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经典最大体积长方体可视化

经典最大体积长方体可视化
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2012-08-13 04:08
立体几何最值优化滑块动画
所属专题 Area, perimeter and volume of shapes Area, Perimeter and Volume of shapes
本示例演示如何通过调整滑块 g、h 和高度来改变长方体的尺寸，从而观察其体积的变化。核心数学概念包括立体几何和导数。使用了 Intersect、Polygon、Mirror、If、Vector、Derivative、Midpoint、Max、Name 等 GeoGebra 命令。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → D
  2. Polygon(D, A, C, B) → poly1, d, a, c, b
  3. Polygon(D, F, E, G) → poly2, d_1, f, e, g_1
  4. Mirror(D, x = Segment[D, A] / 2) → D'
  5. Mirror(F, x = Segment[D, A] / 2) → F'
  6. Mirror(E, x = Segment[D, A] / 2) → E'
  7. Mirror(G, x = Segment[D, A] / 2) → G'
  8. Polygon(D', F', E', G') → poly2', d', f', e', g'
  9. Mirror(D, y = Segment[D, B] / 2) → D'_1
  10. Mirror(A, y = Segment[D, B] / 2) → A'
  11. Mirror(C, y = Segment[D, B] / 2) → C'
  12. Mirror(B, y = Segment[D, B] / 2) → B'
  13. Mirror(D, y = Segment[D, B] / 2) → D'_2
  14. Mirror(F, y = Segment[D, B] / 2) → F'_1
  15. Mirror(E, y = Segment[D, B] / 2) → E'_1
  16. Mirror(G, y = Segment[D, B] / 2) → G'_1
  17. Polygon(D'_2, F'_1, E'_1, G'_1) → poly2'_1, d'_2, f'_1, e'_1, g'_1
  18. If(Segment[D, B] ≥ Segment[D, A], Segment[D, A] / 2, Segment[D, B] / 2) → maxval
  19. If(Segment[D, B] ≥ Segment[D, A], maxval = Segment[D, A] / 2, maxval = Segment[D, B] / 2) → i
  20. Mirror(D', y = Segment[A, C] / 2) → D''
  21. Mirror(F', y = Segment[A, C] / 2) → F''
  22. Mirror(E', y = Segment[A, C] / 2) → E''
  23. Mirror(G', y = Segment[A, C] / 2) → G''
  24. Polygon(D'', F'', E'', G'') → poly2'', d'', f'', e'', g''
  25. Polygon(E'_1, E'', E', E) → poly3, e'_2, e''_1, e'_3, e_1
  26. Vector(H, I) → u
  27. Derivative(V) → p
  28. Midpoint(D, F) → dfavg
  29. Max(V, 0, maxval) → J
  30. Max(V, 0, maxval) → maxofv
  31. Name(height) → A1