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Classic Open Box Optimization Visualization

Classic Open Box Optimization Visualization
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2019-12-05 21:44
FunctionCalculusOptimizationGeometric ConstructionSlider Animation
This example provides a dynamic visualization of a classic optimization problem, demonstrating how adjusting the dimensions of a rectangle maximizes the volume of an open-top box. It involves core math concepts like calculus optimization, quadratic functions, plane geometry, and 3D vectors. The construction uses GeoGebra commands such as Polygon, Point, Segment, Rotate, Line, and Intersect. Ideal for high school students and learners needing to understand optimization problems.

GeoGebra Commands & Parameters

  1. Polygon(A, B, D, C) → q1, a, b, d, c_1
  2. Point(Circle[C, c]) → E
  3. Segment(C, E) → f
  4. Polygon(E, C, 4) → poly1, g, h, i, j, F, G
  5. Point(Circle[A, c]) → H
  6. Segment(A, H) → k
  7. Polygon(A, H, 4) → poly2, l, m, n, p, I, J
  8. Polygon(K, B, 4) → poly3, q, r, s, t, L, M
  9. Polygon(N, D, 4) → poly4, e, f_1, g_1, h_1, O, P
  10. Segment(G, P) → i_1
  11. Segment(P, M) → j_1
  12. Segment(M, J) → k_1
  13. Segment(I, G) → l_1
  14. Point(Circle[S, 8.5 - (2 * c)]) → U
  15. Segment(S, U) → m_1
  16. Rotate(U, 45°, S) → U'
  17. Segment(S, Q) → n_1
  18. Segment(Q, R) → p_1
  19. Segment(R, T) → q_1
  20. Segment(T, S) → r_1
  21. Segment(S, U') → s_1
  22. Line(U', r_1) → t_1
  23. Line(T, s_1) → a_1
  24. Line(R, s_1) → b_1
  25. Intersect(t_1, a_1) → V
  26. Line(V, q_1) → d_1
  27. Intersect(b_1, d_1) → W
  28. Segment(U', V) → e_1
  29. Segment(V, T) → f_2
  30. Segment(V, W) → g_2
  31. Segment(W, R) → h_2