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长方体对角线 by Kaitlin

长方体对角线 by Kaitlin
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2016-11-04 00:02
向量解析几何立体几何
①本范例演示长方体的空间几何特性，特别是对角线的计算与可视化；②涉及核心数学概念包括空间几何、向量运算、三维坐标几何；③构造要点：使用Intersect（相交）、Point（点）、Prism（棱柱）、Segment（线段）等命令，构建长方体及对角线；④适合高中及以上学生学习立体几何、空间向量及三维建模。

GeoGebra 命令及参数

  1. Intersect(zAxis, xAxis) → A
  2. Point(zAxis) → B
  3. Point(xAxis) → C
  4. Point(yAxis) → H
  5. Prism(A, B, D, C, H) → a, E, edgeAB, edgeBD, edgeCD, edgeAC, edgeAH, edgeBE, edgeDF, edgeCG, edgeEH, edgeEF, F, edgeFG, edgeGH, G, faceABDC, faceABEH, faceBDFE, faceCDFG, faceACGH, faceEFGH
  6. Intersect(edgeDF, edgeFG) → I
  7. Segment(A, F) → f
  8. Point(xAxis) → J
  9. Point(xAxis) → K
  10. Prism(J, M, L, K, Q) → b, N, edgeJM, edgeLM, edgeKL, edgeJK, edgeJQ, edgeMN, edgeLO, edgeKP, edgeNQ, edgeNO, O, edgeOP, edgePQ, P, faceJKLM, faceJMNQ, faceLMNO, faceKLOP, faceJKPQ, faceNOPQ
  11. Segment(Q, L) → g
  12. Point(xAxis) → R
  13. Point(xAxis) → S
  14. Prism(R, T, U, S, A_1) → c, V, edgeRT, edgeTU, edgeSU, edgeRS, edge1, edgeTV, edgeUW, edgeSZ, edge2, edgeVW, W, edgeWZ, edge3, Z, faceRSUT, face2, faceTUWV, faceSUWZ, face1, face3
  15. Segment(A_1, R) → h
  16. Segment(U, A_1) → i