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Complex Descartes Spheres

Complex Descartes Spheres
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2015-07-04 07:12
VectorSolid GeometryGeometric Construction
This example demonstrates the geometric construction and properties of Complex Descartes Spheres. It involves core math concepts like spheres, 2D vectors, quadrilaterals, polygons, bar charts, and Poisson distribution. The construction uses GeoGebra commands/objects such as Circle, Intersect, Sphere, and Segment as outlined in the summary. Suitable for high school and above learners to understand complex spatial geometry combined with complex numbers.

GeoGebra Commands & Parameters

  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