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椭圆填充

椭圆填充
几何画板及绘图内容加载中，请稍等……
2014-07-31 03:34
解析几何最值优化不等式几何作图
①本范例演示将椭圆填充到单位正方形中的几何问题；②涉及的核心数学概念包括椭圆、相似三角形、旋转、平行四边形、线性方程和不等式；③作图要点——从下方『构造摘要』提炼用到了Polygon（多边形）、Point（点）、Ellipse（椭圆）等GeoGebra命令/对象；④适合高中数学教学或几何作图练习，用于理解空间填充与优化问题。

GeoGebra 命令及参数

  1. Polygon(P1, P2, 4) → poly1, seg1, seg2, seg3, seg4, P3, P4
  2. Point(Circle[C1, a]) → A1
  3. Ellipse(C1 + (e * (A1 - C1)), C1 - (e * (A1 - C1)), A1) → E1
  4. Point(Circle[C2, a]) → A2
  5. Ellipse(C2 + (e * (A2 - C2)), C2 - (e * (A2 - C2)), A2) → E2
  6. Point(Circle[C3, a]) → A3
  7. Ellipse(C3 + (e * (A3 - C3)), C3 - (e * (A3 - C3)), A3) → E3
  8. Point(Circle[C4, a]) → A4
  9. Ellipse(C4 + (e * (A4 - C4)), C4 - (e * (A4 - C4)), A4) → E4
  10. Point(Circle[C5, a]) → A5
  11. Ellipse(C5 + (e * (A5 - C5)), C5 - (e * (A5 - C5)), A5) → E5
  12. Point(Circle[C6, a]) → A6
  13. Ellipse(C6 + (e * (A6 - C6)), C6 - (e * (A6 - C6)), A6) → E6
  14. Point(Circle[C7, a]) → A7
  15. Ellipse(C7 + (e * (A7 - C7)), C7 - (e * (A7 - C7)), A7) → E7
  16. Point(Circle[C8, a]) → A8
  17. Ellipse(C8 + (e * (A8 - C8)), C8 - (e * (A8 - C8)), A8) → E8
  18. Point(Circle[C9, a]) → A9
  19. Ellipse(C9 + (e * (A9 - C9)), C9 - (e * (A9 - C9)), A9) → E9
  20. Point(Circle[C10, a]) → A10
  21. Ellipse(C10 + (e * (A10 - C10)), C10 - (e * (A10 - C10)), A10) → E10
  22. Point(Circle[C11, a]) → A11
  23. Ellipse(C11 + (e * (A11 - C11)), C11 - (e * (A11 - C11)), A11) → E11
  24. Point(Circle[C12, a]) → A12
  25. Ellipse(C12 + (e * (A12 - C12)), C12 - (e * (A12 - C12)), A12) → E12
  26. Point(Circle[C13, a]) → A13
  27. Ellipse(C13 + (e * (A13 - C13)), C13 - (e * (A13 - C13)), A13) → E13
  28. Point(Circle[C14, a]) → A14
  29. Ellipse(C14 + (e * (A14 - C14)), C14 - (e * (A14 - C14)), A14) → E14
  30. Point(Circle[C15, a]) → A15
  31. Ellipse(C15 + (e * (A15 - C15)), C15 - (e * (A15 - C15)), A15) → E15
  32. Point(Circle[C16, a]) → A16
  33. Ellipse(C16 + (e * (A16 - C16)), C16 - (e * (A16 - C16)), A16) → E16
  34. Point(Circle[C17, a]) → A17
  35. Ellipse(C17 + (e * (A17 - C17)), C17 - (e * (A17 - C17)), A17) → E17
  36. Point(Circle[C18, a]) → A18
  37. Ellipse(C18 + (e * (A18 - C18)), C18 - (e * (A18 - C18)), A18) → E18
  38. Point(Circle[C19, a]) → A19
  39. Ellipse(C19 + (e * (A19 - C19)), C19 - (e * (A19 - C19)), A19) → E19
  40. Point(Circle[C20, a]) → A20
  41. Ellipse(C20 + (e * (A20 - C20)), C20 - (e * (A20 - C20)), A20) → E20
  42. Point(Circle[C21, a]) → A21
  43. Ellipse(C21 + (e * (A21 - C21)), C21 - (e * (A21 - C21)), A21) → E21
  44. Point(Circle[C22, a]) → A22
  45. Ellipse(C22 + (e * (A22 - C22)), C22 - (e * (A22 - C22)), A22) → E22
  46. Point(Circle[C23, a]) → A23
  47. Ellipse(C23 + (e * (A23 - C23)), C23 - (e * (A23 - C23)), A23) → E23
  48. Point(Circle[C24, a]) → A24
  49. Ellipse(C24 + (e * (A24 - C24)), C24 - (e * (A24 - C24)), A24) → E24
  50. Point(Circle[C25, a]) → A25
  51. Ellipse(C25 + (e * (A25 - C25)), C25 - (e * (A25 - C25)), A25) → E25
  52. Point(Circle[C26, a]) → A26
  53. Ellipse(C26 + (e * (A26 - C26)), C26 - (e * (A26 - C26)), A26) → E26
  54. Point(Circle[C27, a]) → A27
  55. Ellipse(C27 + (e * (A27 - C27)), C27 - (e * (A27 - C27)), A27) → E27
  56. Point(Circle[C28, a]) → A28
  57. Ellipse(C28 + (e * (A28 - C28)), C28 - (e * (A28 - C28)), A28) → E28
  58. Point(Circle[C29, a]) → A29
  59. Ellipse(C29 + (e * (A29 - C29)), C29 - (e * (A29 - C29)), A29) → E29
  60. Point(Circle[C30, a]) → A30
  61. Ellipse(C30 + (e * (A30 - C30)), C30 - (e * (A30 - C30)), A30) → E30

AI 绘图提示语参考

在一个单位正方形内，绘制多个相互嵌套的椭圆，展示椭圆的几何构造和空间填充效果。首先绘制一个正方形，然后在正方形内随机放置多个圆心，以这些圆心为基准，绘制多个大小不同的椭圆，使它们相互嵌套并尽可能填满整个正方形，体现几何构造和优化问题的概念。
以上提示语为根据原始绘图命令整理而来，仅供参考。