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正方形面积 by JM Arranz, JA Mora, M Sada y R Losada

正方形面积 by JM Arranz, JA Mora, M Sada y R Losada
几何画板及绘图内容加载中，请稍等……
2023-03-13 03:58
多边形解析几何几何作图
所属专题 geometriadinamica.es
这个范例演示了正方形的面积计算。涉及的核心数学概念包括几何作图和面积计算。通过使用Circle, Ray, OrthogonalLine, Intersect, Polygon, Mirror, Segment, Point等GeoGebra命令，可以构造正方形并计算其面积。适合初中及以上学生学习几何和面积计算。

GeoGebra 命令及参数

  1. Circle(A, lado) → c
  2. Ray(A, B) → a
  3. Circle(A, lado) → d
  4. OrthogonalLine(A, a) → b
  5. Intersect(d, b, 1) → C
  6. OrthogonalLine(C, b) → e
  7. Intersect(c, a, 1) → D
  8. OrthogonalLine(D, a) → f
  9. Intersect(f, e) → E
  10. Polygon(A, C, E, D) → P, a_1, c_1, e_1, d_1
  11. Circle(A, g) → h
  12. Intersect(h, a_1) → F,
  13. Intersect(h, d_1) → G,
  14. Mirror(A, G) → H
  15. Mirror(G, H) → I
  16. Mirror(H, I) → J
  17. Mirror(I, J) → K
  18. Mirror(J, K) → L
  19. Mirror(K, L) → M
  20. Mirror(L, M) → N
  21. Mirror(M, N) → O
  22. Mirror(N, O) → Q
  23. Mirror(O, Q) → R
  24. Mirror(Q, R) → S
  25. Mirror(R, S) → T
  26. Mirror(S, T) → U
  27. Mirror(A, F) → V
  28. Mirror(F, V) → W
  29. Mirror(V, W) → Y
  30. Mirror(W, Y) → Z
  31. Mirror(Y, Z) → A_1
  32. Mirror(Z, A_1) → B_1
  33. Mirror(A_1, B_1) → C_1
  34. Mirror(B_1, C_1) → D_1
  35. OrthogonalLine(G, d_1) → i
  36. OrthogonalLine(H, d_1) → j
  37. OrthogonalLine(I, d_1) → k
  38. OrthogonalLine(J, d_1) → l
  39. OrthogonalLine(K, d_1) → m
  40. OrthogonalLine(L, d_1) → n
  41. OrthogonalLine(M, d_1) → p
  42. OrthogonalLine(N, d_1) → q
  43. OrthogonalLine(O, d_1) → r
  44. OrthogonalLine(Q, d_1) → s
  45. OrthogonalLine(R, d_1) → t
  46. OrthogonalLine(S, d_1) → b_1
  47. OrthogonalLine(T, d_1) → f_1
  48. OrthogonalLine(U, d_1) → g_1
  49. OrthogonalLine(F, a_1) → h_1
  50. OrthogonalLine(V, a_1) → i_1
  51. OrthogonalLine(W, a_1) → j_1
  52. OrthogonalLine(Y, a_1) → k_1
  53. OrthogonalLine(Z, a_1) → l_1
  54. OrthogonalLine(A_1, a_1) → m_1
  55. OrthogonalLine(B_1, a_1) → n_1
  56. OrthogonalLine(C_1, a_1) → p_1
  57. OrthogonalLine(D_1, a_1) → q_1
  58. Intersect(c_1, i) → E_1
  59. Intersect(r, c_1) → F_1
  60. Segment(F_1, O) → r_1
  61. Intersect(j, c_1) → G_1
  62. Intersect(k, c_1) → H_1
  63. Intersect(l, c_1) → I_1
  64. Intersect(m, c_1) → J_1
  65. Intersect(n, c_1) → K_1
  66. Intersect(p, c_1) → L_1
  67. Intersect(q, c_1) → M_1
  68. Intersect(s, c_1) → N_1
  69. Intersect(t, c_1) → O_1
  70. Intersect(b_1, c_1) → P_1
  71. Intersect(f_1, c_1) → Q_1
  72. Intersect(g_1, c_1) → R_1
  73. Intersect(e_1, q_1) → S_1
  74. Intersect(e_1, p_1) → T_1
  75. Intersect(e_1, n_1) → U_1
  76. Intersect(m_1, e_1) → V_1
  77. Intersect(l_1, e_1) → W_1
  78. Intersect(k_1, e_1) → Y_1
  79. Intersect(j_1, e_1) → Z_1
  80. Intersect(i_1, e_1) → A_2
  81. Intersect(h_1, e_1) → B_2
  82. Segment(E_1, G) → s_1
  83. Segment(G_1, H) → t_1
  84. Segment(H_1, I) → a_2
  85. Segment(I_1, J) → b_2
  86. Segment(J_1, K) → c_2
  87. Segment(K_1, L) → d_2
  88. Segment(L_1, M) → e_2
  89. Segment(M_1, N) → f_2
  90. Segment(N_1, Q) → g_2
  91. Segment(O_1, R) → h_2
  92. Segment(P_1, S) → i_2
  93. Segment(Q_1, T) → j_2
  94. Segment(R_1, U) → k_2
  95. Segment(D_1, S_1) → l_2
  96. Segment(C_1, T_1) → m_2
  97. Segment(B_1, U_1) → n_2
  98. Segment(A_1, V_1) → p_2
  99. Segment(Z, W_1) → q_2
  100. Segment(Y, Y_1) → r_2
  101. Segment(W, Z_1) → s_2
  102. Segment(V, A_2) → t_2
  103. Segment(F, B_2) → a_3
  104. Circle(C_2, o) → c_3
  105. Point(c_3) → D_2
  106. Segment(C_2, D_2) → b_3
  107. Circle(D_2, C_2) → d_3
  108. OrthogonalLine(D_2, b_3) → e_3
  109. OrthogonalLine(C_2, b_3) → f_3
  110. Intersect(c_3, f_3, 2) → E_2
  111. Intersect(d_3, e_3, 2) → F_2
  112. Polygon(E_2, F_2, D_2, C_2) → P_2, e_4, f_4, d_4, c_4

AI 绘图提示语参考

画一个正方形，包含一个圆心在正方形中心，半径等于正方形边长的圆。首先画一个圆，圆心在正方形中心，半径为正方形边长。然后画一个射线，从圆心向外延伸。接着画一个与射线垂直的线段。然后找到圆和垂直线段的交点。再画一个与垂直线段垂直的线段。找到圆和新垂直线段的交点。然后画一个与新垂直线段垂直的线段。找到圆和新垂直线段的交点。继续这样下去，画出一个正方形。最后画出一个圆，圆心在正方形中心，半径为正方形边长。
以上提示语为根据原始绘图命令整理而来，仅供参考。