GeoGebra几何作图范例

GeoGebra几何作图范例
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2023-03-19 02:34
所属专题 geometriadinamica.es
①本范例演示了利用GeoGebra进行几何图形的动态构造与演示;②涉及核心数学概念包括周长、向量、指数函数、相关性、相似三角形;③作图要点提炼自构造摘要,使用了OrthogonalLine(正交线)、Circle(圆)、Intersect(交点)、Ellipse(椭圆)、Point(点)、Angle(角)、Translate(平移)、Vector(向量)、Sequence(数列)、Element(元素)、Segment(线段)、Polygon(多边形)、Midpoint(中点)、Line(直线)等命令与对象;④适合高中及以上数学学习者,用于理解几何构造与动态演示。

GeoGebra 命令及参数

  1. OrthogonalLine(C, xAxis) → z2
  2. Circle(C, 0.62) → z0
  3. Intersect(z0, z2, 1) → Z4
  4. Intersect(z0, z2, 2) → Z3
  5. Ellipse(Z3, Z4, 0.65) → zElipse2
  6. Point(zElipse2) → Z
  7. Intersect(zElipse2, z2) → Z7, Z8
  8. Angle(Z8, C, Z) → zAngInc
  9. OrthogonalLine(C, yAxis) → z1
  10. Intersect(z0, z1, 2) → Z2
  11. Intersect(z0, z1, 1) → Z1
  12. Ellipse(Z1, Z2, 0.65) → zElipse1
  13. Point(zElipse1) → XY
  14. Translate((0, 0), v) → O
  15. OrthogonalLine(O, yAxis) → d
  16. Point(d) → G
  17. Vector((0, 0), G) → w
  18. Sequence(PuntoEsfera[C, XY, Z, radio, 0, (s * α)], s, 0, n) → puntosA
  19. Sequence((x(w) + x(Element[puntosA, s]), y(w) + y(Element[puntosA, s])), s, 1, n + 1) → puntosB
  20. Sequence(Segment[Element[puntosB, s], Element[puntosA, s]], s, 1, n) → aristas
  21. Element(aristas, 5) → a5
  22. Point(a5) → J
  23. Element(aristas, 1) → a1
  24. Point(a1) → A
  25. Element(aristas, 2) → a2
  26. Point(a2) → B
  27. Element(aristas, 3) → a3
  28. Point(a3) → D
  29. Element(aristas, 4) → a4
  30. Point(a4) → E
  31. Element(puntosB, 5) → B5
  32. Element(puntosB, 1) → B1
  33. Element(puntosB, 2) → B2
  34. Element(puntosB, 3) → B3
  35. Element(puntosB, 4) → B4
  36. Intersect(zElipse1, z1) → Z5, Z6
  37. Segment(Z5, Z6) → z4
  38. Segment(Z7, Z8) → z3
  39. Intersect(zElipse2, zElipse1, 1) → zPunto1
  40. Intersect(zElipse2, zElipse1, 4) → zPunto2
  41. Polygon(B1, B2, B3, B4, B5) → poly2, a, b, c, e, f
  42. Segment(zPunto1, zPunto2) → zSeg2
  43. Angle(Z6, C, XY) → zAngRot
  44. Sequence(Angle[Element[puntosB, s + 1], Element[puntosB, s], Element[puntosA, s + 1]], s, 1, n) → angulos
  45. Sequence(If[s > 1 ∧ Element[angulos, s - 1] > 180° ∧ Element[angulos, s] > 180°, false, If[s ≟ 1 ∧ Element[angulos, n] > 180° ∧ Element[angulos, s] > 180°, false, true]], s, 1, n) → aristasVisibles
  46. Element(aristas, 1) → a1b
  47. Polygon(A, B, D, E, J) → poly1, g, h, i, j, k_2
  48. Element(aristas, 2) → a2b
  49. Element(aristas, 3) → a3b
  50. Sequence(If[Element[angulos, s] > 180°, false, true], s, 1, n) → carasVisibles
  51. Angle(B1, B2, B3) → β
  52. Element(aristas, 4) → a4b
  53. Polygon(A, D, B) → poly3, b_1, a_1, d_1
  54. Midpoint(A, D) → I
  55. Angle(H, I, F) → γ
  56. Element(aristas, 5) → a5b
  57. Polygon(J, A, E) → poly6, e_1, j_1, a_3
  58. Midpoint(B1, B4) → M
  59. Line(M, a5) → l
  60. Intersect(j_1, l) → N
  61. Angle(L, N, F) → δ
  62. Vector(B1, B5) → z
  63. Vector(B5, B4) → m
  64. Vector(B4, B3) → p
  65. Vector(B3, B2) → q
  66. Vector(B2, B1) → r
  67. Line(P, a5) → s
  68. Line(Q, a5) → t
  69. Line(R, a5) → c_1
  70. Line(S, a5) → f_1
  71. Line(T, a5) → g_1
  72. Intersect(k_2, s) → U
  73. Intersect(j, t) → V
  74. Intersect(i, c_1) → W
  75. Intersect(h, f_1) → A_1
  76. Intersect(g, g_1) → B_1
  77. Polygon(Q, R, S, T, P) → poly4, q_1, r_1, s_1, t_1, p_1
  78. Polygon(B5, B4, B1) → poly5, b1, b5, b4
  79. Intersect(t_1, b5) → C_1
  80. Intersect(q_1, b5) → D_1
  81. Polygon(B1, B3, B2) → poly7, b2, b1_1, b3
  82. Intersect(t_1, b2) → E_1
  83. Intersect(r_1, b2) → F_1
  84. Line(C_1, a5) → h_1
  85. Line(D_1, a5) → i_1
  86. Line(E_1, a5) → k_1
  87. Line(F_1, a5) → l_1
  88. Intersect(j_1, i_1) → G_1
  89. Intersect(j_1, h_1) → H_1
  90. Intersect(b_1, k_1) → I_1
  91. Intersect(b_1, l_1) → J_1
  92. Polygon(H_1, U, V, G_1) → poly8, h_2, u_1, v_1, g_2
  93. Polygon(G_1, W, J_1, I_1, H_1) → poly9, g_3, w_1, j_2, i_2, h_3
  94. Polygon(J_1, A_1, B_1, I_1) → poly10, j_3, a_2, b_2, i_3
  95. Polygon(U, B_1, A_1, W, V) → poly11, u_2, b_3, a_4, w_2, v_2

AI 绘图提示语参考

在坐标平面内先取一点C为圆心作两条相互垂直的坐标轴。以C为圆心、给定半径作圆,圆与水平轴、竖直方向(通过与两条坐标轴的垂线交点)得到若干交点,用这些交点确定两个以C为基础的相似椭圆;取每个椭圆的若干交点形成另一组椭圆线段。再在某个切向相关的角度位置标出从中心到水平基点与到另一交点之间的角,并用该方向对椭圆几何进行平移基准。沿一条由点到基准向量的步进,用参数生成一串点,按相邻点对与对应椭圆点成对连线得到一系列边,选定其中若干点组成多边形;另用两椭圆交点连成一条边,并取多边形与中心相关的角度元素标示形状特征。
以上提示语为根据原始绘图命令整理而来,仅供参考。