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Union and Intersection

Union and Intersection
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2016-12-07 22:10
Geometric ConstructionSlider Animation
This example demonstrates the concepts of set union and intersection. Using GeoGebra commands, it shows how to create and manipulate these sets through geometric constructions. The commands Circle, Intersect, CircleArc, and Polygon are used, suitable for middle school and above students learning set theory.

GeoGebra Commands & Parameters

  1. Circle(A_1, D) → c
  2. Circle(B, E) → d
  3. Circle(C, F) → e
  4. Intersect(c, d) → G, H, ,
  5. Intersect(c, e) → I, J, ,
  6. Intersect(e, d) → K, L, ,
  7. CircleArc(B, G, H) → f
  8. CircleArc(A_1, H, G) → g
  9. CircleArc(B, K, L) → k
  10. CircleArc(C, L, K) → p
  11. CircleArc(A_1, J, I) → q
  12. CircleArc(C, I, J) → r
  13. Polygon(G, L, J) → poly1, j_1, g_1, l_1
  14. Circle(A_1, D) → c_2
  15. Circle(B, E) → d_1

AI Drawing Prompt Reference

Draw three circles centered at points A, B, and C with the same radius. Then find the intersection points of these circles and use these points to draw three circular arcs, forming three lens-shaped regions. Finally, use the intersection points of these lens-shaped regions to draw a triangle.
The prompt above was compiled from the original drawing commands and is for reference only.