三角形棱柱体积演示

三角形棱柱体积演示
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2012-12-19 22:23
①本范例演示了如何通过 GeoGebra 绘制并计算三角形棱柱的体积;②涉及的核心数学概念包括体积计算公式、几何作图、空间几何;③作图要点——从下方『构造摘要』提炼用到了 Point(点)、Segment(线段)、Polygon(多边形)、Translate(平移)等 GeoGebra 命令/对象;④适合高中阶段学生学习立体几何和体积计算,也可用于数学教学演示。

GeoGebra 命令及参数

  1. Point(Circle[A, tinggi]) → B
  2. Segment(A, B) → a
  3. Point(Circle[A, lebar]) → C
  4. Segment(A, C) → b
  5. Point(Circle[A, panjang]) → D
  6. Segment(A, D) → c
  7. Point(Circle[A_1, lebar]) → C_1
  8. Segment(A_1, C_1) → b_1
  9. Point(Circle[A_2, lebar]) → C_2
  10. Segment(A_2, C_2) → b_2
  11. Point(Circle[A_4, tinggi]) → B_1
  12. Segment(A_4, B_1) → a_1
  13. Point(Circle[A_6, tinggi]) → B_2
  14. Segment(A_6, B_2) → a_2
  15. Point(Circle[A_{10}, panjang]) → D_1
  16. Segment(A_{10}, D_1) → c_1
  17. Point(Circle[A_{13}, panjang]) → D_2
  18. Segment(A_{13}, D_2) → c_2
  19. Point(Circle[A_{16}, panjang]) → D_3
  20. Segment(A_{16}, D_3) → c_3
  21. Segment(D, D_2) → d
  22. Segment(D_2, D_3) → e
  23. Polygon(B_1, D_2, D, C) → poly1, b_3, d_2, d_1, c_4
  24. Polygon(B_1, B, A, C) → poly2, b_4, b_5, a_3, c_5
  25. Polygon(B_1, C, D_1, D_3) → poly3, b_6, c_6, d_3, d_4
  26. Polygon(D_2, D_3, D_1, D) → poly4, d_5, d_6, d_7, d_8
  27. Polygon(B, D_2, D, A) → poly5, b_7, d_9, d_{10}, a_4
  28. Polygon(B_1, D_3, D_2, B) → poly11, b_{10}, d_{14}, d_{15}, b_{11}
  29. Polygon(A, C, D_1, D) → poly12, a_5, c_{14}, d_{16}, d_{17}
  30. Point(Circle[A_{27}, panjang]) → D_5
  31. Segment(A_{27}, D_5) → c_{15}
  32. Point(Circle[A_{31}, lebar]) → C_6
  33. Segment(A_{31}, C_6) → b_{13}
  34. Point(Circle[A_{36}, panjang]) → D_7
  35. Segment(A_{36}, D_7) → c_{17}
  36. Point(Circle[A_{37}, lebar]) → C_7
  37. Segment(A_{37}, C_7) → b_{14}
  38. Point(Circle[A_{41}, tinggi]) → B_4
  39. Segment(A_{41}, B_4) → a_7
  40. Point(Circle[A_{42}, lebar]) → C_8
  41. Segment(A_{42}, C_8) → b_{15}
  42. Point(Circle[A_{46}, tinggi]) → B_5
  43. Segment(A_{46}, B_5) → a_8
  44. Point(Circle[A_{47}, lebar]) → C_9
  45. Segment(A_{47}, C_9) → b_{16}
  46. Translate(B_1, Vector[geser1 * Vector[B_1, B_2]]) → pryB_1
  47. Translate(B, Vector[geser1 * Vector[B_1, B_2]]) → pryB
  48. Translate(A, Vector[geser1 * Vector[B_1, B_2]]) → pryA
  49. Translate(C, Vector[geser1 * Vector[B_1, B_2]]) → pryC
  50. Translate(D, Vector[geser1 * Vector[B_1, B_2]]) → pryD
  51. Translate(D_2, Vector[geser1 * Vector[B_1, B_2]]) → pryD_2
  52. Translate(B_1, Vector[geser2 * Vector[B_1, B_2]]) → pryBB
  53. Translate(B_2, Vector[geser2 * Vector[B_1, B_2]]) → pryB_2
  54. Translate(C, Vector[geser2 * Vector[B_1, B_2]]) → pryCC
  55. Translate(C_2, Vector[geser2 * Vector[B_1, B_2]]) → pryC_2
  56. Translate(D, Vector[geser2 * Vector[B_1, B_2]]) → pryDD
  57. Polygon(pryB_1, pryD_2, pryD, pryC) → poly6, pryb_1, pryd_2, pryd, pryc
  58. Translate(D_2, Vector[geser2 * Vector[B_1, B_2]]) → pryDD_2
  59. Polygon(pryBB, pryDD_2, pryDD, pryCC) → poly7, prybb, prydd_2, prydd, prycc
  60. Polygon(pryB_1, pryB, pryA, pryC) → poly8, pryb_2, pryb, prya, pryc_1
  61. Polygon(pryB_1, pryD_2, pryB) → poly9, pryb_3, pryb_4, pryd_1
  62. Polygon(pryA, pryC, pryD) → poly10, pryd_3, prya_1, pryc_2
  63. Polygon(pryB, pryA, pryD, pryD_2) → poly13, pryb_5, prya_2, pryd_4, pryd_5
  64. Polygon(pryBB, pryCC, pryC_2, pryB_2) → poly14, prybb_1, prycc_1, pryc_3, pryb_6
  65. Polygon(pryB_2, pryC_2, pryDD, pryDD_2) → poly15, pryb_7, pryc_4, prydd_1, prydd_3
  66. Polygon(pryBB, pryB_2, pryDD_2) → poly16, prydd_4, prybb_2, pryb_8
  67. Polygon(pryCC, pryC_2, pryDD) → poly17, prydd_5, prycc_2, pryc_5
  68. Polygon(pryA, pryD, pryC) → poly18, pryc_6, prya_3, pryd_6

AI 绘图提示语参考

绘制一个三角形棱柱,首先在点A处创建一个三角形底面,然后通过点A和底面的边构造其他点和线段,形成两个平行的三角形底面。接着,通过点A和底面的边构造垂直于底面的线段,连接两个三角形底面,形成棱柱的侧面。最后,通过平移底面三角形,得到棱柱的另一个底面。
以上提示语为根据原始绘图命令整理而来,仅供参考。