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最大化狗舍面积问题

最大化狗舍面积问题
几何画板及绘图内容加载中，请稍等……
2016-07-08 05:22
最值优化几何作图
本范例演示如何通过调整围栏的形状来最大化狗舍的面积。涉及的核心数学概念包括面积、周长和算术平均值。通过使用GeoGebra命令如Intersect、Segment、Point等进行几何作图。适合初中及以上学生学习面积优化问题。

GeoGebra 命令及参数

  1. Intersect(a, yAxis) → S
  2. Intersect(a, xAxis) → E
  3. Segment(S, E) → b
  4. Point(b) → A
  5. OrthogonalLine(A, xAxis) → c
  6. OrthogonalLine(A, yAxis) → d
  7. Intersect(c, xAxis) → B_1
  8. Intersect(yAxis, xAxis) → C_1
  9. Intersect(d, yAxis) → D
  10. Polygon(A, B_1, C_1, D) → poly1, a_1, b_1, c_1, d_1
  11. Intersect(e, yAxis) → S1
  12. Intersect(e, xAxis) → E1
  13. Segment(S1, E1) → f
  14. Point(f) → B
  15. OrthogonalLine(B, xAxis) → g
  16. OrthogonalLine(B, yAxis) → h
  17. Intersect(h, yAxis) → F
  18. Intersect(g, xAxis) → G
  19. Polygon(B, G, C_1, F) → poly2, b_2, g_1, c_2, f_1
  20. Intersect(yAxis, i) → S2
  21. Intersect(xAxis, i) → E2
  22. Segment(S2, E2) → j
  23. Point(j) → C
  24. OrthogonalLine(C, xAxis) → k
  25. OrthogonalLine(C, yAxis) → l
  26. Intersect(l, yAxis) → H
  27. Intersect(k, xAxis) → I
  28. Segment(H, C) → m
  29. Segment(C, I) → n
  30. Segment(I, C_1) → p
  31. Segment(C_1, H) → q
  32. Point(Circle[H, m / 3]) → J
  33. Segment(H, J) → r
  34. Point(Circle[J, m / 3]) → K
  35. Segment(J, K) → s
  36. Point(Circle[C_1, p / 3]) → L
  37. Segment(C_1, L) → t
  38. Point(Circle[L, p / 3]) → M
  39. Segment(L, M) → e_1
  40. Polygon(C, I, M, K) → poly3, c_3, i_1, m_1, k_1
  41. Polygon(K, M, L, J) → poly4, k_2, m_2, l_1, j_1
  42. Polygon(J, L, C_1, H) → poly5, j_2, l_2, c_4, h_1
  43. Polygon(C, I, C_1, H) → poly6, c_5, i_2, c_6, h_2