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立方体体积计算与几何作图

立方体体积计算与几何作图
几何画板及绘图内容加载中，请稍等……
2016-05-31 02:17
解析几何立体几何几何作图
所属专题 Geo&Alg:Area Volume Pythagorean Th.
本范例演示如何通过拼接立方体计算体积，涉及立体几何与空间坐标概念。作图要点包括使用Point、Cube、Translate命令创建立方体对象，并通过面、边等几何元素进行可视化。适合初中生学习几何体积计算及空间想象能力培养。

GeoGebra 命令及参数

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Point(Circle[J, Distance[I, J], Segment[I, J]]) → K
  3. Point(Circle[R, Distance[Q, R], Segment[Q, R]]) → S
  4. Point(Circle[H_1, Distance[G_1, H_1], Segment[G_1, H_1]]) → I_1
  5. Cube(G_1, H_1, I_1) → e_1, J_1, face11, facez, edge13, edge12, edge15, edge17, edge14, edge19, edge21, edge20, K_1, edge16, edge22, edge18, edge23, L_1, M_1, N_1, face7, face9, facey, facex
  6. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (2, 1)]) → f
  7. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (1, 0)]) → g
  8. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (1, 1, 1)]) → h
  9. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (1, 1)]) → e
  10. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (1, 1)]) → e'
  11. Translate(facex, Vector[(0, 0, 0), (0, -1, 0)]) → facex010
  12. Translate(facey, Vector[(0, 0), (1, 0, 0)]) → facey100
  13. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (2, 1)]) → f'
  14. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(2, 0)]) → a
  15. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(2, 0)]) → a'
  16. Translate(facez, Vector[(0, 0, 0), (0, -1, 0)]) → facez010
  17. Translate(facey, Vector[(0, 0, 1)]) → facey001
  18. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(1, 0, 1)]) → b
  19. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(1, 0, 1)]) → b'
  20. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (1, 0)]) → g'
  21. Translate(Cube[(0, 0), (1, 0), Point[Circle[(1, 0), Distance[(0, 0), (1, 0)], Segment[(0, 0), (1, 0)]]]], Vector[(0, 0), (1, 1, 1)]) → h'
  22. Translate(Prism[Polygon[(-4, 2), (-2, 2), (-2, 2, 1), (-3, 2, 1), (-3, 2, 2), (-4, 2, 2)], (-4, 0, 0)], Vector[(0, 0)]) → c
  23. Translate(Prism[Polygon[(-4, 2), (-2, 2), (-2, 2, 1), (-3, 2, 1), (-3, 2, 2), (-4, 2, 2)], (-4, 0, 0)], Vector[(0, 0)]) → d
  24. Translate(Polygon[(-4, 1), (-2, 1), (-2, 1, 1), (-3, 1, 1), (-3, 1, 2), (-4, 1, 2)], Vector[(0, 0)]) → poly1
  25. Translate(Polygon[(-4, 0, 1), (-3, 0, 1), (-3, 2, 1), (-4, 2, 1)], Vector[(0, 0)]) → poly2
  26. Translate(Polygon[(-3, 0, 0), (-3, 2, 0), (-3, 2, 1), (-3, 0, 1)], Vector[(0, 0)]) → poly3

AI 绘图提示语参考

绘制一个立方体拼接的体积计算示例，展示通过立方体组合来计算体积。首先创建几个点，然后基于这些点构建立方体，并使用平移命令将立方体移动到不同位置，形成多个立方体组合。突出显示立方体的面和边，以便清晰地展示体积计算的过程，适合用于教学演示。
以上提示语为根据原始绘图命令整理而来，仅供参考。