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Maximize Dog Pen Area Problem

Maximize Dog Pen Area Problem
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2016-07-08 05:22
OptimizationGeometric Construction
This example demonstrates how to maximize the area of a dog pen by adjusting its shape. Key mathematical concepts include area, perimeter, and arithmetic mean. The construction uses GeoGebra commands such as Intersect, Segment, and Point. Suitable for middle school and above students to learn area optimization problems.

GeoGebra Commands & Parameters

  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