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金字塔构造演示 by nsriley

金字塔构造演示 by nsriley
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2016-04-13 02:22
多边形立体几何几何作图
①本范例演示了金字塔的三维几何构造与展开图；②涉及的核心数学概念包括立体几何、多边形、三角形、空间几何关系；③作图要点——从下方『构造摘要』提炼用到了 Point（点）、Pyramid（金字塔）、Net（展开图）等 GeoGebra 命令/对象；④适合高中立体几何教学或几何作图练习。

GeoGebra 命令及参数

  1. Point(yAxis) → A
  2. Point(xAxis) → B
  3. Point(yAxis) → C
  4. Point(xAxis) → D
  5. Point(zAxis) → E
  6. Pyramid(A, B, C, D, E) → a, faceABCD, edgeAE, edgeBE, edgeCE, edgeDE, faceABE, faceBCE, faceCDE, faceADE, edgeAB, edgeBC, edgeCD, edgeAD
  7. Point(zAxis) → F
  8. Pyramid(faceADE, F) → b, faceADF, faceAEF, faceDEF, edgeDF, edgeAF, edgeEF
  9. Point(zAxis) → G
  10. Point(xAxis) → H
  11. Point(xAxis) → I
  12. Net(a, c) → d, J, faceJKN, faceKLO, faceLMP, faceJMQ, edgeJK, edgeKL, edgeLM, edgeJM, edgeJN, edgeKN, K, edgeKO, edgeLO, edgeLP, edgeMP, edgeMQ, edgeJQ, L, M, N, O, P, Q, faceJKLM
  13. Net(a, e) → f, R, faceRSV, faceSTW, faceTUZ, face1, edgeRS, edgeST, edgeTU, edgeRU, edgeRV, edgeSV, S, edgeSW, edgeTW, edgeTZ, edgeUZ, edge2, edge1, T, U, V, W, Z, A_1, faceRSTU
  14. Net(a, g) → h, B_1, face2, face4, face5, face3, edge3, edge7, edge10, edge4, edge5, edge8, C_1, edge9, edge11, edge12, edge13, edge14, edge6, D_1, E_1, F_1, G_1, H_1, I_1, face6
  15. Net(a, i) → j, J_1, face7, face9, face10, face8, edge15, edge19, edge22, edge16, edge17, edge20, K_1, edge21, edge23, edge24, edge25, edge26, edge18, L_1, M_1, N_1, O_1, P_1, Q_1, face11