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Optimization - Pizza Box

Optimization - Pizza Box
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2019-12-06 00:03
CalculusOptimizationGeometric ConstructionGraphing
This example provides a quick visualization of a classic optimization problem, demonstrating how to maximize the volume of a pizza box. It involves core math concepts like calculus optimization, geometry constructions with circles and polygons, and transformations like rotation. The construction uses commands such as Segment, Polygon, Point, Rotate, Line, and Intersect in GeoGebra. Suitable for high school and above students learning calculus optimization, or for educational demonstrations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, D) → g
  3. Segment(D, C) → h
  4. Segment(C, A) → i
  5. Segment(G, F) → j
  6. Segment(F, E) → k
  7. Segment(Q, S) → l
  8. Segment(S, T) → m
  9. Segment(T, R) → n
  10. Segment(K, M) → p
  11. Segment(M, L) → q
  12. Segment(P, O) → r
  13. Segment(O, N) → s
  14. Segment(W, Z) → t
  15. Segment(Z, U) → a
  16. Segment(U, V) → b
  17. Segment(I, J) → d
  18. Segment(J, H) → e
  19. Segment(J, U) → f_1
  20. Segment(Z, O) → g_1
  21. Segment(O, M) → h_1
  22. Segment(M, T) → i_1
  23. Segment(S, F) → j_1
  24. Segment(F, J) → k_1
  25. Segment(U, S) → l_1
  26. Segment(Z, T) → m_1
  27. Polygon(A, B, D, C) → q1, a_1, b_1, d_1, c_1
  28. Polygon(C, H, J, I) → q2, c_2, h_2, j_2, i_2
  29. Polygon(V, U, Z, W) → q3, v, u, z_1, w
  30. Polygon(N, O, P, D) → q4, n_1, o, p_1, d_2
  31. Polygon(G, A, E, F) → q5, g_2, a_2, e_1, f_2
  32. Polygon(Q, R, T, S) → q6, q_1, r_1, t_1, s_1
  33. Polygon(K, B, L, M) → q7, k_2, b_2, l_2, m_2
  34. Segment(C, A) → n_2
  35. Segment(A, B) → p_2
  36. Segment(B, D) → q_2
  37. Segment(D, C) → r_2
  38. Point(Circle[C_1, 8 - (2 * c)]) → E_1
  39. Segment(C_1, E_1) → s_2
  40. Rotate(E_1, 35°, C_1) → F_1
  41. Segment(C_1, A_1) → t_2
  42. Segment(A_1, B_1) → e_2
  43. Segment(B_1, D_1) → f_3
  44. Segment(D_1, C_1) → g_3
  45. Segment(C_1, F_1) → h_3
  46. Line(F_1, g_3) → i_3
  47. Line(D_1, h_3) → j_3
  48. Line(B_1, h_3) → k_3
  49. Intersect(i_3, j_3) → G_1
  50. Line(G_1, f_3) → l_3
  51. Segment(F_1, G_1) → m_3
  52. Intersect(k_3, l_3) → H_1
  53. Segment(G_1, H_1) → n_3
  54. Segment(H_1, B_1) → p_3
  55. Segment(D_1, G_1) → q_3