梯子上的猫 by Malin Christersson (2)

梯子上的猫 by Malin Christersson (2)
几何画板及绘图内容加载中,请稍等……
2014-02-22 23:35
①本范例演示了椭圆与几何变换的综合应用;②涉及的核心数学概念包括椭圆、中点、镜像、线段、多边形、不等式等;③作图要点提炼自构造摘要,使用了Intersect(交点)、Midpoint(中点)、Mirror(镜像)、Segment(线段)、Ellipse(椭圆)、Polygon(多边形)等GeoGebra命令;④适合高中及以上数学学习者,用于理解几何变换与椭圆性质。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Midpoint(C, D) → A1
  3. Midpoint(A1, C) → A2
  4. Midpoint(A2, C) → A3
  5. Midpoint(A2, B) → A4
  6. Midpoint(B, D) → A5
  7. Midpoint(A5, D) → A6
  8. Midpoint(A5, B) → A7
  9. Mirror(A1, yAxis) → C1
  10. Mirror(A2, yAxis) → C2
  11. Mirror(A3, yAxis) → C3
  12. Mirror(A4, yAxis) → C4
  13. Mirror(A5, yAxis) → C5
  14. Mirror(A6, yAxis) → C6
  15. Mirror(A7, yAxis) → C7
  16. Mirror(B1, yAxis) → D1
  17. Mirror(B2, yAxis) → D2
  18. Mirror(B3, yAxis) → D3
  19. Mirror(B4, yAxis) → D4
  20. Mirror(B5, yAxis) → D5
  21. Mirror(B6, yAxis) → D6
  22. Mirror(B7, yAxis) → D7
  23. Mirror(D, yAxis) → D'
  24. Segment(C, D) → e
  25. Ellipse(E1, F1, G1) → H1
  26. Polygon(F1, G1, 3) → I1, f, h, i, F
  27. Polygon(F2, G2, 3) → I2, m, n, p, H
  28. Polygon(F3, G3, 3) → I3, q, s, a_1, I
  29. Polygon(F4, G4, 3) → I4, b_1, c_1, d_1, J
  30. Polygon(F5, G5, 3) → I5, e_1, f_1, g_1, K
  31. Polygon(F6, G6, 3) → I6, h_1, i_1, j_1, L
  32. Polygon(F7, G7, 3) → I7, k_1, l_1, m_1, M
  33. Polygon(F8, G8, 3) → I8, n_1, p_1, q_1, N
  34. Polygon(F9, G9, 3) → I9, r_1, s_1, t_1, O
  35. Polygon(G1, E1, 3) → N1, j, k, l, G
  36. Polygon(G2, E2, 3) → N2, a_2, b_2, c_2, P
  37. Polygon(G3, E3, 3) → N3, d_2, e_2, f_2, Q
  38. Polygon(G4, E4, 3) → N4, g_2, h_2, i_2, R
  39. Polygon(G5, E5, 3) → N5, j_2, k_2, l_2, S
  40. Polygon(G6, E6, 3) → N6, m_2, n_2, p_2, T
  41. Polygon(G7, E7, 3) → N7, q_2, r_2, s_2, U
  42. Polygon(G8, E8, 3) → N8, t_2, a_3, b_3, V
  43. Polygon(G9, E9, 3) → N9, c_3, d_3, e_3, W
  44. Ellipse(E2, F2, G2) → H2
  45. Ellipse(E3, F3, G3) → H3
  46. Ellipse(E4, F4, G4) → H4
  47. Ellipse(E5, F5, G5) → H5
  48. Ellipse(E6, F6, G6) → H6
  49. Ellipse(E7, F7, G7) → H7
  50. Ellipse(E8, F8, G8) → H8
  51. Ellipse(E9, F9, G9) → H9

AI 绘图提示语参考

绘制一个梯子上的猫,使用椭圆和几何变换。首先在坐标轴上找到交点A,然后通过多次中点和镜像操作生成一系列点。接着用这些点构造多个椭圆和多边形,形成梯子和猫的轮廓。最后调整位置和大小,确保图形完整且美观。
以上提示语为根据原始绘图命令整理而来,仅供参考。