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直棱柱与体积

直棱柱与体积
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2015-09-04 05:48
三角函数立体几何
该范例演示直棱柱的几何构造及其体积计算。涉及的核心数学概念包括立体几何中的棱柱、体积计算以及三角函数的应用。通过使用GeoGebra命令如Sequence、Element、Point等，可以动态展示棱柱的构造过程。适合高中数学教学或学习立体几何的学生。

GeoGebra 命令及参数

  1. Sequence(Mat * Element[cube, k], k, 1, 8) → cube'
  2. Element(Element[AE, 3], 1) → droite
  3. Sequence((Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepoints
  4. Point(listepoints) → A
  5. Point(listepoints) → E
  6. Point(listepoints) → C_1
  7. Point(listepoints) → D
  8. Polygon(A, E, C_1, D) → poly1, a_1, b, c_1, d
  9. Point(listepoints) → B
  10. Point(listepoints) → F
  11. Point(listepoints) → G
  12. Point(listepoints) → H
  13. Polygon(B, F, G, H) → poly2, e, f, g, h
  14. Point(listepoints) → C
  15. Polygon(F, C, A, B) → poly3, f_1, i, a_2, b_1
  16. Element(AB, 3, 1) → avant
  17. Polygon(C_1, G, H, E) → poly4, c_2, g_1, h_1, e_1
  18. Element(AC, 3, 1) → dessus
  19. Polygon(F, C, C_1, G) → poly5, f_2, c_3, c_4, g_2
  20. Polygon(A, B, H, E) → poly6, a_3, b_2, h_2, e_2
  21. Segment(E, A) → c
  22. Segment(A, C) → j
  23. Segment(A, B) → k
  24. Segment(C, C_1) → l
  25. Segment(C_1, E) → m
  26. Segment(H, E) → n
  27. Segment(A, B) → p
  28. Segment(B, H) → q
  29. Segment(H, E) → r
  30. Segment(H, G) → s
  31. Segment(B, F) → t
  32. Segment(G, C_1) → d_1
  33. Segment(F, G) → i_1
  34. Segment(F, C) → j_1
  35. Sequence(Sequence[Sequence[Polygon[Translate[A, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[E, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[C_1, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[D, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]]], k, 0, u], l, 0, k_1], i, 0, l_1) → liste1
  36. Sequence(Sequence[Sequence[Polygon[Translate[B, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[F, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[G, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[H, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]]], k, 0, u], l, 0, k_1], i, 0, l_1) → liste2
  37. Sequence(Sequence[Sequence[Polygon[Translate[F, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[C, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[A, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[B, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]]], k, 0, u], l, 0, k_1], i, 0, l_1) → liste3
  38. Sequence(Sequence[Sequence[Polygon[Translate[C_1, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[G, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[H, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[E, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]]], k, 0, u], l, 0, k_1], i, 0, l_1) → liste4
  39. Sequence(Sequence[Sequence[Polygon[Translate[F, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[C, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[C_1, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[G, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]]], k, 0, u], l, 0, k_1], i, 0, l_1) → liste5
  40. Sequence(Sequence[Sequence[Polygon[Translate[A, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[B, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[H, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[E, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]]], k, 0, u], l, 0, k_1], i, 0, l_1) → liste6