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Zariski-closure of 3-ellipse (dynamic coloring)

Zariski-closure of 3-ellipse (dynamic coloring)
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2020-03-23 21:32
FunctionCoordinate GeometryGeometric ConstructionLocus
This example demonstrates the Zariski-closure of a 3-ellipse with dynamic coloring of its branches. It involves key mathematical concepts like Zariski-closure, coordinate geometry, and dynamic geometry. The construction uses commands and objects such as Segment, LocusEquation, and Point in GeoGebra. Suitable for high school students and educators exploring advanced geometric ideas and dynamic visualizations.

GeoGebra Commands & Parameters

  1. Segment(P, A_1) → a
  2. Segment(P, A_2) → b
  3. Segment(P, A_3) → c
  4. Segment(Q, R) → s
  5. LocusEquation(a + b + c ≟ s, P) → eq1
  6. Point(eq1) → P'
  7. Segment(P', A_1) → f
  8. Segment(P', A_2) → g
  9. Segment(P', A_3) → h