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Simple Planar Graph Example

Simple Planar Graph Example
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2020-10-14 07:04
Coordinate GeometryGeometric Construction
This is a simple planar graph example that demonstrates how to use GeoGebra to draw the intersection points of straight lines and circles. By examining the commands in the construction summary, one can understand how to use Segment (line segment), Intersect (intersection), and If (conditional statement) commands to create the graph. Suitable for middle school and above students to learn plane geometry and linear equations.

GeoGebra Commands & Parameters

  1. Segment(A, B) → L1
  2. Segment(B, C) → L2
  3. Segment(C, D) → L3
  4. Segment(D, E) → L4
  5. Segment(E, A) → L5
  6. Segment(A, D) → L6
  7. Segment(E, C) → L7
  8. Intersect(L1, L3) → P13
  9. Intersect(L1, L4) → P14
  10. Intersect(L2, L4) → P24
  11. Intersect(L2, L5) → P25
  12. Intersect(L3, L5) → P35
  13. Intersect(L2, L6) → P26
  14. Intersect(L1, L7) → P17
  15. Intersect(L6, L7) → P67
  16. If(Defined[P13] ∨ Defined[P14] ∨ Defined[P24] ∨ Defined[P25] ∨ Defined[P35] ∨ Defined[P26] ∨ Defined[P17] ∨ Defined[P67], 0, 1) → output

AI Drawing Prompt Reference

Draw a simple planar graph on a plane. Start by choosing five vertices and connecting them with line segments to form a closed pentagon, then add two extra diagonals to keep the structure connected. Next, compute the intersection points for selected pairs of segments: include intersections between certain pentagon edges and diagonals, as well as intersections involving a diagonal with another segment. Display only the intersection points that are actually defined, producing a network of valid intersection nodes.
The prompt above was compiled from the original drawing commands and is for reference only.