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勒贝格三维曲线

勒贝格三维曲线
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2019-04-14 20:13
向量立体几何参数方程几何作图
①本范例演示了勒贝格三维曲线的构造与可视化；②涉及的核心数学概念包括立体几何、参数方程、向量分析；③作图要点：使用Point, Cube, PolyLine, Sequence, Flatten等GeoGebra命令构建三维曲线；④适合高中及以上学生及数学爱好者学习三维曲线与空间几何。

GeoGebra 命令及参数

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB_1, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. PolyLine(l1) → f
  4. Sequence(Dilate[l1, 1 / 3, l1(w)], w, 1, 8) → l2
  5. PolyLine(Flatten[l2]) → g
  6. Flatten(l2) → l3
  7. Sequence(Dilate[l3, 3 / 7, l1(w)], w, 1, 8) → l4
  8. PolyLine(Flatten[l4]) → h
  9. Flatten(l4) → l5
  10. Sequence(Dilate[l5, 7 / 15, l1(w)], w, 1, 8) → l6
  11. PolyLine(Flatten[l6]) → i
  12. Point(Circle[B, Distance[A, B], Segment[A, B]]) → I
  13. Cube(A, B, I) → c, J, faceIJNM, faceKLMN, edgeAJ, edgeAB, edgeBI, edgeIJ, edgeAK, edgeJN, edgeKN, edgeKL, K, edgeBL, edgeLM, edgeIM, edgeMN, L, M, N, faceABIJ, faceAJNK, faceABLK, faceBIML