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Weighted Geometric Median (Weber Problem)

Weighted Geometric Median (Weber Problem)
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2018-12-21 19:51
PolygonVectorCoordinate GeometryOptimization
This example demonstrates the calculation and visualization of the weighted geometric median, finding the point minimizing the weighted sum of distances to a set of points with weights. Key math concepts include vectors, polygons, coordinate geometry, and optimization. It uses GeoGebra commands like Polygon, Segment, Textfield, and Sphere. Suitable for high school and above learners to understand the application of weighted geometric median in real-world problems.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → t1, c, a, b
  2. Segment(A, F) → f
  3. Segment(B, F) → g
  4. Segment(C, F) → h
  5. Textfield(pA) → CasillaDeEntrada1
  6. Textfield(pB) → CasillaDeEntrada2
  7. Textfield(pC) → CasillaDeEntrada3
  8. Sphere(A', (rPorcent * pA^(1 / 3))) → d
  9. Sphere(B', (rPorcent * pB^(1 / 3))) → e
  10. Sphere(C', (rPorcent * pC^(1 / 3))) → i
  11. Segment(A, A') → j
  12. Segment(B, B') → k
  13. Segment(C, C') → l