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A4 Paper Box Volume Optimization

A4 Paper Box Volume Optimization
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2016-08-03 04:18
TrigonometrySolid GeometryCalculusOptimizationGeometric Construction
This example visually demonstrates the problem of maximizing the volume of a box folded from an A4 paper using calculus principles. It involves core math concepts like optimization, solid geometry volume calculation, symmetry, and trigonometry. Constructed with GeoGebra commands such as Polygon, Prism, Mirror, and Segment, it is suitable for high school and above students to understand the application of calculus in real-world problems and geometric modeling.

GeoGebra Commands & Parameters

  1. Polygon(C, B, D, A) → poly1, c, b, d, a
  2. Polygon(K, L, B, C) → poly2, k, l_1, b_1, c_1
  3. Polygon(G, C, A, H) → poly3, g, c_2, a_1, h_1
  4. Polygon(I, A, D, J) → poly4, i, a_2, d_1, j
  5. Polygon(D, F, E, B) → poly5, d_2, f, e, b_2
  6. Prism(poly1, N) → m, O, edgeBO, edgeDP, edgeAQ, edgeNO, edgeOP, edgePQ, edgeNQ, P, Q, faceBCNO, faceBDPO, faceADPQ, faceACNQ, faceNOPQ, edgeCN
  7. Mirror(M, yAxis) → M'
  8. Mirror(M, xAxis) → M'_1
  9. Mirror(M', xAxis) → M''
  10. Segment(M'', M'_1) → p
  11. Segment(M'_1, M) → q
  12. Segment(M, M') → r
  13. Segment(M', M'') → s