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密度、质量与体积关系演示

密度、质量与体积关系演示
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2017-04-03 01:45
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①本范例通过交互式图形演示密度、质量与体积之间的基本物理关系；②涉及核心数学概念包括体积计算、角度、比例、集合理论、差值与斜率、幂函数；③构造过程中运用了正交线、点、交点、多边形、点在内部等 GeoGebra 命令与对象；④适合初中及以上学生用于理解基础物理公式及数学建模思想。

GeoGebra 命令及参数

  1. OrthogonalLine(A_1, xAxis) → a
  2. Point(xAxis) → B_1
  3. OrthogonalLine(B_1, xAxis) → b
  4. OrthogonalLine(C, xAxis) → c
  5. OrthogonalLine(A_1, a) → d
  6. OrthogonalLine(C, b) → e
  7. Intersect(d, yAxis) → D
  8. Intersect(xAxis, yAxis) → E
  9. Intersect(a, xAxis) → F
  10. Polygon(A_1, D, E, F) → BoxA, a_1, d_1, e_1, f
  11. Intersect(c, xAxis) → G
  12. Intersect(b, e) → H
  13. Polygon(C, G, B_1, H) → BoxB, c_1, g, b_1, h
  14. Point(Circle[I, 1]) → J
  15. Point(Circle[I_1, 1]) → J_1
  16. Point(Circle[I_2, 1]) → J_2
  17. Point(Circle[I_3, 1]) → J_3
  18. Point(Circle[I_4, 1]) → J_4
  19. Point(Circle[I_5, 1]) → J_5
  20. Point(Circle[I_6, 1]) → J_6
  21. Point(Circle[I_7, 1]) → J_7
  22. PointIn(BoxA) → M
  23. PointIn(BoxA) → N
  24. PointIn(BoxA) → O
  25. PointIn(BoxA) → P
  26. PointIn(BoxA) → Q
  27. PointIn(BoxA) → R
  28. PointIn(BoxA) → S
  29. PointIn(BoxA) → T
  30. PointIn(BoxA) → U
  31. PointIn(BoxA) → V
  32. PointIn(BoxB) → Z
  33. PointIn(BoxB) → C_1
  34. PointIn(BoxB) → D_1
  35. PointIn(BoxB) → E_1
  36. PointIn(BoxB) → F_1
  37. PointIn(BoxB) → G_1
  38. PointIn(BoxB) → H_1
  39. PointIn(BoxB) → M_1
  40. PointIn(BoxB) → N_1
  41. PointIn(BoxB) → O_1
  42. PointIn(BoxB) → P_1
  43. PointIn(BoxB) → Q_1
  44. PointIn(BoxB) → R_1
  45. PointIn(BoxB) → S_1
  46. PointIn(BoxB) → A
  47. PointIn(BoxB) → B
  48. PointIn(BoxB) → T_1
  49. PointIn(BoxB) → U_1
  50. PointIn(BoxB) → V_1
  51. PointIn(BoxB) → W_1
  52. PointIn(BoxA) → W
  53. PointIn(BoxA) → Z_1
  54. PointIn(BoxA) → A_2
  55. PointIn(BoxA) → B_2
  56. PointIn(BoxA) → C_2
  57. PointIn(BoxA) → D_2
  58. PointIn(BoxA) → E_2
  59. PointIn(BoxA) → F_2
  60. PointIn(BoxA) → G_2
  61. PointIn(BoxA) → H_2
  62. Point(Circle[I_8, 1]) → J_8
  63. Point(Circle[I_9, 1]) → J_9
  64. Point(Circle[I_{10}, 1]) → J_{10}
  65. Point(Circle[I_{11}, 1]) → J_{11}
  66. Point(Circle[I_{12}, 1]) → J_{12}
  67. Point(Circle[I_{13}, 1]) → J_{13}
  68. Point(Circle[I_{14}, 1]) → J_{14}
  69. Point(Circle[I_{15}, 1]) → J_{15}