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动态几何图形演示 by Tim Brzezinski (3)

动态几何图形演示 by Tim Brzezinski (3)
几何画板及绘图内容加载中，请稍等……
2018-03-28 08:55
函数微积分几何作图滑块动画函数图像
①本范例动态演示了由 Antonio Gutierrez 提出的几何问题，通过交互式图形展示问题核心；②涉及指数函数、假设检验、树状图、抛物线、积分等核心数学概念；③作图要点：运用了 Line, Polygon, Segment, Angle, Rotate, Ray, Intersect, OrthogonalLine, Circle, Midpoint, Translate, Dilate, Vector, Point 等GeoGebra命令与对象；④适合高中及以上数学学习者和教师用于探索复杂几何问题与高等数学应用。

GeoGebra 命令及参数

  1. Line(A, B) → r
  2. Polygon(A, B, C, D) → q1, a_3, b_2, c_3, d_2
  3. Polygon(A, C, D) → t1, d_1, a_1, c_1
  4. Polygon(A, B, C) → t2, c_2, a_2, b_1
  5. Segment(D, A) → a
  6. Segment(A, C) → g
  7. Segment(C, D) → b
  8. Segment(C, B) → c
  9. Segment(B, A) → d
  10. Angle(A, D, C) → α
  11. Angle(D, C, A) → β
  12. Angle(C, B, A) → γ
  13. Angle(B, A, C) → δ
  14. Rotate(A, α / 2, D) → A'
  15. Angle(A, D, A') → ε
  16. Rotate(D, β / 2, C) → D'
  17. Angle(D, C, D') → ζ
  18. Rotate(B, δ / 2, A) → B'
  19. Angle(B, A, B') → η
  20. Ray(A, B') → k
  21. Ray(D, A') → l
  22. Ray(C, D') → m
  23. Rotate(C, γ / 2, B) → C'
  24. Angle(C, B, C') → θ_1
  25. Ray(B, C') → n
  26. Intersect(l, m) → E
  27. Intersect(n, k) → F
  28. OrthogonalLine(E, g) → p
  29. OrthogonalLine(F, g) → q
  30. Intersect(g, p) → G
  31. Intersect(g, q) → H
  32. Circle(E, G) → e
  33. Circle(F, H) → f
  34. Midpoint(a) → I
  35. Midpoint(b) → J
  36. Midpoint(c) → K
  37. Midpoint(d) → L
  38. Segment(A, G) → h
  39. Segment(G, H) → i
  40. Segment(H, C) → j
  41. Translate(r, (0, (-o))) → r'
  42. OrthogonalLine(A, r') → s
  43. OrthogonalLine(L, r') → t
  44. Intersect(r', t) → M
  45. Circle(M, Distance[D, J]) → e_1
  46. Intersect(e_1, r') → N, O
  47. Translate(r, (0, (-2 * o))) → r'_1
  48. Intersect(r', s) → P
  49. OrthogonalLine(O, r'_1) → f_1
  50. Intersect(r'_1, f_1) → Q
  51. Circle(Q, Distance[B, K]) → g_1
  52. Intersect(g_1, r'_1) → R, S
  53. Circle(R, Distance[A, I]) → h_1
  54. Intersect(h_1, r'_1) → T, U
  55. Intersect(s, r'_1) → V
  56. Dilate(A, If[0 < u ≤ 1, 1 - u, 0], L) → A'_1
  57. Segment(A, A'_1) → i_1
  58. Rotate(A, If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], L) → A'_2
  59. Rotate(A'_1, If[1 < u ≤ 2, ((-(u - 1)) * π), (-π)], L) → W
  60. Segment(A'_2, W) → j_1
  61. Dilate(D, If[3 < u ≤ 4, 4 - u, 0], J) → D'_1
  62. Segment(D, D'_1) → k_1
  63. Dilate(A, If[2 < u ≤ 3, 3 - u, 0], P) → A'_3
  64. Vector(A, A'_3) → v
  65. Translate(A, v) → A'_4
  66. Translate(A'_1, v) → Z
  67. Segment(A'_4, Z) → l_1
  68. Vector(L, Z) → w
  69. Rotate(D, If[4 < u ≤ 5, ((u - 4) * π), π], J) → D'_2
  70. Rotate(D'_1, If[4 < u ≤ 5, ((u - 4) * π), π], J) → A_1
  71. Segment(D'_2, A_1) → m_1
  72. Ray(M, O) → n_1
  73. Circle(O, 2) → p_1
  74. Intersect(p_1, n_1, 2) → B_1
  75. Ray(O, B_1) → q_1
  76. Segment(M, O) → r_1
  77. Line(C, r'_1) → s_1
  78. Point(s_1) → C_1
  79. Angle(D, C, C_1) → θ
  80. Dilate(J, If[5 < u ≤ 6, 6 - u, 0], M) → J'
  81. Vector(J, J') → u_1
  82. Translate(D'_2, u_1) → D_1
  83. Translate(A_1, u_1) → E_1
  84. Segment(D_1, E_1) → t_1
  85. Rotate(D_1, If[5 < u ≤ 6, ((u - 5) * θ), θ], J') → F_1
  86. Rotate(E_1, If[5 < u ≤ 6, ((u - 5) * θ), θ], J') → G_1
  87. Segment(F_1, G_1) → f_2
  88. OrthogonalLine(R, r'_1) → g_2
  89. OrthogonalLine(T, r'_1) → h_2
  90. Intersect(r', h_2) → H_1
  91. Intersect(g_2, r') → I_1
  92. Segment(P, H_1) → i_2
  93. Segment(H_1, I_1) → j_2
  94. Segment(I_1, O) → k_2
  95. Dilate(P, If[6 < u ≤ 7, 7 - u, 0], V) → P'
  96. Vector(P, P') → v_1
  97. Dilate(O, If[6 < u ≤ 7, 7 - u, 0], Q) → O'
  98. Vector(O, O') → w_1
  99. Translate(P, v_1) → P'_1
  100. Translate(H_1, v_1) → J_1
  101. Segment(P'_1, J_1) → l_2
  102. Translate(H_1, v_1) → K_1
  103. Translate(I_1, v_1) → L_1
  104. Segment(K_1, L_1) → m_2
  105. Translate(I_1, v_1) → M_1
  106. Translate(O, v_1) → O'_1
  107. Segment(M_1, O'_1) → n_2
  108. Dilate(C, If[7 < u ≤ 8, 8 - u, 0], K) → B'_1
  109. Rotate(B, If[8 < u ≤ 9, ((-(u - 8)) * π), (-π)], K) → B'_2
  110. Rotate(B'_1, If[8 < u ≤ 9, ((-(u - 8)) * π), (-π)], K) → N_1
  111. Segment(C, B'_1) → p_2
  112. Rotate(C, If[8 < u ≤ 9, ((u - 8) * π), π], K) → C'_1
  113. Rotate(B'_1, If[8 < u ≤ 9, ((u - 8) * π), π], K) → O_1
  114. Segment(C'_1, O_1) → q_2
  115. Dilate(B, If[9 < u ≤ 10, 10 - u, 0], O'_1) → B'_3
  116. Vector(B, B'_3) → u_2
  117. Translate(C'_1, u_2) → P_1
  118. Translate(O_1, u_2) → Q_1
  119. Segment(P_1, Q_1) → r_2
  120. Rotate(P_1, If[9 < u ≤ 10, ((u - 9) * γ), γ], P_1) → R_1
  121. Rotate(Q_1, If[9 < u ≤ 10, ((u - 9) * γ), γ], P_1) → S_1
  122. Segment(R_1, S_1) → s_2
  123. Dilate(D, If[10 < u ≤ 11, 11 - u, 0], I) → D'_3
  124. Segment(D, D'_3) → t_2
  125. Rotate(D, If[11 < u ≤ 12, ((-(u - 11)) * π), (-π)], I) → D'_4
  126. Rotate(D'_3, If[11 < u ≤ 12, ((-(u - 11)) * π), (-π)], I) → T_1
  127. Segment(D'_4, T_1) → e_2
  128. Angle(C, A, D) → λ
  129. Dilate(A, If[12 < u ≤ 13, 13 - u, 0], T) → A'_5
  130. Vector(A, A'_5) → v_2
  131. Translate(D'_4, v_2) → U_1
  132. Translate(T_1, v_2) → V_1
  133. Segment(U_1, V_1) → f_3
  134. Rotate(U_1, If[12 < u ≤ 13, ((-(u - 12)) * (λ + δ)), (-(λ + δ))], A'_5) → W_1
  135. Rotate(V_1, If[12 < u ≤ 13, ((-(u - 12)) * (λ + δ)), (-(λ + δ))], A'_5) → Z_1
  136. Segment(W_1, Z_1) → g_3
  137. Dilate(A, If[14 < u ≤ 15, 15 - u, 0], G) → A'_6
  138. Dilate(C, If[14 < u ≤ 15, 15 - u, 0], H) → C'_2
  139. Segment(A, A'_6) → h_3
  140. Segment(C, C'_2) → i_3
  141. Dilate(T, If[15 < u ≤ 16, 16 - u, 0], V) → T'
  142. Segment(T, T') → j_3
  143. Line(V, h_3) → k_3
  144. Point(k_3) → A_2
  145. Angle(T, V, A_2) → ρ
  146. Dilate(T, If[17 < u ≤ 18, 18 - u, 0], H) → T'_1
  147. Vector(T, T'_1) → w_2
  148. Translate(T, w_2) → T'_2
  149. Translate(T', w_2) → T''
  150. Segment(T'_2, T'') → l_3
  151. Rotate(T'_2, If[16 < u ≤ 17, ((-(u - 16)) * ((2 * π) - ρ)), ρ - (2 * π)], T'_2) → B_2
  152. Rotate(T'', If[16 < u ≤ 17, ((-(u - 16)) * ((2 * π) - ρ)), ρ - (2 * π)], T'_2) → T'''
  153. Rotate(T'_2, If[16 < u ≤ 17, ((u - 16) * ρ), ρ], T'_2) → C_2
  154. Rotate(T'_2, If[17 < u ≤ 18, ((u - 17) * ρ), ρ], T'_2) → D_2
  155. Rotate(T'', If[17 < u ≤ 18, ((u - 17) * ρ), ρ], T'_2) → T'''_1
  156. Segment(D_2, T'''_1) → m_3