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棱锥体积猜想（复制）

棱锥体积猜想（复制）
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2017-08-30 13:42
多边形数列立体几何几何作图滑块动画
① 本范例通过动态几何演示棱锥体积与底面积、高之间的关系，引导用户猜想棱锥体积公式 V = (1/3)Sh。② 核心数学概念包括立体几何中的棱锥体积、比例与极限思想，以及通过散点图（Scatter Plot）观察数据规律。③ 作图要点：使用 GeoGebra 的 Sequence、Element、Point、Polygon、Segment、PointIn、Translate 等命令构造棱锥及其截面，并利用滑块（slider）调整参数；对象包括 z、w、v、a、O、P、β、sinβ、cosβ、α、sinα、cosα、X、Y、Z、echelle、R_x、R_y、cube、texte1、texte2、Mat、cube'、AE、droite、listepoints、A、E、C_1、D、poly1、a_1、b、c_1、d、B、F、G、H、poly2 等，通过平移和点列生成体积测量数据。④ 适合中学高年级（如初中几何拓展或高中立体几何入门）用于探究棱锥体积公式，也可用于数学实验课或教师演示，帮助学生从直观操作过渡到公式推导。

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. PointIn(poly5) → J
  36. Translate(J, Vector[val1 * Vector[A, B]]) → pyr1_1
  37. Translate(A, Vector[val1 * Vector[A, B]]) → pyr1_2
  38. Translate(B, Vector[val1 * Vector[A, B]]) → pyr1_3
  39. Translate(H, Vector[val1 * Vector[A, B]]) → pyr1_4
  40. Translate(E, Vector[val1 * Vector[A, B]]) → pyr1_5
  41. Polygon(pyr1_1, pyr1_2, pyr1_3) → poly11, pyr1_6, pyr1_7, pyr1_8
  42. Polygon(pyr1_1, pyr1_3, pyr1_4) → poly12, pyr1_9, pyr1_{10}, pyr1_{11}
  43. Polygon(pyr1_5, pyr1_1, pyr1_2) → poly13, pyr1_{12}, pyr1_{13}, pyr1_{14}
  44. Polygon(pyr1_5, pyr1_4, pyr1_3, pyr1_2) → poly14, pyr1_{15}, pyr1_{16}, pyr1_{17}, pyr1_{18}
  45. Translate(J, Vector[val2 * Vector[A, E]]) → pyr2_1
  46. Translate(E, Vector[val2 * Vector[A, E]]) → pyr2_2
  47. Translate(H, Vector[val2 * Vector[A, E]]) → pyr2_3
  48. Translate(C_1, Vector[val2 * Vector[A, E]]) → pyr2_4
  49. Translate(G, Vector[val2 * Vector[A, E]]) → pyr2_5
  50. Polygon(pyr2_1, pyr2_2, pyr2_3) → poly15, pyr2_6, pyr2_7, pyr2_8
  51. Polygon(pyr2_1, pyr2_4, pyr2_5) → poly16, pyr2_9, pyr2_{10}, pyr2_{11}
  52. Polygon(pyr2_1, pyr2_3, pyr2_5) → poly17, pyr2_{12}, pyr2_{13}, pyr2_{14}
  53. Polygon(pyr2_4, pyr2_2, pyr2_3, pyr2_5) → poly18, pyr2_{15}, pyr2_{16}, pyr2_{17}, pyr2_{18}
  54. Translate(J, Vector[val3 * Vector[D, A]]) → pyr3_1
  55. Translate(F, Vector[val3 * Vector[D, A]]) → pyr3_2
  56. Translate(B, Vector[val3 * Vector[D, A]]) → pyr3_3
  57. Translate(G, Vector[val3 * Vector[D, A]]) → pyr3_4
  58. Translate(H, Vector[val3 * Vector[D, A]]) → pyr3_5
  59. Polygon(pyr3_1, pyr3_3, pyr3_2) → poly19, pyr3_6, pyr3_7, pyr3_8
  60. Polygon(pyr3_2, pyr3_4, pyr3_5, pyr3_3) → poly20, pyr3_9, pyr3_{10}, pyr3_{11}, pyr3_{12}
  61. Polygon(pyr3_1, pyr3_2, pyr3_4) → poly21, pyr3_{13}, pyr3_{14}, pyr3_{15}
  62. Polygon(pyr3_1, pyr3_5, pyr3_4) → poly22, pyr3_{16}, pyr3_{17}, pyr3_{18}

AI 绘图提示语参考

画一个金字塔，展示其体积与底面积和高的关系，用散点图可视化数据。金字塔由多个多边形构成，包括底面和侧面，通过滑块调整参数。显示金字塔的多个截面，并用动态图形展示体积测量数据，引导学生猜想体积公式 V = (1/3)Sh。
以上提示语为根据原始绘图命令整理而来，仅供参考。