计算周长与面积

计算周长与面积
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2017-01-09 03:51
①本范例演示了如何使用 GeoGebra 计算并可视化三角形的周长与面积;②涉及的核心数学概念包括周长、面积、几何作图;③作图要点——从下方『构造摘要』提炼用到了 Random, OrthogonalLine, Intersect, Segment, Point 等命令/对象;④适合初中及以上学生学习和探索几何图形的基本属性。

GeoGebra 命令及参数

  1. Random(1, 10) → Height
  2. Random(1, 10) → Base
  3. OrthogonalLine(B, xAxis) → a
  4. OrthogonalLine(A, yAxis) → b
  5. Intersect(a, b) → C
  6. Segment(B, C) → c
  7. Segment(C, A) → d
  8. OrthogonalLine(B, c) → e
  9. OrthogonalLine(A, d) → f
  10. Intersect(e, f) → D
  11. Segment(A, D) → g
  12. Segment(D, B) → h
  13. Point(xAxis) → E
  14. Point(xAxis) → F
  15. Point(xAxis) → G
  16. Point(xAxis) → H
  17. Point(xAxis) → I
  18. Point(xAxis) → J
  19. Point(xAxis) → K
  20. Point(xAxis) → L
  21. Point(xAxis) → M
  22. OrthogonalLine(E, xAxis) → i
  23. OrthogonalLine(F, xAxis) → j
  24. OrthogonalLine(G, xAxis) → k
  25. OrthogonalLine(H, xAxis) → l
  26. OrthogonalLine(I, xAxis) → m
  27. OrthogonalLine(J, xAxis) → n
  28. OrthogonalLine(K, xAxis) → p
  29. OrthogonalLine(L, xAxis) → q
  30. OrthogonalLine(M, xAxis) → r
  31. Intersect(i, d) → N
  32. Intersect(j, d) → O
  33. Intersect(k, d) → P
  34. Intersect(l, d) → Q
  35. Intersect(m, d) → R
  36. Intersect(n, d) → S
  37. Intersect(p, d) → T
  38. Intersect(q, d) → U
  39. Intersect(r, d) → V
  40. Intersect(r, h) → W
  41. Intersect(q, h) → Z
  42. Intersect(p, h) → A_1
  43. Intersect(n, h) → B_1
  44. Intersect(m, h) → C_1
  45. Intersect(l, h) → D_1
  46. Intersect(k, h) → E_1
  47. Intersect(j, h) → F_1
  48. Intersect(i, h) → G_1
  49. Segment(N, G_1) → s
  50. Segment(O, F_1) → t
  51. Segment(E_1, P) → a_1
  52. Segment(Q, D_1) → b_1
  53. Segment(C_1, R) → c_1
  54. Segment(S, B_1) → d_1
  55. Segment(A_1, T) → e_1
  56. Segment(U, Z) → f_1
  57. Segment(W, V) → g_1
  58. Point(yAxis) → H_1
  59. Point(yAxis) → I_1
  60. Point(yAxis) → J_1
  61. Point(yAxis) → K_1
  62. Point(yAxis) → L_1
  63. Point(yAxis) → M_1
  64. Point(yAxis) → N_1
  65. Point(yAxis) → O_1
  66. Point(yAxis) → P_1
  67. Point(yAxis) → Q_1
  68. OrthogonalLine(H_1, s) → h_1
  69. OrthogonalLine(I_1, s) → i_1
  70. OrthogonalLine(J_1, s) → j_1
  71. OrthogonalLine(K_1, s) → k_1
  72. OrthogonalLine(L_1, s) → l_1
  73. OrthogonalLine(M_1, s) → m_1
  74. OrthogonalLine(N_1, s) → n_1
  75. OrthogonalLine(O_1, s) → p_1
  76. OrthogonalLine(P_1, s) → q_1
  77. OrthogonalLine(Q_1, s) → r_1
  78. Intersect(r_1, g) → R_1
  79. Intersect(q_1, g) → S_1
  80. Intersect(p_1, g) → T_1
  81. Intersect(n_1, g) → U_1
  82. Intersect(m_1, g) → V_1
  83. Intersect(l_1, g) → W_1
  84. Intersect(k_1, g) → Z_1
  85. Intersect(j_1, g) → A_2
  86. Intersect(i_1, g) → B_2
  87. Intersect(h_1, g) → C_2
  88. Intersect(h_1, c) → D_2
  89. Intersect(i_1, c) → E_2
  90. Intersect(j_1, c) → F_2
  91. Intersect(k_1, c) → G_2
  92. Intersect(l_1, c) → H_2
  93. Intersect(m_1, c) → I_2
  94. Intersect(n_1, c) → J_2
  95. Intersect(p_1, c) → K_2
  96. Intersect(q_1, c) → L_2
  97. Intersect(r_1, c) → M_2
  98. Segment(C_2, D_2) → s_1
  99. Segment(E_2, B_2) → t_1
  100. Segment(A_2, F_2) → a_2
  101. Segment(G_2, Z_1) → b_2
  102. Segment(W_1, H_2) → c_2
  103. Segment(I_2, V_1) → d_2
  104. Segment(U_1, J_2) → e_2
  105. Segment(K_2, T_1) → f_2
  106. Segment(S_1, L_2) → g_2
  107. Segment(M_2, R_1) → h_2

AI 绘图提示语参考

绘制一个直角三角形,其两条直角边长度随机生成。从直角顶点分别向两条坐标轴作垂线,交于一点形成三角形。再分别从另外两个顶点向对边作垂线,交于一点,连接该点与两个顶点形成矩形。在底边(x轴)上随机取多个点,分别作x轴的垂线,这些垂线与三角形的两条斜边相交,形成一系列交点,从而在三角形内部和外部生成网格状辅助线,用于展示周长和面积的计算过程。
以上提示语为根据原始绘图命令整理而来,仅供参考。