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棱锥体积计算（方法一）

棱锥体积计算（方法一）
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2020-07-22 15:37
立体几何变换几何作图
本范例演示了如何通过几何作图计算棱锥的体积。核心概念包括棱锥的体积公式和几何变换。通过使用GeoGebra命令如Point, Cube, Net, Polygon, Pyramid等，可以直观地展示棱锥的构造过程。适合初中及以上学生或教师使用。

GeoGebra 命令及参数

  1. Point(Circle[A, Distance[O, A], Segment[O, A]]) → B
  2. Cube(O, A, B) → b, C, faceBCGF, faceDEFG, edgeCO, edgeAO, edgeAB, edgeBC, edgeDO, edgeCG, edgeDG, edgeDE, D, edgeAE, edgeEF, edgeBF, edgeFG, E, F, G, faceABCO, faceCGDO, faceAEDO, faceABFE
  3. Net(b, Fold) → d, H, R, S, T, U, V, faceHIJK, faceHKML, faceHIRQ, faceIJTS, faceJKVU, I, faceLMNP, edgeHK, edgeHI, edgeIJ, edgeJK, edgeKM, edgeLM, edgeHL, edgeHQ, edgeQR, J, edgeIR, edgeIS, edgeST, edgeJT, edgeJU, edgeUV, edgeKV, edgeMN, edgeNP, edgeLP, K, L, M, N, P, Q
  4. Polygon(N, P, L, M) → q1, n, p, l, m
  5. Pyramid(q1, Size / 2) → e, W, faceNPW, faceLPW, faceLMW, faceMNW, edgeNW, edgePW, edgeLW, edgeMW
  6. Polygon(M, L, O, K) → q2, m_1, l_1, o, k
  7. Pyramid(q2, Size / 2) → f, Z, faceLMZ, faceLOZ, faceKOZ, faceKMZ, edgeMZ, edgeLZ, edgeOZ, edgeKZ
  8. Polygon(O, Q, R, I) → q3, o_1, q, r, i
  9. Pyramid(q3, Size / 2) → g, A_1, face2, face4, face3, face1, edge1, edge3, edge4, edge2
  10. Polygon(I, B, K, O) → q4, i_1, b_1, k_1, o_2
  11. Pyramid(q4, Size / 2) → h, B_1, face7, face8, face6, face5, edge7, edge6, edge8, edge5
  12. Polygon(I, S, T, B) → q5, i_2, s, t, b_2
  13. Pyramid(q5, Size / 2) → j, C_1, face11, face12, face10, face9, edge10, edge11, edge12, edge9
  14. Polygon(B, U, V, K) → q6, b_3, u, v, k_2
  15. Pyramid(q6, Size / 2) → w, D_1, face14, face16, face15, face13, edge13, edge15, edge16, edge14