ 4, ((-(e - 3)) * π / 2), -1.5707963267948966], D) → S
  42. Segment(R', S) → f'''
  43. Dilate(B_2, If[4 < e ≤ 5, 5 - e, 0], C) → B'
  44. Vector(B_2, B') → u
  45. Translate(s, u) → s'
  46. Rotate(s', If[5 < e ≤ 6, ((e - 5) * π / 2), 1.5707963267948966], C) → s''
  47. Dilate(C, If[6 < e ≤ 7, 7 - e, 0], D) → C'
  48. Vector(C, C') → v
  49. Translate(s'', v) → s'''
  50. Rotate(s''', If[7 < e ≤ 8, ((e - 7) * π / 2), 1.5707963267948966], D) → t
  51. Dilate(D, If[8 < e ≤ 9, 9 - e, 0], A) → D'
  52. Vector(D, D') → w
  53. Translate(t, w) → t'
  54. Rotate(t', If[9 < e ≤ 10, ((e - 9) * π / 2), 1.5707963267948966], A) → t''
  55. Dilate(B_2, If[18 < e ≤ 19, 19 - e, 0], C) → B'_1
  56. Dilate(B_2, If[18 < e ≤ 19, 19 - e, 0], A) → B'_2
  57. Dilate(B_2, If[18 < e ≤ 19, 19 - e, 0], D) → B'_3
  58. Vector(B_2, B'_1) → v_1
  59. Vector(B_2, B'_3) → w_1
  60. Vector(B_2, B'_2) → i_1
  61. Circle(A, n - j_1) → h_2
  62. Intersect(h_2, n, 1) → A_1
  63. Midpoint(A, A_1) → B_1
  64. Dilate(B, If[10 < e ≤ 11, 11 - e, 0], C) → W'
  65. Dilate(B, If[10 < e ≤ 11, 11 - e, 0], A_1) → W'_1
  66. Segment(B, W') → m_1
  67. Segment(B, W'_1) → n_1
  68. Dilate(A_1, If[11 < e ≤ 12, 12 - e, 0], B_1) → E
  69. Segment(A_1, E) → f_1
  70. Dilate(B_1, If[12 < e ≤ 13, 13 - e, 0], A) → T
  71. Segment(B_1, T) → g_1
  72. Dilate(B_2, If[13 < e ≤ 14, 14 - e, 0], B) → B'_4
  73. Vector(B_2, B'_4) → u_1
  74. Translate(s, u_1) → s'_1
  75. Line(B, f') → a_1
  76. Point(a_1) → U
  77. Angle(U, B, C) → α
  78. Rotate(s'_1, If[13 < e ≤ 14, ((e - 13) * (α - π / 2)), α - π / 2], B'_4) → c_1
  79. Rotate(B, If[14 < e ≤ 15, ((-(e - 14)) * π / 2), ((-π)) / 2], B) → W'_2
  80. Rotate(W', If[14 < e ≤ 15, ((-(e - 14)) * π / 2), ((-π)) / 2], B) → W''
  81. Segment(W'_2, W'') → b_1
  82. Rotate(A_1, If[15 < e ≤ 16, ((-(e - 15)) * π), (-π)], B_1) → C_1
  83. Rotate(E, If[15 < e ≤ 16, ((-(e - 15)) * π), (-π)], B_1) → E'
  84. Segment(C_1, E') → d_1
  85. Circle(A, B_1) → e_1
  86. Line(A, B_2) → h_1
  87. Intersect(e_1, h_1, 1) → D_1
  88. Intersect(e_1, f''', 1) → E_1
  89. Ray(A, D_1) → k_1
  90. Angle(B, A, D) → β
  91. Rotate(C_1, If[16 < e ≤ 17, ((e - 16) * β), β], A) → F_1
  92. Rotate(E', If[16 < e ≤ 17, ((e - 16) * β), β], A) → E''
  93. Segment(F_1, E'') → p_1
  94. Circle(D_1, 1) → q_1
  95. Intersect(q_1, k_1, 2) → G_1
  96. Ray(D_1, G_1) → r_1
  97. Segment(A, D_1) → s_1
  98. Rotate(F_1, If[17 < e ≤ 18, ((e - 17) * π / 2), π / 2], A) → H_1
  99. Rotate(E'', If[17 < e ≤ 18, ((e - 17) * π / 2), π / 2], A) → E'''
  100. Segment(H_1, E''') → t_1
  101. Dilate(D, If[19 < e ≤ 20, 20 - e, 0], B) → D'_1
  102. Segment(D, D'_1) → f_2
  103. Rotate(t'', If[18 < e ≤ 19, ((e - 18) * π / 2), π / 2], A) → t'''
  104. Dilate(D, If[20 < e ≤ 21, 21 - e, 0], E'') → D'_2
  105. Vector(D, D'_2) → u_2
  106. Translate(D, u_2) → D'_3
  107. Translate(D'_1, u_2) → I_1
  108. Segment(D'_3, I_1) → i_2
  109. Mirror(C, D) → C'_1
  110. Line(E'', f_2) → j_2
  111. Point(j_2) → J_1
  112. Angle(J_1, E'', E''') → γ
  113. Rotate(D'_3, If[21 < e ≤ 22, ((e - 21) * γ), γ], E'') → K_1
  114. Rotate(I_1, If[21 < e ≤ 22, ((e - 21) * γ), γ], E'') → L_1
  115. Segment(K_1, L_1) → k_2
  116. Polygon(E''', A, E'') → poly2, e'', e''', a_2