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肥皂立方体最小曲面模拟

肥皂立方体最小曲面模拟
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2015-09-04 18:07
函数解析几何立体几何不等式几何作图
①本范例演示肥皂立方体形成的最小曲面图形；②涉及的核心数学概念包括曲面、函数、不等式、解析几何；③作图要点：使用GeoGebra命令Segment（线段）、Polygon（多边形）等构造图形，涉及对象h、t、a、A系列及poly系列等；④适合高中及以上学生及数学爱好者学习曲面几何与参数化构造。

GeoGebra 命令及参数

  1. Segment(A_0, A_1) → a_0
  2. Segment(A_2, A_1) → a_1
  3. Segment(A_2, A_3) → a_2
  4. Segment(A_0, A_3) → a_3
  5. Segment(A_7, A_3) → a_4
  6. Segment(A_2, A_6) → a_5
  7. Segment(A_5, A_1) → a_6
  8. Segment(A_0, A_4) → a_7
  9. Segment(A_7, A_4) → a_8
  10. Segment(A_7, A_6) → a_9
  11. Segment(A_5, A_6) → a_a
  12. Segment(A_5, A_4) → a_b
  13. Polygon(S_1, S_2, S_3, S_4) → poly1, s_1, s_2, s_3, s_4
  14. Polygon(A_2, A_3, S_2) → poly2, s_5, a_{10}, a_{11}
  15. Polygon(A_0, A_1, S_1) → poly3, s_6, a_{12}, a_{13}
  16. Polygon(A_6, A_7, S_3) → poly4, s_7, a_{14}, a_{15}
  17. Polygon(A_5, A_4, S_4) → poly5, s_9, a_{18}, a_{19}
  18. Polygon(S_1, S_2, A_2, A_1) → polya, b, c, d, e
  19. Polygon(A_0, A_3, S_2, S_1) → polyb, a_{16}, a_{17}, s_8, s_{10}
  20. Polygon(A_5, A_6, S_3, S_4) → polyc, a_{20}, a_{21}, s_{11}, s_{12}
  21. Polygon(A_4, A_7, S_3, S_4) → polyd, a_{22}, a_{23}, s_{13}, s_{14}
  22. Polygon(A_2, A_6, S_3, S_2) → polye, a_{24}, a_{25}, s_{15}, s_{16}
  23. Polygon(A_3, A_7, S_3, S_2) → polyf, a_{26}, a_{27}, s_{17}, s_{18}
  24. Polygon(A_0, A_4, S_4, S_1) → polyg, a_{28}, a_{29}, s_{19}, s_{20}
  25. Polygon(A_1, A_5, S_4, S_1) → polyh, a_{30}, a_{31}, s_{21}, s_{22}