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复数 Descartes 球体

复数 Descartes 球体
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2015-07-04 07:12
向量立体几何几何作图
①本范例演示了复数 Descartes 球体的几何构造与性质；②涉及的核心数学概念包括球体、二维向量、四边形、多边形、条形图、泊松分布；③作图要点提炼自构造摘要，使用了 Circle（圆）、Intersect（相交）、Sphere（球体）、Segment（线段）等 GeoGebra 命令/对象；④适合高中及以上数学学习者，用于理解空间几何与复数结合的复杂图形。

GeoGebra 命令及参数

  1. Circle(A_1, r_1) → C_1
  2. Circle(A_2, r_2) → C_2
  3. Circle(A_3, r_3) → C_3
  4. Circle(A_4, r_4) → C_4
  5. Intersect(C_1, C_2) → z12, , ,
  6. Intersect(C_1, C_3) → z13, , ,
  7. Intersect(C_1, C_4) → z14, , ,
  8. Intersect(C_2, C_3) → z23, , ,
  9. Intersect(C_2, C_4) → z24, , ,
  10. Intersect(C_3, C_4) → z34, , ,
  11. Circle(z23, z24, z34) → C1p
  12. Circle(z13, z14, z34) → C2p
  13. Circle(z12, z24, z14) → C3p
  14. Circle(z12, z23, z13) → C4p
  15. Sphere(z12 + (0, 0, 1 / k12), 1 / k12) → S_{12}
  16. Sphere(z13 + (0, 0, 1 / k13), 1 / k13) → S_{13}
  17. Sphere(z14 + (0, 0, 1 / k14), 1 / k14) → S_{14}
  18. Sphere(z23 + (0, 0, 1 / k23), 1 / k23) → S_{23}
  19. Sphere(z24 + (0, 0, 1 / k24), 1 / k24) → S_{24}
  20. Sphere(z34 + (0, 0, 1 / k34), 1 / k34) → S_{34}
  21. Segment(C_{12}, C_{13}) → l1213
  22. Segment(C_{12}, C_{14}) → l1214
  23. Segment(C_{12}, C_{23}) → l1223
  24. Segment(C_{12}, C_{24}) → l1224
  25. Segment(C_{13}, C_{14}) → l1314
  26. Segment(C_{13}, C_{23}) → l1323
  27. Segment(C_{13}, C_{34}) → l1334
  28. Segment(C_{14}, C_{24}) → l1424
  29. Segment(C_{14}, C_{34}) → l1434
  30. Segment(C_{23}, C_{24}) → l2324
  31. Segment(C_{24}, C_{34}) → l2434
  32. Segment(C_{23}, C_{34}) → l2334