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Planar Graph 2: Geometric Construction and Limits

Planar Graph 2: Geometric Construction and Limits
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2020-10-15 01:39
VectorLimitGeometric Construction
This example demonstrates geometric constructions and limit phenomena in planar graphs. Key mathematical concepts include geometric construction, vectors, and limits. Construction involves GeoGebra commands such as Segment, Intersect, and If with various objects. Suitable for high school students or college undergraduates learning geometry and coordinate geometry.

GeoGebra Commands & Parameters

  1. Segment(E, F) → L8
  2. Segment(D, E) → L4
  3. Segment(F, C) → L10
  4. Intersect(L4, L10) → P4X
  5. Segment(E, C) → L7
  6. Segment(C, D) → L3
  7. Intersect(L3, L8) → P38
  8. Segment(B, C) → L2
  9. Intersect(L2, L8) → P28
  10. Intersect(L2, L4) → P24
  11. Segment(F, A) → L9
  12. Intersect(L4, L9) → P49
  13. Intersect(L3, L9) → P39
  14. Intersect(L2, L9) → P29
  15. Segment(A, D) → L6
  16. Intersect(L6, L10) → P6X
  17. Intersect(L6, L8) → P68
  18. Intersect(L6, L7) → P67
  19. Intersect(L2, L6) → P26
  20. Segment(E, A) → L5
  21. Intersect(L5, L10) → P5X
  22. Intersect(L3, L5) → P35
  23. Intersect(L2, L5) → P25
  24. Segment(A, B) → L1
  25. Intersect(L1, L10) → P1X
  26. Intersect(L1, L8) → P18
  27. Intersect(L1, L7) → P17
  28. Intersect(L1, L4) → P14
  29. Intersect(L1, L3) → P13
  30. If(Defined[P13] ∨ Defined[P14] ∨ Defined[P17] ∨ Defined[P18] ∨ Defined[P24] ∨ Defined[P25] ∨ Defined[P26] ∨ Defined[P28] ∨ Defined[P29] ∨ Defined[P35] ∨ Defined[P38] ∨ Defined[P39] ∨ Defined[P49] ∨ Defined[P67] ∨ Defined[P68] ∨ Defined[P1X] ∨ Defined[P4X] ∨ Defined[P5X] ∨ Defined[P6X], 0, 1) → output
  31. Intersect(L7, L9) → P79

AI Drawing Prompt Reference

Draw a plane graph with multiple line segments and intersection points. Start by drawing several line segments and finding their intersections. Then, continue to draw new line segments based on the positions of these intersection points, and find more intersections. Repeat this process until all key points are connected. The final graph should illustrate geometric constructions and limit phenomena, suitable for students learning geometry and coordinate geometry.
The prompt above was compiled from the original drawing commands and is for reference only.