等值分数的可视化

等值分数的可视化
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2019-01-25 15:34
①本范例通过动态图形演示等值分数的几何意义;②涉及核心数学概念包括分数、几何表示、相似三角形;③构造要点:使用 Point, Circle, OrthogonalLine, Intersect, Rotate, CircleSector, Segment, Vector, Translate, Polygon 等命令及 Slider 动态展示分数关系;④适合初中及以上数学教学,用于分数概念的可视化教学与理解。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Circle(A, 3) → e
  3. OrthogonalLine(A, xAxis) → f
  4. Intersect(e, f, 2) → C
  5. Rotate(C, (360 * ° / Slider), A) → C'
  6. Rotate(C', (360 * ° / Slider), A) → C''
  7. Rotate(C'', (360 * ° / Slider), A) → C'''
  8. Rotate(C''', (360 * ° / Slider), A) → D
  9. Rotate(D, (360 * ° / Slider), A) → D'
  10. Rotate(D', (360 * ° / Slider), A) → D''
  11. Rotate(D'', (360 * ° / Slider), A) → D'''
  12. Rotate(D''', (360 * ° / Slider), A) → E
  13. Rotate(E, (360 * ° / Slider), A) → E'
  14. Rotate(E', (360 * ° / Slider), A) → E''
  15. Rotate(E'', (360 * ° / Slider), A) → E'''
  16. Rotate(E''', (360 * ° / Slider), A) → F
  17. Rotate(F, (360 * ° / Slider), A) → F'
  18. Rotate(F', (360 * ° / Slider), A) → F''
  19. Rotate(F'', (360 * ° / Slider), A) → F'''
  20. Rotate(F''', (360 * ° / Slider), A) → G
  21. Rotate(G, (360 * ° / Slider), A) → G'
  22. Rotate(G', (360 * ° / Slider), A) → G''
  23. Rotate(G'', (360 * ° / Slider), A) → G'''
  24. CircleSector(A, C, C') → g
  25. CircleSector(A, C', C'') → h
  26. CircleSector(A, C'', C''') → k
  27. CircleSector(A, C''', D) → p
  28. CircleSector(A, D, D') → q
  29. CircleSector(A, D', D'') → r
  30. CircleSector(A, D'', D''') → s
  31. CircleSector(A, D''', E) → t
  32. CircleSector(A, E, E') → c_1
  33. CircleSector(A, E', E'') → d_1
  34. CircleSector(A, E'', E''') → e_1
  35. CircleSector(A, E''', F) → f_1
  36. CircleSector(A, F, F') → g_1
  37. CircleSector(A, F', F'') → h_1
  38. CircleSector(A, F'', F''') → k_1
  39. CircleSector(A, F''', G) → p_1
  40. CircleSector(A, G, G') → q_1
  41. CircleSector(A, G', G'') → r_1
  42. CircleSector(A, G'', G''') → s_1
  43. CircleSector(A, G''', C) → t_1
  44. Segment(A, C) → i
  45. Segment(A, C') → j
  46. Segment(A, C'') → l
  47. Segment(A, C''') → m
  48. Segment(A, D) → n
  49. Segment(A, D') → a_1
  50. Segment(A, D'') → b_1
  51. Segment(A, D''') → i_1
  52. Segment(A, E) → j_1
  53. Segment(A, E') → l_1
  54. Segment(A, E'') → m_1
  55. Segment(A, E''') → n_1
  56. Segment(A, F) → a_2
  57. Segment(A, F') → b_2
  58. Segment(A, F'') → c_2
  59. Segment(A, F''') → d_2
  60. Segment(A, G) → e_2
  61. Segment(A, G') → f_2
  62. Segment(A, G'') → g_2
  63. Segment(A, G''') → h_2
  64. Intersect(e, xAxis, 1) → H
  65. Intersect(e, xAxis, 2) → I
  66. OrthogonalLine(H, xAxis) → i_2
  67. OrthogonalLine(I, xAxis) → j_2
  68. OrthogonalLine(J, i_2) → k_2
  69. OrthogonalLine(K, i_2) → l_2
  70. Intersect(j_2, k_2) → L
  71. Intersect(j_2, l_2) → M
  72. Segment(J, L) → m_2
  73. Segment(K, M) → n_2
  74. Segment(K, J) → p_2
  75. Segment(M, L) → q_2
  76. Vector(J, L) → u
  77. Translate(i_2, Vector[u / Slider]) → r_2
  78. Translate(i_2, Vector[(u * 2 / Slider)]) → s_2
  79. Translate(i_2, Vector[(u * 18 / Slider)]) → t_2
  80. Translate(i_2, Vector[(u * 19 / Slider)]) → a_3
  81. Translate(i_2, Vector[(u * 17 / Slider)]) → b_3
  82. Translate(i_2, Vector[(u * 16 / Slider)]) → c_3
  83. Translate(i_2, Vector[(u * 15 / Slider)]) → d_3
  84. Translate(i_2, Vector[(u * 14 / Slider)]) → e_3
  85. Translate(i_2, Vector[(u * 13 / Slider)]) → f_3
  86. Translate(i_2, Vector[(u * 12 / Slider)]) → h_3
  87. Translate(i_2, Vector[(u * 11 / Slider)]) → i_3
  88. Translate(i_2, Vector[(u * 10 / Slider)]) → j_3
  89. Translate(i_2, Vector[(u * 9 / Slider)]) → k_3
  90. Translate(i_2, Vector[(u * 8 / Slider)]) → l_3
  91. Translate(i_2, Vector[(u * 7 / Slider)]) → m_3
  92. Translate(i_2, Vector[(u * 6 / Slider)]) → n_3
  93. Translate(i_2, Vector[(u * 5 / Slider)]) → p_3
  94. Translate(i_2, Vector[(u * 4 / Slider)]) → q_3
  95. Translate(i_2, Vector[(u * 3 / Slider)]) → r_3
  96. Intersect(r_2, n_2) → N
  97. Intersect(r_2, m_2) → O
  98. Intersect(s_2, m_2) → P
  99. Intersect(r_3, m_2) → Q
  100. Intersect(q_3, m_2) → R
  101. Intersect(p_3, m_2) → S
  102. Intersect(n_3, m_2) → T
  103. Intersect(m_3, m_2) → U
  104. Intersect(l_3, m_2) → V
  105. Intersect(k_3, m_2) → W
  106. Intersect(j_3, m_2) → Z
  107. Intersect(i_3, m_2) → A_1
  108. Intersect(h_3, m_2) → B_1
  109. Intersect(m_2, f_3) → D_1
  110. Intersect(e_3, m_2) → E_1
  111. Intersect(d_3, m_2) → F_1
  112. Intersect(c_3, m_2) → G_1
  113. Intersect(b_3, m_2) → H_1
  114. Intersect(t_2, m_2) → I_1
  115. Intersect(a_3, m_2) → J_1
  116. Intersect(a_3, n_2) → K_1
  117. Intersect(t_2, n_2) → L_1
  118. Intersect(b_3, n_2) → M_1
  119. Intersect(c_3, n_2) → N_1
  120. Intersect(d_3, n_2) → O_1
  121. Intersect(e_3, n_2) → P_1
  122. Intersect(n_2, h_3) → R_1
  123. Intersect(i_3, n_2) → S_1
  124. Intersect(j_3, n_2) → T_1
  125. Intersect(k_3, n_2) → U_1
  126. Intersect(l_3, n_2) → V_1
  127. Intersect(m_3, n_2) → W_1
  128. Intersect(n_3, n_2) → Z_1
  129. Intersect(p_3, n_2) → A_2
  130. Intersect(q_3, n_2) → B_2
  131. Intersect(r_3, n_2) → C_2
  132. Intersect(s_2, n_2) → D_2
  133. Intersect(f_3, n_2) → C_1
  134. Polygon(J, O, N, K) → poly1, j_4, o, n_4, k_4
  135. Polygon(N, D_2, P, O) → poly2, n_5, d_4, p_4, o_1
  136. Polygon(D_2, C_2, Q, P) → poly3, d_5, c_4, q_4, p_5
  137. Polygon(C_2, B_2, R, Q) → poly4, c_5, b_4, r_4, q_5
  138. Polygon(A_2, B_2, R, S) → poly5, a_4, b_5, r_5, s_3
  139. Polygon(A_2, Z_1, T, S) → poly6, a_5, z_1, t_3, s_4
  140. Polygon(Z_1, W_1, U, T) → poly7, z_2, w_1, u_1, t_4
  141. Polygon(W_1, V_1, V, U) → poly8, w_2, v_1, v, u_2
  142. Polygon(V_1, U_1, W, V) → poly9, v_2, u_3, w, v_3
  143. Polygon(U_1, T_1, Z, W) → poly10, u_4, t_5, z, w_3
  144. Polygon(T_1, S_1, A_1, Z) → poly11, t_6, s_5, a_6, z_3
  145. Polygon(S_1, R_1, B_1, A_1) → poly12, s_6, r_6, b_6, a_7
  146. Polygon(R_1, C_1, D_1, B_1) → poly13, r_7, c_6, d_6, b_7
  147. Polygon(C_1, P_1, E_1, D_1) → poly14, c_7, p_6, e_4, d_7
  148. Polygon(P_1, O_1, F_1, E_1) → poly15, p_7, o_2, f_4, e_5
  149. Polygon(O_1, N_1, G_1, F_1) → poly16, o_3, n_6, g_3, f_5
  150. Polygon(M_1, N_1, G_1, H_1) → poly17, m_4, n_7, g_4, h_4
  151. Polygon(M_1, L_1, I_1, H_1) → poly18, m_5, l_4, i_4, h_5
  152. Polygon(L_1, K_1, J_1, I_1) → poly19, l_5, k_5, j_5, i_5
  153. Polygon(K_1, M, L, J_1) → poly20, k_6, m_6, l_6, j_6

AI 绘图提示语参考

画一个圆形,从圆心向外作一条水平线,并在圆上找到与水平线成一定角度的点。以圆心为轴,将这个点旋转多次,每次旋转的角度由一个滑动条控制,形成多个扇形。用线段连接圆心和这些点,展示出不同角度下的扇形区域,直观表达分数的几何意义和旋转关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。