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棱锥体积的证明

棱锥体积的证明
几何画板及绘图内容加载中，请稍等……
2017-05-27 18:07
立体几何几何作图
这个范例演示了如何通过几何作图证明棱锥的体积公式。核心数学概念包括棱锥、体积以及立体几何。使用了Polygon、Pyramid、Segment、Angle等GeoGebra命令进行构造。适合高中数学教学和学习立体几何的学生。

GeoGebra 命令及参数

  1. Intersect(xAxis, zAxis) → A
  2. Point(xAxis) → B
  3. Point(yAxis) → D
  4. Polygon(A, B, C, D) → poly1, a, b, c, d
  5. Pyramid(poly1, -2) → e, E, faceABE, faceBCE, faceCDE, faceADE, edgeAE, edgeBE, edgeCE, edgeDE
  6. Point(zAxis) → G
  7. Polygon(A, G, F, B) → poly2, a_1, g, f, b_1
  8. Pyramid(poly2, -2) → h, H, faceAGH, faceFGH, faceBFH, faceABH, edgeAH, edgeGH, edgeFH, edgeBH
  9. Polygon(B, C, I, F) → poly3, b_2, c_1, i_1, f_1
  10. Pyramid(poly3, 2) → j, J, faceBCJ, faceCIJ, faceFIJ, faceBFJ, edgeBJ, edgeCJ, edgeIJ, edgeFJ
  11. Polygon(C, D, K, I) → poly4, c_2, d_1, k, i_2
  12. Pyramid(poly4, 2) → l, L, faceCDL, faceDKL, faceIKL, faceCIL, edgeCL, edgeDL, edgeKL, edgeIL
  13. Polygon(D, A, G, K) → poly5, d_2, a_2, g_1, k_1
  14. Pyramid(poly5, 2) → m, M, faceADM, faceAGM, faceGKM, faceDKM, edgeDM, edgeAM, edgeGM, edgeKM
  15. Intersect(zAxis, g_1) → N
  16. Polygon(G, F, I, K) → poly6, g_2, f_2, i_3, k_2
  17. Pyramid(poly6, (-(-2))) → n, O, faceFGO, faceFIO, faceIKO, faceGKO, edgeGO, edgeFO, edgeIO, edgeKO
  18. Segment(D, C) → p
  19. Segment(B, F) → q
  20. Segment(I, C) → r
  21. Segment(I, K) → s
  22. Segment(K, D) → t
  23. Segment(K, G) → h_1
  24. Segment(G, F) → j_1
  25. Segment(D, A) → l_1
  26. Intersect(yAxis, a_2) → P
  27. Segment(B, P) → m_1
  28. Segment(I, F) → p_1
  29. Segment(G, K) → q_1
  30. Segment(P, G) → n_1
  31. Segment(Q, E) → r_1
  32. Segment(Q, R) → s_1
  33. Angle(r_1, s_1) → α