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Fermat Points and the Centroid

Fermat Points and the Centroid
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2017-01-22 22:47
TriangleVectorCoordinate GeometryGeometric Construction
In collections Besondere Punkte/Special Points
This example demonstrates the geometric relationship between Fermat points and the centroid of a triangle. Key math concepts include Fermat points, centroids, vectors, and coordinate geometry. Construction involves commands like Line, Polygon, Circle, Midpoint, Center, Mirror, Intersect, and Centroid in GeoGebra. Suitable for high school mathematics teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. Line(A, B) → f
  2. Line(B, C) → g
  3. Line(C, A) → h
  4. Polygon(A, B, C) → poly1, c, a, b
  5. Circle(A, B, C) → d
  6. Midpoint(A, B) → D
  7. Midpoint(B, C) → E
  8. Midpoint(C, A) → F_1
  9. Circle(D, F_1, E) → e
  10. Center(d) → O
  11. Center(e) → N
  12. Mirror(O, N) → H
  13. Polygon(C, B, 3) → poly2, i, j, k, G_1
  14. Polygon(B, A, 3) → poly3, l, m, n, I
  15. Line(I, C) → p
  16. Line(G_1, A) → q
  17. Intersect(p, q) → F_2
  18. Polygon(A, B, 3) → poly4, r, s, t, K
  19. Polygon(B, C, 3) → poly5, f_1, g_1, h_1, L
  20. Line(A, L) → i_1
  21. Line(K, C) → j_1
  22. Intersect(i_1, j_1) → F
  23. Circle(F, F_2, N) → c_1
  24. Line(H, O) → k_1
  25. Centroid(poly1) → G
  26. Midpoint(H, G) → J
  27. Circle(J, G) → d_1
  28. Circle(F, F_2, G) → e_1