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金字塔体积计算 by Miguel Quinonez

金字塔体积计算 by Miguel Quinonez
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2017-10-04 03:23
解析几何立体几何几何作图
①本范例演示如何通过 GeoGebra 绘制金字塔并计算其体积；②涉及的核心数学概念包括体积公式、三维坐标、多边形构造、解析几何；③作图要点——从下方『构造摘要』提炼用到了 Polygon（多边形）、Point（点）、Pyramid（金字塔）、Net（展开图）、Intersect（相交）、Segment（线段）等 GeoGebra 命令/对象；④适合高中立体几何教学或数学爱好者探索几何体体积计算。

GeoGebra 命令及参数

  1. Polygon(A, B, 8) → poly1, f, D, E, F, G, H, g, h, i, j, k, l, m, C
  2. Point(zAxis) → I
  3. Pyramid(poly1, I) → a, faceABI, edgeBI, edgeCI, edgeDI, edgeEI, edgeFI, edgeGI, edgeHI, faceBCI, faceCDI, faceDEI, faceEFI, faceFGI, faceGHI, faceAHI, edgeAI
  4. Net(a, b) → c, J, S, T, U, V, W, Z, A_1, faceJKLMNOPQ, faceJKR, faceKLS, K, faceLMT, faceMNU, faceNOV, faceOPW, facePQZ, face1, edgeJK, edgeKL, edgeLM, edgeMN, L, edgeNO, edgeOP, edgePQ, edgeJQ, edgeJR, edgeKR, edgeKS, edgeLS, edgeLT, edgeMT, M, edgeMU, edgeNU, edgeNV, edgeOV, edgeOW, edgePW, edgePZ, edgeQZ, edge2, edge1, N, O, P, Q, R
  5. Intersect(xAxis, yAxis) → B_1
  6. Intersect(edgeOV, edgePZ) → C_1
  7. Segment(B_1, C_1) → n
  8. Intersect(yAxis, edgeNO) → D_1
  9. Segment(D_1, C_1) → q
  10. Segment(D_1, B_1) → r
  11. Segment(B_1, C_1) → s
  12. Segment(D_1, B_1) → p
  13. Intersect(edgeFI, edgeGI) → E_1
  14. Segment(B_1, E_1) → t
  15. Point(edgeNO) → F_1
  16. Point(edgeNO) → G_1
  17. Polygon(F_1, G_1, B_1) → t1, b_1, f_1, g_1
  18. Segment(E_1, B_1) → e
  19. Intersect(edgeNV, edgeOV) → H_1
  20. Segment(D_1, H_1) → h_1
  21. Segment(E_1, D_1) → i_1